From bef60183550ac21465e75980f4f68f26f20b039b Mon Sep 17 00:00:00 2001 From: snowykami Date: Fri, 6 Sep 2024 11:59:45 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20docs=20from=20@=20snowykami/mb?= =?UTF-8?q?cp@9ee3eb3509f804de6b5cd64f769930b3dc420259=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 404.html | 6 +++--- api/index.html | 8 ++++---- api/mp_math/angle.html | 8 ++++---- api/mp_math/const.html | 8 ++++---- api/mp_math/equation.html | 8 ++++---- api/mp_math/function.html | 8 ++++---- api/mp_math/index.html | 8 ++++---- api/mp_math/line.html | 12 ++++++------ api/mp_math/mp_math_typing.html | 8 ++++---- api/mp_math/plane.html | 16 ++++++++-------- api/mp_math/point.html | 8 ++++---- api/mp_math/segment.html | 8 ++++---- api/mp_math/utils.html | 8 ++++---- api/mp_math/vector.html | 8 ++++---- api/particle/index.html | 8 ++++---- api/presets/index.html | 8 ++++---- api/presets/model/index.html | 8 ++++---- ...9EytA4.js => api_mp_math_line.md.lCQRkZtk.js} | 2 +- ...n.js => api_mp_math_line.md.lCQRkZtk.lean.js} | 0 ...NcHy5.js => api_mp_math_plane.md.2ZclJA1V.js} | 14 +++++++------- ....js => api_mp_math_plane.md.2ZclJA1V.lean.js} | 2 +- assets/{app.BUlGQzcU.js => app.BnE8Xesd.js} | 2 +- assets/chunks/@localSearchIndexen.BJkPsfRt.js | 1 + assets/chunks/@localSearchIndexen.BiKPGziK.js | 1 - assets/chunks/@localSearchIndexja.NAYqQakD.js | 1 - assets/chunks/@localSearchIndexja.RtIw4HCL.js | 1 + assets/chunks/@localSearchIndexroot.C4Y9aF6Z.js | 1 + assets/chunks/@localSearchIndexroot.DH9jnGhe.js | 1 - assets/chunks/@localSearchIndexzht.BOVgxEGY.js | 1 + assets/chunks/@localSearchIndexzht.DIej9wva.js | 1 - ....Lyrn-94G.js => VPLocalSearchBox.DhHzxM_l.js} | 2 +- .../{theme.4Aq0plHp.js => theme.Cq7NoE_k.js} | 4 ++-- ...iC3.js => en_api_mp_math_line.md.DFwE8llX.js} | 2 +- ...s => en_api_mp_math_line.md.DFwE8llX.lean.js} | 0 ...aU.js => en_api_mp_math_plane.md.CBNCeDF4.js} | 12 ++++++------ ... => en_api_mp_math_plane.md.CBNCeDF4.lean.js} | 2 +- ...dDH.js => ja_api_mp_math_line.md.CMckwGpV.js} | 2 +- ...s => ja_api_mp_math_line.md.CMckwGpV.lean.js} | 0 ..._C.js => ja_api_mp_math_plane.md.D549kBN0.js} | 14 +++++++------- ... => ja_api_mp_math_plane.md.D549kBN0.lean.js} | 2 +- assets/style.Bh0M9mVm.css | 1 - assets/style.Czi07tLB.css | 1 + ...VZ.js => zht_api_mp_math_line.md.BmXiOeCt.js} | 2 +- ... => zht_api_mp_math_line.md.BmXiOeCt.lean.js} | 0 ...z.js => zht_api_mp_math_plane.md.DYh81-YI.js} | 14 +++++++------- ...=> zht_api_mp_math_plane.md.DYh81-YI.lean.js} | 2 +- demo/best-practice.html | 8 ++++---- demo/index.html | 8 ++++---- en/api/index.html | 8 ++++---- en/api/mp_math/angle.html | 8 ++++---- en/api/mp_math/const.html | 8 ++++---- en/api/mp_math/equation.html | 8 ++++---- en/api/mp_math/function.html | 8 ++++---- en/api/mp_math/index.html | 8 ++++---- en/api/mp_math/line.html | 12 ++++++------ en/api/mp_math/mp_math_typing.html | 8 ++++---- en/api/mp_math/plane.html | 16 ++++++++-------- en/api/mp_math/point.html | 8 ++++---- en/api/mp_math/segment.html | 8 ++++---- en/api/mp_math/utils.html | 8 ++++---- en/api/mp_math/vector.html | 8 ++++---- en/api/particle/index.html | 8 ++++---- en/api/presets/index.html | 8 ++++---- en/api/presets/model/index.html | 8 ++++---- en/demo/best-practice.html | 8 ++++---- en/guide/index.html | 8 ++++---- en/index.html | 8 ++++---- en/refer/index.html | 8 ++++---- guide/index.html | 8 ++++---- hashmap.json | 2 +- index.html | 8 ++++---- ja/api/index.html | 8 ++++---- ja/api/mp_math/angle.html | 8 ++++---- ja/api/mp_math/const.html | 8 ++++---- ja/api/mp_math/equation.html | 8 ++++---- ja/api/mp_math/function.html | 8 ++++---- ja/api/mp_math/index.html | 8 ++++---- ja/api/mp_math/line.html | 12 ++++++------ ja/api/mp_math/mp_math_typing.html | 8 ++++---- ja/api/mp_math/plane.html | 16 ++++++++-------- ja/api/mp_math/point.html | 8 ++++---- ja/api/mp_math/segment.html | 8 ++++---- ja/api/mp_math/utils.html | 8 ++++---- ja/api/mp_math/vector.html | 8 ++++---- ja/api/particle/index.html | 8 ++++---- ja/api/presets/index.html | 8 ++++---- ja/api/presets/model/index.html | 8 ++++---- ja/demo/best-practice.html | 8 ++++---- ja/guide/index.html | 8 ++++---- ja/index.html | 8 ++++---- ja/refer/index.html | 8 ++++---- refer/7-differential-euqtion/index.html | 8 ++++---- refer/function/curry.html | 8 ++++---- refer/function/function.html | 8 ++++---- refer/index.html | 8 ++++---- zht/api/index.html | 8 ++++---- zht/api/mp_math/angle.html | 8 ++++---- zht/api/mp_math/const.html | 8 ++++---- zht/api/mp_math/equation.html | 8 ++++---- zht/api/mp_math/function.html | 8 ++++---- zht/api/mp_math/index.html | 8 ++++---- zht/api/mp_math/line.html | 12 ++++++------ zht/api/mp_math/mp_math_typing.html | 8 ++++---- zht/api/mp_math/plane.html | 16 ++++++++-------- zht/api/mp_math/point.html | 8 ++++---- zht/api/mp_math/segment.html | 8 ++++---- zht/api/mp_math/utils.html | 8 ++++---- zht/api/mp_math/vector.html | 8 ++++---- zht/api/particle/index.html | 8 ++++---- zht/api/presets/index.html | 8 ++++---- zht/api/presets/model/index.html | 8 ++++---- zht/demo/best-practice.html | 8 ++++---- zht/guide/index.html | 8 ++++---- zht/index.html | 8 ++++---- zht/refer/index.html | 8 ++++---- 115 files changed, 408 insertions(+), 408 deletions(-) rename assets/{api_mp_math_line.md.Ld9EytA4.js => api_mp_math_line.md.lCQRkZtk.js} (96%) rename assets/{api_mp_math_line.md.Ld9EytA4.lean.js => api_mp_math_line.md.lCQRkZtk.lean.js} (100%) rename assets/{api_mp_math_plane.md.DRZNcHy5.js => api_mp_math_plane.md.2ZclJA1V.js} (97%) rename assets/{api_mp_math_plane.md.DRZNcHy5.lean.js => api_mp_math_plane.md.2ZclJA1V.lean.js} (95%) rename assets/{app.BUlGQzcU.js => app.BnE8Xesd.js} (95%) create mode 100644 assets/chunks/@localSearchIndexen.BJkPsfRt.js delete mode 100644 assets/chunks/@localSearchIndexen.BiKPGziK.js delete mode 100644 assets/chunks/@localSearchIndexja.NAYqQakD.js create mode 100644 assets/chunks/@localSearchIndexja.RtIw4HCL.js create mode 100644 assets/chunks/@localSearchIndexroot.C4Y9aF6Z.js delete mode 100644 assets/chunks/@localSearchIndexroot.DH9jnGhe.js create mode 100644 assets/chunks/@localSearchIndexzht.BOVgxEGY.js delete mode 100644 assets/chunks/@localSearchIndexzht.DIej9wva.js rename assets/chunks/{VPLocalSearchBox.Lyrn-94G.js => VPLocalSearchBox.DhHzxM_l.js} (99%) rename assets/chunks/{theme.4Aq0plHp.js => theme.Cq7NoE_k.js} (99%) rename assets/{en_api_mp_math_line.md.Bd5Z3iC3.js => en_api_mp_math_line.md.DFwE8llX.js} (96%) rename assets/{en_api_mp_math_line.md.Bd5Z3iC3.lean.js => en_api_mp_math_line.md.DFwE8llX.lean.js} (100%) rename assets/{en_api_mp_math_plane.md.D91Vt6aU.js => en_api_mp_math_plane.md.CBNCeDF4.js} (97%) rename assets/{en_api_mp_math_plane.md.D91Vt6aU.lean.js => en_api_mp_math_plane.md.CBNCeDF4.lean.js} (98%) rename assets/{ja_api_mp_math_line.md.BbbGydDH.js => ja_api_mp_math_line.md.CMckwGpV.js} (96%) rename assets/{ja_api_mp_math_line.md.BbbGydDH.lean.js => ja_api_mp_math_line.md.CMckwGpV.lean.js} (100%) rename assets/{ja_api_mp_math_plane.md.BvT51o_C.js => ja_api_mp_math_plane.md.D549kBN0.js} (97%) rename assets/{ja_api_mp_math_plane.md.BvT51o_C.lean.js => ja_api_mp_math_plane.md.D549kBN0.lean.js} (95%) delete mode 100644 assets/style.Bh0M9mVm.css create mode 100644 assets/style.Czi07tLB.css rename assets/{zht_api_mp_math_line.md.DopGqzVZ.js => zht_api_mp_math_line.md.BmXiOeCt.js} (96%) rename assets/{zht_api_mp_math_line.md.DopGqzVZ.lean.js => zht_api_mp_math_line.md.BmXiOeCt.lean.js} (100%) rename assets/{zht_api_mp_math_plane.md.OnI32y0z.js => zht_api_mp_math_plane.md.DYh81-YI.js} (97%) rename assets/{zht_api_mp_math_plane.md.OnI32y0z.lean.js => zht_api_mp_math_plane.md.DYh81-YI.lean.js} (95%) diff --git a/404.html b/404.html index 42d03bf..2cd660b 100644 --- a/404.html +++ b/404.html @@ -6,9 +6,9 @@ 404 | MBCP 文档 - + - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index bf11d1d..c499c90 100644 --- a/api/index.html +++ b/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/angle.html b/api/mp_math/angle.html index 5e971c4..b9f329c 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP 文档 - + - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True) - + \ No newline at end of file diff --git a/api/mp_math/const.html b/api/mp_math/const.html index c55967e..85f7af9 100644 --- a/api/mp_math/const.html +++ b/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 说明: 常量 π

  • 默认值: math.pi

var E ​

  • 说明: 自然对数的底 exp(1)

  • 默认值: math.e

var GOLDEN_RATIO ​

  • 说明: 黄金分割比

  • 默认值: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 说明: 欧拉常数

  • 默认值: 0.5772156649015329

var EPSILON ​

  • 说明: 精度误差

  • 默认值: 0.0001

var APPROX ​

  • 说明: 约等于判定误差

  • 默认值: 0.001

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html index 14ef05a..48f5f0a 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP 文档 - + - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type') - + \ No newline at end of file diff --git a/api/mp_math/function.html b/api/mp_math/function.html index bc4e85a..d66e992 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP 文档 - + - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func - + \ No newline at end of file diff --git a/api/mp_math/index.html b/api/mp_math/index.html index ae20195..cd054a1 100644 --- a/api/mp_math/index.html +++ b/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/line.html b/api/mp_math/line.html index 3877bc3..813c27b 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP 文档 - + - - + + - + @@ -58,7 +58,7 @@ self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

说明: 工厂函数 由两点构造直线。

参数:

返回: Line3: 直线

源代码 或 在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

参数:

返回: Line3 | Point3 | None: 交集

源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

参数:

返回: Line3 | Point3 | None: 交集

源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
@@ -66,7 +66,7 @@
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
- + \ No newline at end of file diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html index b7dcad2..f134059 100644 --- a/api/mp_math/mp_math_typing.html +++ b/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 说明: 实数

  • 类型: TypeAlias

  • 默认值: int | float

var Number ​

  • 说明: 数

  • 类型: TypeAlias

  • 默认值: RealNumber | complex

var SingleVar ​

  • 说明: 单变量

  • 默认值: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • 说明: 数组变量

  • 默认值: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • 说明: 变量

  • 类型: TypeAlias

  • 默认值: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 说明: 一元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • 说明: 一元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • 说明: 一元函数

  • 类型: TypeAlias

  • 默认值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 说明: 二元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • 说明: 二元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • 说明: 二元函数

  • 类型: TypeAlias

  • 默认值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 说明: 三元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • 说明: 三元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • 说明: 三元函数

  • 类型: TypeAlias

  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 说明: 多元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 说明: 多元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 说明: 多元函数

  • 类型: TypeAlias

  • 默认值: MultiSingleVarsFunc | MultiArraysFunc

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html index 5e4a05a..afb79d0 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP 文档 - + - - + + - + @@ -88,11 +88,11 @@ v2 = l2.get_point(1) - l1.point return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method __and__(self, other: Line3) -> Point3 | None ​

源代码 或 在GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None ​

源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method __and__(self, other: Plane3) -> Line3 | None ​

源代码 或 在GitHub上查看
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None ​

源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method __and__(self, other) ​

说明: 取两平面的交集（人话：交线）

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码 或 在GitHub上查看
python
def __and__(self, other):
+    ...

method self & other ​

说明: 取两平面的交集（人话：交线）

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码 或 在GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -105,7 +105,7 @@
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method __rand__(self, other: Line3) -> Point3 ​

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html index 6aa37e8..09b91e5 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP 文档 - + - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

说明: P - P -> V

P - V -> P 已在 Vector3 中实现

参数:

返回: Vector3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
- + \ No newline at end of file diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html index 8d9acf4..77e1c08 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP 文档 - + - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2) - + \ No newline at end of file diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html index c61f6b5..1fccbf9 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP 文档 - + - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return '' - + \ No newline at end of file diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html index 553ddef..ef7eadd 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -6,10 +6,10 @@ mbcp.mp_math.vector | MBCP 文档 - + - - + + @@ -78,7 +78,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

说明: 取负。

返回: Vector3: 负向量

源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

- + \ No newline at end of file diff --git a/api/particle/index.html b/api/particle/index.html index 69c5d59..10dbe8a 100644 --- a/api/particle/index.html +++ b/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.particle ​

本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/presets/index.html b/api/presets/index.html index c3d6e92..c2fd4e5 100644 --- a/api/presets/index.html +++ b/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.presets ​

本模块塞了一些预设

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/api/presets/model/index.html b/api/presets/model/index.html index 4821238..b8f929b 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP 文档 - + - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)] - + \ No newline at end of file diff --git a/assets/api_mp_math_line.md.Ld9EytA4.js b/assets/api_mp_math_line.md.lCQRkZtk.js similarity index 96% rename from assets/api_mp_math_line.md.Ld9EytA4.js rename to assets/api_mp_math_line.md.lCQRkZtk.js index 0420ad2..14c396c 100644 --- a/assets/api_mp_math_line.md.Ld9EytA4.js +++ b/assets/api_mp_math_line.md.lCQRkZtk.js @@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

说明: 工厂函数 由两点构造直线。

参数:

返回: Line3: 直线

源代码 或 在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

参数:

返回: Line3 | Point3 | None: 交集

源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

参数:

返回: Line3 | Point3 | None: 交集

源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
diff --git a/assets/api_mp_math_line.md.Ld9EytA4.lean.js b/assets/api_mp_math_line.md.lCQRkZtk.lean.js
similarity index 100%
rename from assets/api_mp_math_line.md.Ld9EytA4.lean.js
rename to assets/api_mp_math_line.md.lCQRkZtk.lean.js
diff --git a/assets/api_mp_math_plane.md.DRZNcHy5.js b/assets/api_mp_math_plane.md.2ZclJA1V.js
similarity index 97%
rename from assets/api_mp_math_plane.md.DRZNcHy5.js
rename to assets/api_mp_math_plane.md.2ZclJA1V.js
index e1a9cf1..0e257fc 100644
--- a/assets/api_mp_math_plane.md.DRZNcHy5.js
+++ b/assets/api_mp_math_plane.md.2ZclJA1V.js
@@ -1,4 +1,4 @@
-import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=t(`
模块 mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),n={name:"api/mp_math/plane.md"},h=t(`
模块 mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,7 +13,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t('',1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t(`
参数:
返回: AnyAngle: 夹角
引发:
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t('',1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t(`
参数:
返回: AnyAngle: 夹角
引发:
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     elif isinstance(other, Plane3):
@@ -25,7 +25,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t('',1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
参数:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ls=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t('',1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
参数:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -68,11 +68,11 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         v2 = l2.get_point(1) - l1.point
     return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method self & other: Line3 => Point3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self & other: Plane3 => Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
返回: Line3 | Point3 | None: 交集
引发:
源代码 或 在GitHub上查看
python
def __and__(self, other):
+    ...
method self & other ​
说明: 取两平面的交集（人话：交线）
参数:
返回: Line3 | Point3 | None: 交集
引发:
源代码 或 在GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -84,4 +84,4 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     else:
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
说明: 判断两个平面是否等价。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default};
+    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default};
diff --git a/assets/api_mp_math_plane.md.DRZNcHy5.lean.js b/assets/api_mp_math_plane.md.2ZclJA1V.lean.js
similarity index 95%
rename from assets/api_mp_math_plane.md.DRZNcHy5.lean.js
rename to assets/api_mp_math_plane.md.2ZclJA1V.lean.js
index 6c117e1..e746214 100644
--- a/assets/api_mp_math_plane.md.DRZNcHy5.lean.js
+++ b/assets/api_mp_math_plane.md.2ZclJA1V.lean.js
@@ -1 +1 @@
-import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t("",1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t("",16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t("",1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default};
+import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),n={name:"api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t("",1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t("",16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ls=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t("",1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default};
diff --git a/assets/app.BUlGQzcU.js b/assets/app.BnE8Xesd.js
similarity index 95%
rename from assets/app.BUlGQzcU.js
rename to assets/app.BnE8Xesd.js
index cfe0134..7a979cb 100644
--- a/assets/app.BUlGQzcU.js
+++ b/assets/app.BnE8Xesd.js
@@ -1 +1 @@
-import{t as p}from"./chunks/theme.4Aq0plHp.js";import{U as o,a5 as u,a6 as c,a7 as l,a8 as f,a9 as d,aa as m,ab as h,ac as g,ad as A,ae as y,d as P,u as v,y as C,x as b,af as w,ag as E,ah as R,ai as S}from"./chunks/framework.DpC1ZpOZ.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return C(()=>{b(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&w(),E(),R(),s.setup&&s.setup(),()=>S(s.Layout)}});async function x(){globalThis.__VITEPRESS__=!0;const e=_(),a=D();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function D(){return g(T)}function _(){let e=o,a;return A(t=>{let n=y(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&x().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{x as createApp};
+import{t as p}from"./chunks/theme.Cq7NoE_k.js";import{U as o,a5 as u,a6 as c,a7 as l,a8 as f,a9 as d,aa as m,ab as h,ac as g,ad as A,ae as y,d as P,u as v,y as C,x as b,af as w,ag as E,ah as R,ai as S}from"./chunks/framework.DpC1ZpOZ.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return C(()=>{b(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&w(),E(),R(),s.setup&&s.setup(),()=>S(s.Layout)}});async function x(){globalThis.__VITEPRESS__=!0;const e=_(),a=D();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function D(){return g(T)}function _(){let e=o,a;return A(t=>{let n=y(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&x().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{x as createApp};
diff --git a/assets/chunks/@localSearchIndexen.BJkPsfRt.js b/assets/chunks/@localSearchIndexen.BJkPsfRt.js
new file mode 100644
index 0000000..74d4302
--- /dev/null
+++ b/assets/chunks/@localSearchIndexen.BJkPsfRt.js
@@ -0,0 +1 @@
+const t='{"documentCount":160,"nextId":160,"documentIds":{"0":"/en/api/#module-mbcp","1":"/en/api/mp_math/angle.html#module-mbcp-mp-math-angle","2":"/en/api/mp_math/angle.html#class-angle","3":"/en/api/mp_math/angle.html#class-anyangle-angle","4":"/en/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/en/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/en/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/en/api/mp_math/angle.html#method-degree-self-float","8":"/en/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/en/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/en/api/mp_math/angle.html#method-sin-self-float","11":"/en/api/mp_math/angle.html#method-cos-self-float","12":"/en/api/mp_math/angle.html#method-tan-self-float","13":"/en/api/mp_math/angle.html#method-cot-self-float","14":"/en/api/mp_math/angle.html#method-sec-self-float","15":"/en/api/mp_math/angle.html#method-csc-self-float","16":"/en/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/en/api/mp_math/angle.html#method-eq-self-other","18":"/en/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/en/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/en/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/en/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/en/api/mp_math/angle.html#method-self-other","23":"/en/api/mp_math/const.html#module-mbcp-mp-math-const","24":"/en/api/mp_math/const.html#var-pi","25":"/en/api/mp_math/const.html#var-e","26":"/en/api/mp_math/const.html#var-golden-ratio","27":"/en/api/mp_math/const.html#var-gamma","28":"/en/api/mp_math/const.html#var-epsilon","29":"/en/api/mp_math/const.html#var-approx","30":"/en/api/mp_math/equation.html#module-mbcp-mp-math-equation","31":"/en/api/mp_math/equation.html#class-curveequation","32":"/en/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","33":"/en/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","34":"/en/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","35":"/en/api/mp_math/function.html#module-mbcp-mp-math-function","36":"/en/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/en/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/en/api/mp_math/#module-mbcp-mp-math","39":"/en/api/mp_math/line.html#module-mbcp-mp-math-line","40":"/en/api/mp_math/line.html#class-line3","41":"/en/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/en/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/en/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/en/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/en/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/en/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/en/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/en/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/en/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/en/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/en/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/en/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/en/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/en/api/mp_math/line.html#method-simplify-self","55":"/en/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/en/api/mp_math/line.html#method-self-other-line3-line3-point3-none","57":"/en/api/mp_math/line.html#method-eq-self-other-bool","58":"/en/api/mp_math/mp_math_typing.html#module-mbcp-mp-math-mp-math-typing","59":"/en/api/mp_math/mp_math_typing.html#var-realnumber","60":"/en/api/mp_math/mp_math_typing.html#var-number","61":"/en/api/mp_math/mp_math_typing.html#var-singlevar","62":"/en/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/en/api/mp_math/mp_math_typing.html#var-var","64":"/en/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/en/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/en/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/en/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/en/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/en/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/en/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/en/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/en/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/en/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/en/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/en/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/en/api/mp_math/plane.html#module-mbcp-mp-math-plane","77":"/en/api/mp_math/plane.html#class-plane3","78":"/en/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/en/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/en/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/en/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/en/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/en/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/en/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/en/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/en/api/mp_math/plane.html#method-normal-self-vector3","87":"/en/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/en/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/en/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/en/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/en/api/mp_math/plane.html#method-self-other-line3-point3-none","92":"/en/api/mp_math/plane.html#method-self-other-plane3-line3-none","93":"/en/api/mp_math/plane.html#method-self-other","94":"/en/api/mp_math/plane.html#method-eq-self-other-bool","95":"/en/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/en/api/mp_math/point.html#module-mbcp-mp-math-point","97":"/en/api/mp_math/point.html#class-point3","98":"/en/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/en/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/en/api/mp_math/point.html#method-self-other-vector3-point3","101":"/en/api/mp_math/point.html#method-self-other-point3-point3","102":"/en/api/mp_math/point.html#method-self-other","103":"/en/api/mp_math/point.html#method-eq-self-other","104":"/en/api/mp_math/point.html#method-self-other-point3-vector3","105":"/en/api/mp_math/segment.html#module-mbcp-mp-math-segment","106":"/en/api/mp_math/segment.html#class-segment3","107":"/en/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/en/api/mp_math/utils.html#module-mbcp-mp-math-utils","109":"/en/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/en/api/mp_math/utils.html#class-approx","111":"/en/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/en/api/mp_math/utils.html#method-eq-self-other","113":"/en/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/en/api/mp_math/utils.html#method-ne-self-other","115":"/en/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/en/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/en/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/en/api/mp_math/vector.html#module-mbcp-mp-math-vector","119":"/en/api/mp_math/vector.html#class-vector3","120":"/en/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/en/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/en/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/en/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/en/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/en/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/en/api/mp_math/vector.html#method-normalize-self","127":"/en/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/en/api/mp_math/vector.html#method-length-self-float","129":"/en/api/mp_math/vector.html#method-unit-self-vector3","130":"/en/api/mp_math/vector.html#method-abs-self","131":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/en/api/mp_math/vector.html#method-self-other-point3-point3","133":"/en/api/mp_math/vector.html#method-self-other","134":"/en/api/mp_math/vector.html#method-eq-self-other","135":"/en/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/en/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/en/api/mp_math/vector.html#method-self-other-1","139":"/en/api/mp_math/vector.html#method-self-other-point3","140":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/en/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/en/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/en/api/mp_math/vector.html#method-self-vector3","147":"/en/api/mp_math/vector.html#var-zero-vector3","148":"/en/api/mp_math/vector.html#var-x-axis","149":"/en/api/mp_math/vector.html#var-y-axis","150":"/en/api/mp_math/vector.html#var-z-axis","151":"/en/api/particle/#module-mbcp-particle","152":"/en/api/presets/#module-mbcp-presets","153":"/en/api/presets/model/#module-mbcp-presets-model","154":"/en/api/presets/model/#class-geometricmodels","155":"/en/api/presets/model/#method-sphere-radius-float-density-float","156":"/en/demo/best-practice.html#best-practice","157":"/en/demo/best-practice.html#works","158":"/en/guide/#开始不了一点","159":"/en/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,27],"5":[5,9,26],"6":[5,9,25],"7":[5,9,22],"8":[6,9,23],"9":[6,9,25],"10":[5,9,20],"11":[5,9,20],"12":[5,9,20],"13":[5,9,22],"14":[5,9,22],"15":[5,9,22],"16":[7,9,18],"17":[5,9,14],"18":[6,9,17],"19":[7,9,19],"20":[7,9,16],"21":[7,9,16],"22":[3,9,18],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[2,5,1],"32":[9,7,22],"33":[10,7,36],"34":[14,5,63],"35":[5,1,2],"36":[13,5,48],"37":[7,5,43],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,21],"42":[11,7,30],"43":[8,7,23],"44":[10,7,45],"45":[8,7,43],"46":[8,7,24],"47":[8,7,27],"48":[9,7,28],"49":[14,7,29],"50":[8,7,23],"51":[8,7,26],"52":[8,7,23],"53":[8,7,29],"54":[4,7,30],"55":[10,7,30],"56":[10,7,36],"57":[6,7,31],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,28],"79":[7,7,33],"80":[10,7,58],"81":[10,7,47],"82":[9,7,67],"83":[9,7,54],"84":[9,7,26],"85":[8,7,24],"86":[5,7,23],"87":[10,7,37],"88":[11,7,37],"89":[10,7,41],"90":[10,7,31],"91":[10,7,18],"92":[10,7,18],"93":[4,7,50],"94":[6,7,22],"95":[7,7,18],"96":[5,1,2],"97":[2,5,1],"98":[8,7,19],"99":[11,7,32],"100":[8,7,16],"101":[7,7,15],"102":[4,7,27],"103":[5,7,25],"104":[7,7,31],"105":[5,1,2],"106":[2,5,1],"107":[7,7,30],"108":[5,1,2],"109":[7,5,23],"110":[2,5,1],"111":[6,7,17],"112":[5,7,34],"113":[7,7,18],"114":[5,7,14],"115":[11,5,31],"116":[11,5,33],"117":[12,5,39],"118":[5,1,3],"119":[2,5,1],"120":[8,7,21],"121":[11,7,31],"122":[8,7,31],"123":[6,7,36],"124":[13,7,30],"125":[8,7,26],"126":[4,7,20],"127":[6,7,21],"128":[5,7,26],"129":[5,7,20],"130":[4,7,13],"131":[7,7,15],"132":[7,7,15],"133":[4,7,40],"134":[5,7,25],"135":[7,7,28],"136":[6,7,15],"137":[6,7,15],"138":[3,7,39],"139":[4,7,38],"140":[6,7,15],"141":[7,7,16],"142":[9,7,42],"143":[7,7,16],"144":[7,7,26],"145":[7,7,18],"146":[5,7,20],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,49],"156":[2,1,1],"157":[1,2,25],"158":[1,1,2],"159":[1,1,7]},"averageFieldLength":[5.762499999999999,5.931249999999998,19.8],"storedFields":{"0":{"title":"Module mbcp","titles":[]},"1":{"title":"Module mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["Module mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["Module mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"Module mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["Module mbcp.mp_math.const"]},"25":{"title":"var E","titles":["Module mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["Module mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["Module mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["Module mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["Module mbcp.mp_math.const"]},"30":{"title":"Module mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["Module mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["Module mbcp.mp_math.equation"]},"35":{"title":"Module mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["Module mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["Module mbcp.mp_math.function"]},"38":{"title":"Module mbcp.mp_math","titles":[]},"39":{"title":"Module mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["Module mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["Module mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["Module mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["Module mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["Module mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["Module mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["Module mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"58":{"title":"Module mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["Module mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["Module mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["Module mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"76":{"title":"Module mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["Module mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["Module mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["Module mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["Module mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"96":{"title":"Module mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["Module mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["Module mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["Module mbcp.mp_math.point","class Point3"]},"105":{"title":"Module mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["Module mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["Module mbcp.mp_math.segment","class Segment3"]},"108":{"title":"Module mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["Module mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["Module mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["Module mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"118":{"title":"Module mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["Module mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["Module mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["Module mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["Module mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["Module mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["Module mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["Module mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["Module mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["Module mbcp.mp_math.vector"]},"151":{"title":"Module mbcp.particle","titles":[]},"152":{"title":"Module mbcp.presets","titles":[]},"153":{"title":"Module mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["Module mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["Module mbcp.presets.model","class GeometricModels"]},"156":{"title":"Best Practice","titles":[]},"157":{"title":"Works","titles":["Best Practice"]},"158":{"title":"开始不了一点","titles":[]},"159":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"158":1}}],["开始不了一点",{"0":{"158":1}}],["红石音乐",{"2":{"157":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["works",{"0":{"157":1}}],["warning",{"2":{"34":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"34":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"159":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"104":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"104":1,"138":1}}],["新的点",{"2":{"102":1,"135":1,"139":1}}],["已在",{"2":{"104":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"98":3}}],["笛卡尔坐标系中的点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"159":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"82":1}}],["high",{"2":{"34":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"34":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"34":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"103":1}}],["判断两个点是否近似相等",{"2":{"99":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"103":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"99":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中点的类",{"2":{"96":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"30":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"157":1}}],["best",{"0":{"156":1},"1":{"157":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"99":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"159":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"107":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"34":1},"2":{"34":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["default",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"34":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["description",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"33":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"155":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["偏导函数",{"2":{"34":1}}],["偏移量",{"2":{"34":1,"36":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"34":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"34":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"34":1}}],["目标点",{"2":{"33":1}}],["慎用",{"2":{"34":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"155":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"33":1,"37":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"98":1,"120":1,"150":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"98":1,"115":1,"120":1,"149":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"99":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"98":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"33":3,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"81":1}}],["黄金分割比",{"2":{"26":1}}],["π",{"2":{"24":1}}],["to",{"2":{"159":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"83":2,"159":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2,"147":1,"148":1,"149":1,"150":1}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1}}],["tuple",{"0":{"33":1,"34":1,"48":1},"2":{"33":2,"34":2,"48":2}}],["t",{"0":{"33":1,"47":1},"2":{"33":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"42":1,"49":1,"99":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"42":4,"49":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["examples",{"2":{"37":1}}],["exp",{"2":{"25":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"134":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"128":3,"155":2}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"159":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"34":4}}],["return",{"2":{"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":1,"17":1,"18":1,"19":1,"22":2,"33":3,"34":5,"36":2,"37":4,"42":2,"43":2,"44":6,"45":2,"46":2,"47":2,"48":2,"49":2,"50":2,"51":2,"52":2,"53":2,"55":2,"56":4,"57":2,"79":5,"80":3,"81":3,"82":2,"83":2,"84":2,"85":2,"86":2,"87":2,"88":2,"89":2,"90":2,"93":5,"94":2,"95":1,"99":2,"102":2,"103":2,"104":2,"109":2,"112":2,"114":1,"115":2,"116":4,"117":4,"121":2,"122":2,"123":2,"124":2,"125":2,"127":2,"128":2,"129":2,"130":1,"133":3,"134":2,"135":2,"138":3,"139":2,"142":3,"143":1,"144":2,"145":1,"146":2,"155":2}}],["range",{"2":{"155":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["raises",{"2":{"34":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["ratio",{"0":{"26":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"102":2,"104":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["github",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"99":5,"100":1,"101":1,"102":5,"103":5,"104":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"37":1,"66":1},"2":{"32":6,"37":1}}],["on",{"0":{"52":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":2,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["order",{"2":{"34":2}}],["or",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":2,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":2,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"100":1,"102":1,"104":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"102":1,"104":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["view",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"33":1},"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"97":1,"106":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["code",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["source",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"26":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"104":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"32":4,"33":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":4,"99":4,"100":1,"101":1,"102":4,"103":4,"104":4,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["默认为否",{"2":{"4":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"155":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"155":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["arguments",{"2":{"4":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"29":1,"42":2,"49":1,"79":1,"99":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1}}],["and",{"0":{"87":1,"90":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"103":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["任意角度",{"2":{"4":1,"38":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"32":3,"34":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"99":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"33":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"34":1,"36":1,"42":1,"49":1,"56":1,"91":1,"92":1,"99":1,"100":1,"101":1,"104":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":3,"107":5,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"159":1}}],["import",{"2":{"104":1}}],["i",{"2":{"155":4,"157":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"142":1},"2":{"34":3,"37":4,"59":1,"112":2,"142":2,"155":1}}],["in",{"2":{"33":1,"34":1,"155":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"107":1},"2":{"55":3,"57":1,"88":3,"107":8}}],["p1",{"0":{"55":1,"88":1,"107":1},"2":{"55":4,"57":1,"88":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"34":3}}],["p",{"0":{"36":1},"2":{"36":20,"102":5,"104":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"96":1},"1":{"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"97":1,"99":1,"100":1,"101":2,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"33":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"99":2,"100":1,"101":2,"102":3,"103":1,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["practice",{"0":{"156":1},"1":{"157":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["提供了一些工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["module",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"34":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"75":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexen.BiKPGziK.js b/assets/chunks/@localSearchIndexen.BiKPGziK.js
deleted file mode 100644
index af10e6d..0000000
--- a/assets/chunks/@localSearchIndexen.BiKPGziK.js
+++ /dev/null
@@ -1 +0,0 @@
-const t='{"documentCount":160,"nextId":160,"documentIds":{"0":"/en/api/#module-mbcp","1":"/en/api/mp_math/angle.html#module-mbcp-mp-math-angle","2":"/en/api/mp_math/angle.html#class-angle","3":"/en/api/mp_math/angle.html#class-anyangle-angle","4":"/en/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/en/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/en/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/en/api/mp_math/angle.html#method-degree-self-float","8":"/en/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/en/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/en/api/mp_math/angle.html#method-sin-self-float","11":"/en/api/mp_math/angle.html#method-cos-self-float","12":"/en/api/mp_math/angle.html#method-tan-self-float","13":"/en/api/mp_math/angle.html#method-cot-self-float","14":"/en/api/mp_math/angle.html#method-sec-self-float","15":"/en/api/mp_math/angle.html#method-csc-self-float","16":"/en/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/en/api/mp_math/angle.html#method-eq-self-other","18":"/en/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/en/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/en/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/en/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/en/api/mp_math/angle.html#method-self-other","23":"/en/api/mp_math/const.html#module-mbcp-mp-math-const","24":"/en/api/mp_math/const.html#var-pi","25":"/en/api/mp_math/const.html#var-e","26":"/en/api/mp_math/const.html#var-golden-ratio","27":"/en/api/mp_math/const.html#var-gamma","28":"/en/api/mp_math/const.html#var-epsilon","29":"/en/api/mp_math/const.html#var-approx","30":"/en/api/mp_math/equation.html#module-mbcp-mp-math-equation","31":"/en/api/mp_math/equation.html#class-curveequation","32":"/en/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","33":"/en/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","34":"/en/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","35":"/en/api/mp_math/function.html#module-mbcp-mp-math-function","36":"/en/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/en/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/en/api/mp_math/#module-mbcp-mp-math","39":"/en/api/mp_math/line.html#module-mbcp-mp-math-line","40":"/en/api/mp_math/line.html#class-line3","41":"/en/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/en/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/en/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/en/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/en/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/en/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/en/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/en/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/en/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/en/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/en/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/en/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/en/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/en/api/mp_math/line.html#method-simplify-self","55":"/en/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/en/api/mp_math/line.html#method-and-self-other-line3-line3-point3-none","57":"/en/api/mp_math/line.html#method-eq-self-other-bool","58":"/en/api/mp_math/mp_math_typing.html#module-mbcp-mp-math-mp-math-typing","59":"/en/api/mp_math/mp_math_typing.html#var-realnumber","60":"/en/api/mp_math/mp_math_typing.html#var-number","61":"/en/api/mp_math/mp_math_typing.html#var-singlevar","62":"/en/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/en/api/mp_math/mp_math_typing.html#var-var","64":"/en/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/en/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/en/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/en/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/en/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/en/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/en/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/en/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/en/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/en/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/en/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/en/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/en/api/mp_math/plane.html#module-mbcp-mp-math-plane","77":"/en/api/mp_math/plane.html#class-plane3","78":"/en/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/en/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/en/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/en/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/en/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/en/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/en/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/en/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/en/api/mp_math/plane.html#method-normal-self-vector3","87":"/en/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/en/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/en/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/en/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/en/api/mp_math/plane.html#method-and-self-other-line3-point3-none","92":"/en/api/mp_math/plane.html#method-and-self-other-plane3-line3-none","93":"/en/api/mp_math/plane.html#method-and-self-other","94":"/en/api/mp_math/plane.html#method-eq-self-other-bool","95":"/en/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/en/api/mp_math/point.html#module-mbcp-mp-math-point","97":"/en/api/mp_math/point.html#class-point3","98":"/en/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/en/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/en/api/mp_math/point.html#method-self-other-vector3-point3","101":"/en/api/mp_math/point.html#method-self-other-point3-point3","102":"/en/api/mp_math/point.html#method-self-other","103":"/en/api/mp_math/point.html#method-eq-self-other","104":"/en/api/mp_math/point.html#method-self-other-point3-vector3","105":"/en/api/mp_math/segment.html#module-mbcp-mp-math-segment","106":"/en/api/mp_math/segment.html#class-segment3","107":"/en/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/en/api/mp_math/utils.html#module-mbcp-mp-math-utils","109":"/en/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/en/api/mp_math/utils.html#class-approx","111":"/en/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/en/api/mp_math/utils.html#method-eq-self-other","113":"/en/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/en/api/mp_math/utils.html#method-ne-self-other","115":"/en/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/en/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/en/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/en/api/mp_math/vector.html#module-mbcp-mp-math-vector","119":"/en/api/mp_math/vector.html#class-vector3","120":"/en/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/en/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/en/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/en/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/en/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/en/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/en/api/mp_math/vector.html#method-normalize-self","127":"/en/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/en/api/mp_math/vector.html#method-length-self-float","129":"/en/api/mp_math/vector.html#method-unit-self-vector3","130":"/en/api/mp_math/vector.html#method-abs-self","131":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/en/api/mp_math/vector.html#method-self-other-point3-point3","133":"/en/api/mp_math/vector.html#method-self-other","134":"/en/api/mp_math/vector.html#method-eq-self-other","135":"/en/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/en/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/en/api/mp_math/vector.html#method-self-other-1","139":"/en/api/mp_math/vector.html#method-self-other-point3","140":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/en/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/en/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/en/api/mp_math/vector.html#method-self-vector3","147":"/en/api/mp_math/vector.html#var-zero-vector3","148":"/en/api/mp_math/vector.html#var-x-axis","149":"/en/api/mp_math/vector.html#var-y-axis","150":"/en/api/mp_math/vector.html#var-z-axis","151":"/en/api/particle/#module-mbcp-particle","152":"/en/api/presets/#module-mbcp-presets","153":"/en/api/presets/model/#module-mbcp-presets-model","154":"/en/api/presets/model/#class-geometricmodels","155":"/en/api/presets/model/#method-sphere-radius-float-density-float","156":"/en/demo/best-practice.html#best-practice","157":"/en/demo/best-practice.html#works","158":"/en/guide/#开始不了一点","159":"/en/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,27],"5":[5,9,26],"6":[5,9,25],"7":[5,9,22],"8":[6,9,23],"9":[6,9,25],"10":[5,9,20],"11":[5,9,20],"12":[5,9,20],"13":[5,9,22],"14":[5,9,22],"15":[5,9,22],"16":[7,9,18],"17":[5,9,14],"18":[6,9,17],"19":[7,9,19],"20":[7,9,16],"21":[7,9,16],"22":[3,9,18],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[2,5,1],"32":[9,7,22],"33":[10,7,36],"34":[14,5,63],"35":[5,1,2],"36":[13,5,48],"37":[7,5,43],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,21],"42":[11,7,30],"43":[8,7,23],"44":[10,7,45],"45":[8,7,43],"46":[8,7,24],"47":[8,7,27],"48":[9,7,28],"49":[14,7,29],"50":[8,7,23],"51":[8,7,26],"52":[8,7,23],"53":[8,7,29],"54":[4,7,30],"55":[10,7,30],"56":[9,7,36],"57":[6,7,31],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,28],"79":[7,7,33],"80":[10,7,58],"81":[10,7,47],"82":[9,7,67],"83":[9,7,54],"84":[9,7,26],"85":[8,7,24],"86":[5,7,23],"87":[10,7,37],"88":[11,7,37],"89":[10,7,41],"90":[10,7,31],"91":[9,7,18],"92":[9,7,18],"93":[5,7,50],"94":[6,7,22],"95":[7,7,18],"96":[5,1,2],"97":[2,5,1],"98":[8,7,19],"99":[11,7,32],"100":[8,7,16],"101":[7,7,15],"102":[4,7,27],"103":[5,7,25],"104":[7,7,31],"105":[5,1,2],"106":[2,5,1],"107":[7,7,30],"108":[5,1,2],"109":[7,5,23],"110":[2,5,1],"111":[6,7,17],"112":[5,7,34],"113":[7,7,18],"114":[5,7,14],"115":[11,5,31],"116":[11,5,33],"117":[12,5,39],"118":[5,1,3],"119":[2,5,1],"120":[8,7,21],"121":[11,7,31],"122":[8,7,31],"123":[6,7,36],"124":[13,7,30],"125":[8,7,26],"126":[4,7,20],"127":[6,7,21],"128":[5,7,26],"129":[5,7,20],"130":[4,7,13],"131":[7,7,15],"132":[7,7,15],"133":[4,7,40],"134":[5,7,25],"135":[7,7,28],"136":[6,7,15],"137":[6,7,15],"138":[3,7,39],"139":[4,7,38],"140":[6,7,15],"141":[7,7,16],"142":[9,7,42],"143":[7,7,16],"144":[7,7,26],"145":[7,7,18],"146":[5,7,20],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,49],"156":[2,1,1],"157":[1,2,25],"158":[1,1,2],"159":[1,1,7]},"averageFieldLength":[5.749999999999999,5.931249999999998,19.8],"storedFields":{"0":{"title":"Module mbcp","titles":[]},"1":{"title":"Module mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["Module mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["Module mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["Module mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"Module mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["Module mbcp.mp_math.const"]},"25":{"title":"var E","titles":["Module mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["Module mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["Module mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["Module mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["Module mbcp.mp_math.const"]},"30":{"title":"Module mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["Module mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["Module mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["Module mbcp.mp_math.equation"]},"35":{"title":"Module mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["Module mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["Module mbcp.mp_math.function"]},"38":{"title":"Module mbcp.mp_math","titles":[]},"39":{"title":"Module mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["Module mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["Module mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["Module mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["Module mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["Module mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["Module mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["Module mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["Module mbcp.mp_math.line","class Line3"]},"56":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["Module mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["Module mbcp.mp_math.line","class Line3"]},"58":{"title":"Module mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["Module mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["Module mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["Module mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["Module mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["Module mbcp.mp_math.mp_math_typing"]},"76":{"title":"Module mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["Module mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["Module mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["Module mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method __and__(self, other)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"96":{"title":"Module mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["Module mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["Module mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["Module mbcp.mp_math.point","class Point3"]},"105":{"title":"Module mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["Module mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["Module mbcp.mp_math.segment","class Segment3"]},"108":{"title":"Module mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["Module mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["Module mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["Module mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"118":{"title":"Module mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["Module mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["Module mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["Module mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["Module mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["Module mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["Module mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["Module mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["Module mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["Module mbcp.mp_math.vector"]},"151":{"title":"Module mbcp.particle","titles":[]},"152":{"title":"Module mbcp.presets","titles":[]},"153":{"title":"Module mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["Module mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["Module mbcp.presets.model","class GeometricModels"]},"156":{"title":"Best Practice","titles":[]},"157":{"title":"Works","titles":["Best Practice"]},"158":{"title":"开始不了一点","titles":[]},"159":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"158":1}}],["开始不了一点",{"0":{"158":1}}],["红石音乐",{"2":{"157":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["works",{"0":{"157":1}}],["warning",{"2":{"34":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"34":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"159":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"104":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"104":1,"138":1}}],["新的点",{"2":{"102":1,"135":1,"139":1}}],["已在",{"2":{"104":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"98":3}}],["笛卡尔坐标系中的点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"159":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"82":1}}],["high",{"2":{"34":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"34":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"34":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"103":1}}],["判断两个点是否近似相等",{"2":{"99":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"103":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"99":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中点的类",{"2":{"96":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"30":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"157":1}}],["best",{"0":{"156":1},"1":{"157":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"99":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"159":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"107":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"34":1},"2":{"34":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["default",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"34":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["description",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"33":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"155":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["偏导函数",{"2":{"34":1}}],["偏移量",{"2":{"34":1,"36":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"34":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"34":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"34":1}}],["目标点",{"2":{"33":1}}],["慎用",{"2":{"34":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"155":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"33":1,"37":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"98":1,"120":1,"150":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"98":1,"115":1,"120":1,"149":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"99":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"98":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"33":3,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"81":1}}],["黄金分割比",{"2":{"26":1}}],["π",{"2":{"24":1}}],["to",{"2":{"159":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"83":2,"159":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2,"147":1,"148":1,"149":1,"150":1}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1}}],["tuple",{"0":{"33":1,"34":1,"48":1},"2":{"33":2,"34":2,"48":2}}],["t",{"0":{"33":1,"47":1},"2":{"33":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"42":1,"49":1,"99":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"42":4,"49":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["examples",{"2":{"37":1}}],["exp",{"2":{"25":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"134":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"128":3,"155":2}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"159":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"34":4}}],["return",{"2":{"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":1,"17":1,"18":1,"19":1,"22":2,"33":3,"34":5,"36":2,"37":4,"42":2,"43":2,"44":6,"45":2,"46":2,"47":2,"48":2,"49":2,"50":2,"51":2,"52":2,"53":2,"55":2,"56":4,"57":2,"79":5,"80":3,"81":3,"82":2,"83":2,"84":2,"85":2,"86":2,"87":2,"88":2,"89":2,"90":2,"93":5,"94":2,"95":1,"99":2,"102":2,"103":2,"104":2,"109":2,"112":2,"114":1,"115":2,"116":4,"117":4,"121":2,"122":2,"123":2,"124":2,"125":2,"127":2,"128":2,"129":2,"130":1,"133":3,"134":2,"135":2,"138":3,"139":2,"142":3,"143":1,"144":2,"145":1,"146":2,"155":2}}],["range",{"2":{"155":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["raises",{"2":{"34":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["ratio",{"0":{"26":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"102":2,"104":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["github",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"99":5,"100":1,"101":1,"102":5,"103":5,"104":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"37":1,"66":1},"2":{"32":6,"37":1}}],["on",{"0":{"52":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":2,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["order",{"2":{"34":2}}],["or",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":2,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":2,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"100":1,"102":1,"104":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"102":1,"104":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["view",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"33":1},"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"97":1,"106":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["code",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["source",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"26":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"104":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"32":4,"33":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":4,"99":4,"100":1,"101":1,"102":4,"103":4,"104":4,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["默认为否",{"2":{"4":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"155":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"155":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["arguments",{"2":{"4":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"29":1,"42":2,"49":1,"79":1,"99":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1}}],["and",{"0":{"56":1,"87":1,"90":1,"91":1,"92":1,"93":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"103":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["任意角度",{"2":{"4":1,"38":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"32":3,"34":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"99":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"33":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"34":1,"36":1,"42":1,"49":1,"99":1,"100":1,"101":1,"104":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":3,"107":5,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"159":1}}],["import",{"2":{"104":1}}],["i",{"2":{"155":4,"157":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"142":1},"2":{"34":3,"37":4,"59":1,"112":2,"142":2,"155":1}}],["in",{"2":{"33":1,"34":1,"155":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"107":1},"2":{"55":3,"57":1,"88":3,"107":8}}],["p1",{"0":{"55":1,"88":1,"107":1},"2":{"55":4,"57":1,"88":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"34":3}}],["p",{"0":{"36":1},"2":{"36":20,"102":5,"104":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"96":1},"1":{"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"97":1,"99":1,"100":1,"101":2,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"33":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"99":2,"100":1,"101":2,"102":3,"103":1,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["practice",{"0":{"156":1},"1":{"157":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["提供了一些工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["module",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"34":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"75":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexja.NAYqQakD.js b/assets/chunks/@localSearchIndexja.NAYqQakD.js
deleted file mode 100644
index c6d670a..0000000
--- a/assets/chunks/@localSearchIndexja.NAYqQakD.js
+++ /dev/null
@@ -1 +0,0 @@
-const t='{"documentCount":160,"nextId":160,"documentIds":{"0":"/ja/api/#モジュール-mbcp","1":"/ja/api/mp_math/angle.html#モジュール-mbcp-mp-math-angle","2":"/ja/api/mp_math/angle.html#class-angle","3":"/ja/api/mp_math/angle.html#class-anyangle-angle","4":"/ja/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/ja/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/ja/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/ja/api/mp_math/angle.html#method-degree-self-float","8":"/ja/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/ja/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/ja/api/mp_math/angle.html#method-sin-self-float","11":"/ja/api/mp_math/angle.html#method-cos-self-float","12":"/ja/api/mp_math/angle.html#method-tan-self-float","13":"/ja/api/mp_math/angle.html#method-cot-self-float","14":"/ja/api/mp_math/angle.html#method-sec-self-float","15":"/ja/api/mp_math/angle.html#method-csc-self-float","16":"/ja/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/ja/api/mp_math/angle.html#method-eq-self-other","18":"/ja/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/ja/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/ja/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/ja/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/ja/api/mp_math/angle.html#method-self-other","23":"/ja/api/mp_math/const.html#モジュール-mbcp-mp-math-const","24":"/ja/api/mp_math/const.html#var-pi","25":"/ja/api/mp_math/const.html#var-e","26":"/ja/api/mp_math/const.html#var-golden-ratio","27":"/ja/api/mp_math/const.html#var-gamma","28":"/ja/api/mp_math/const.html#var-epsilon","29":"/ja/api/mp_math/const.html#var-approx","30":"/ja/api/mp_math/equation.html#モジュール-mbcp-mp-math-equation","31":"/ja/api/mp_math/equation.html#class-curveequation","32":"/ja/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","33":"/ja/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","34":"/ja/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","35":"/ja/api/mp_math/function.html#モジュール-mbcp-mp-math-function","36":"/ja/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/ja/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/ja/api/mp_math/#モジュール-mbcp-mp-math","39":"/ja/api/mp_math/line.html#モジュール-mbcp-mp-math-line","40":"/ja/api/mp_math/line.html#class-line3","41":"/ja/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/ja/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/ja/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/ja/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/ja/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/ja/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/ja/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/ja/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/ja/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/ja/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/ja/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/ja/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/ja/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/ja/api/mp_math/line.html#method-simplify-self","55":"/ja/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/ja/api/mp_math/line.html#method-and-self-other-line3-line3-point3-none","57":"/ja/api/mp_math/line.html#method-eq-self-other-bool","58":"/ja/api/mp_math/mp_math_typing.html#モジュール-mbcp-mp-math-mp-math-typing","59":"/ja/api/mp_math/mp_math_typing.html#var-realnumber","60":"/ja/api/mp_math/mp_math_typing.html#var-number","61":"/ja/api/mp_math/mp_math_typing.html#var-singlevar","62":"/ja/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/ja/api/mp_math/mp_math_typing.html#var-var","64":"/ja/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/ja/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/ja/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/ja/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/ja/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/ja/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/ja/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/ja/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/ja/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/ja/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/ja/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/ja/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/ja/api/mp_math/plane.html#モジュール-mbcp-mp-math-plane","77":"/ja/api/mp_math/plane.html#class-plane3","78":"/ja/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/ja/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/ja/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/ja/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/ja/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/ja/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/ja/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/ja/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/ja/api/mp_math/plane.html#method-normal-self-vector3","87":"/ja/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/ja/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/ja/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/ja/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/ja/api/mp_math/plane.html#method-and-self-other-line3-point3-none","92":"/ja/api/mp_math/plane.html#method-and-self-other-plane3-line3-none","93":"/ja/api/mp_math/plane.html#method-and-self-other","94":"/ja/api/mp_math/plane.html#method-eq-self-other-bool","95":"/ja/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/ja/api/mp_math/point.html#モジュール-mbcp-mp-math-point","97":"/ja/api/mp_math/point.html#class-point3","98":"/ja/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/ja/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/ja/api/mp_math/point.html#method-self-other-vector3-point3","101":"/ja/api/mp_math/point.html#method-self-other-point3-point3","102":"/ja/api/mp_math/point.html#method-self-other","103":"/ja/api/mp_math/point.html#method-eq-self-other","104":"/ja/api/mp_math/point.html#method-self-other-point3-vector3","105":"/ja/api/mp_math/segment.html#モジュール-mbcp-mp-math-segment","106":"/ja/api/mp_math/segment.html#class-segment3","107":"/ja/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/ja/api/mp_math/utils.html#モジュール-mbcp-mp-math-utils","109":"/ja/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/ja/api/mp_math/utils.html#class-approx","111":"/ja/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/ja/api/mp_math/utils.html#method-eq-self-other","113":"/ja/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/ja/api/mp_math/utils.html#method-ne-self-other","115":"/ja/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/ja/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/ja/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/ja/api/mp_math/vector.html#モジュール-mbcp-mp-math-vector","119":"/ja/api/mp_math/vector.html#class-vector3","120":"/ja/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/ja/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/ja/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/ja/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/ja/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/ja/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/ja/api/mp_math/vector.html#method-normalize-self","127":"/ja/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/ja/api/mp_math/vector.html#method-length-self-float","129":"/ja/api/mp_math/vector.html#method-unit-self-vector3","130":"/ja/api/mp_math/vector.html#method-abs-self","131":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/ja/api/mp_math/vector.html#method-self-other-point3-point3","133":"/ja/api/mp_math/vector.html#method-self-other","134":"/ja/api/mp_math/vector.html#method-eq-self-other","135":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/ja/api/mp_math/vector.html#method-self-other-1","139":"/ja/api/mp_math/vector.html#method-self-other-point3","140":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/ja/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/ja/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/ja/api/mp_math/vector.html#method-self-vector3","147":"/ja/api/mp_math/vector.html#var-zero-vector3","148":"/ja/api/mp_math/vector.html#var-x-axis","149":"/ja/api/mp_math/vector.html#var-y-axis","150":"/ja/api/mp_math/vector.html#var-z-axis","151":"/ja/api/particle/#モジュール-mbcp-particle","152":"/ja/api/presets/#モジュール-mbcp-presets","153":"/ja/api/presets/model/#モジュール-mbcp-presets-model","154":"/ja/api/presets/model/#class-geometricmodels","155":"/ja/api/presets/model/#method-sphere-radius-float-density-float","156":"/ja/demo/best-practice.html#ベストプラクティス","157":"/ja/demo/best-practice.html#作品","158":"/ja/guide/#开始不了一点","159":"/ja/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,24],"5":[5,9,23],"6":[5,9,22],"7":[5,9,19],"8":[6,9,20],"9":[6,9,22],"10":[5,9,17],"11":[5,9,17],"12":[5,9,17],"13":[5,9,19],"14":[5,9,19],"15":[5,9,19],"16":[7,9,15],"17":[5,9,11],"18":[6,9,14],"19":[7,9,16],"20":[7,9,13],"21":[7,9,13],"22":[3,9,15],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[2,5,1],"32":[9,7,19],"33":[10,7,33],"34":[14,5,60],"35":[5,1,2],"36":[13,5,45],"37":[7,5,40],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,18],"42":[11,7,27],"43":[8,7,20],"44":[10,7,42],"45":[8,7,40],"46":[8,7,21],"47":[8,7,24],"48":[9,7,25],"49":[14,7,26],"50":[8,7,20],"51":[8,7,23],"52":[8,7,21],"53":[8,7,26],"54":[4,7,27],"55":[10,7,27],"56":[9,7,34],"57":[6,7,28],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,25],"79":[7,7,30],"80":[10,7,55],"81":[10,7,44],"82":[9,7,64],"83":[9,7,52],"84":[9,7,23],"85":[8,7,21],"86":[5,7,20],"87":[10,7,34],"88":[11,7,34],"89":[10,7,38],"90":[10,7,28],"91":[9,7,15],"92":[9,7,15],"93":[5,7,47],"94":[6,7,19],"95":[7,7,15],"96":[5,1,2],"97":[2,5,1],"98":[8,7,16],"99":[11,7,29],"100":[8,7,13],"101":[7,7,12],"102":[4,7,24],"103":[5,7,22],"104":[7,7,28],"105":[5,1,2],"106":[2,5,1],"107":[7,7,27],"108":[5,1,2],"109":[7,5,20],"110":[2,5,1],"111":[6,7,14],"112":[5,7,31],"113":[7,7,15],"114":[5,7,11],"115":[11,5,28],"116":[11,5,30],"117":[12,5,36],"118":[5,1,3],"119":[2,5,1],"120":[8,7,18],"121":[11,7,28],"122":[8,7,28],"123":[6,7,33],"124":[13,7,27],"125":[8,7,23],"126":[4,7,17],"127":[6,7,18],"128":[5,7,23],"129":[5,7,17],"130":[4,7,10],"131":[7,7,12],"132":[7,7,12],"133":[4,7,37],"134":[5,7,22],"135":[7,7,25],"136":[6,7,12],"137":[6,7,12],"138":[3,7,36],"139":[4,7,35],"140":[6,7,12],"141":[7,7,13],"142":[9,7,39],"143":[7,7,13],"144":[7,7,23],"145":[7,7,15],"146":[5,7,17],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,46],"156":[1,1,1],"157":[1,1,25],"158":[1,1,2],"159":[1,1,7]},"averageFieldLength":[5.7437499999999995,5.924999999999998,17.88750000000001],"storedFields":{"0":{"title":"モジュール mbcp","titles":[]},"1":{"title":"モジュール mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["モジュール mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["モジュール mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"モジュール mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["モジュール mbcp.mp_math.const"]},"25":{"title":"var E","titles":["モジュール mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["モジュール mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["モジュール mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["モジュール mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["モジュール mbcp.mp_math.const"]},"30":{"title":"モジュール mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["モジュール mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["モジュール mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["モジュール mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["モジュール mbcp.mp_math.equation"]},"35":{"title":"モジュール mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["モジュール mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["モジュール mbcp.mp_math.function"]},"38":{"title":"モジュール mbcp.mp_math","titles":[]},"39":{"title":"モジュール mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["モジュール mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["モジュール mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["モジュール mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["モジュール mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["モジュール mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["モジュール mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"56":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["モジュール mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"58":{"title":"モジュール mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"76":{"title":"モジュール mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["モジュール mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method __and__(self, other)","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"96":{"title":"モジュール mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["モジュール mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["モジュール mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["モジュール mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"105":{"title":"モジュール mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["モジュール mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["モジュール mbcp.mp_math.segment","class Segment3"]},"108":{"title":"モジュール mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["モジュール mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["モジュール mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["モジュール mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["モジュール mbcp.mp_math.utils"]},"118":{"title":"モジュール mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["モジュール mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["モジュール mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["モジュール mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["モジュール mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["モジュール mbcp.mp_math.vector"]},"151":{"title":"モジュール mbcp.particle","titles":[]},"152":{"title":"モジュール mbcp.presets","titles":[]},"153":{"title":"モジュール mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["モジュール mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["モジュール mbcp.presets.model","class GeometricModels"]},"156":{"title":"ベストプラクティス","titles":[]},"157":{"title":"作品","titles":["ベストプラクティス"]},"158":{"title":"开始不了一点","titles":[]},"159":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"158":1}}],["开始不了一点",{"0":{"158":1}}],["红石音乐",{"2":{"157":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["作品",{"0":{"157":1}}],["ベストプラクティス",{"0":{"156":1},"1":{"157":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"34":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"159":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"104":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"104":1,"138":1}}],["新的点",{"2":{"102":1,"135":1,"139":1}}],["已在",{"2":{"104":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"98":3}}],["笛卡尔坐标系中的点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"159":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"82":1}}],["high",{"2":{"34":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"34":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"34":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["タイプ",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"103":1}}],["判断两个点是否近似相等",{"2":{"99":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"103":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"99":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中点的类",{"2":{"96":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"30":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"157":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"99":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["例",{"2":{"37":1}}],["例外",{"2":{"34":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"159":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"107":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"34":1},"2":{"34":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"34":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"33":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"100":1,"102":1,"104":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"102":1,"104":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"155":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["偏导函数",{"2":{"34":1}}],["偏移量",{"2":{"34":1,"36":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"34":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"34":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"34":1}}],["目标点",{"2":{"33":1}}],["warning",{"2":{"34":1}}],["慎用",{"2":{"34":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"155":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"33":1,"37":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"98":1,"120":1,"150":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"98":1,"115":1,"120":1,"149":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"99":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"98":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"33":3,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"81":1}}],["黄金分割比",{"2":{"26":1}}],["デフォルト",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["π",{"2":{"24":1}}],["to",{"2":{"159":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"83":2,"159":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1}}],["tuple",{"0":{"33":1,"34":1,"48":1},"2":{"33":2,"34":2,"48":2}}],["t",{"0":{"33":1,"47":1},"2":{"33":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["or",{"2":{"56":1,"83":1}}],["order",{"2":{"34":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"52":1},"2":{"52":1}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"37":1,"66":1},"2":{"32":6,"37":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"99":5,"100":1,"101":1,"102":5,"103":5,"104":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"42":1,"49":1,"99":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"42":4,"49":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["exp",{"2":{"25":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"134":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"155":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"155":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"29":1,"42":2,"49":1,"79":1,"99":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1}}],["and",{"0":{"56":1,"87":1,"90":1,"91":1,"92":1,"93":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"103":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"26":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"104":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"32":4,"33":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":4,"99":4,"100":1,"101":1,"102":4,"103":4,"104":4,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"128":3,"155":2}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"159":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"34":4}}],["return",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"22":2,"33":2,"34":4,"36":1,"37":3,"42":1,"43":1,"44":5,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":3,"57":1,"79":4,"80":2,"81":2,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":4,"94":1,"95":1,"99":1,"102":1,"103":1,"104":1,"109":1,"112":2,"114":1,"115":1,"116":3,"117":3,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"130":1,"133":2,"134":1,"135":1,"138":2,"139":1,"142":2,"143":1,"144":1,"145":1,"146":1,"155":1}}],["range",{"2":{"155":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["ratio",{"0":{"26":1}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["戻り値",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"99":1,"102":1,"103":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"155":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"102":2,"104":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["githubで表示",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"33":1},"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"97":1,"106":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["または",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["ソースコード",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["默认为否",{"2":{"4":1}}],["引数",{"2":{"4":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["任意角度",{"2":{"4":1,"38":1}}],["説明",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"32":3,"34":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"99":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"33":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"34":1,"36":1,"42":1,"49":1,"99":1,"100":1,"101":1,"104":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":3,"107":5,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"159":1}}],["import",{"2":{"104":1}}],["i",{"2":{"155":4,"157":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"142":1},"2":{"34":3,"37":4,"59":1,"112":2,"142":2,"155":1}}],["in",{"2":{"33":1,"34":1,"155":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"107":1},"2":{"55":3,"57":1,"88":3,"107":8}}],["p1",{"0":{"55":1,"88":1,"107":1},"2":{"55":4,"57":1,"88":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"34":3}}],["p",{"0":{"36":1},"2":{"36":20,"102":5,"104":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"96":1},"1":{"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"97":1,"99":1,"100":1,"101":2,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"33":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"99":2,"100":1,"101":2,"102":3,"103":1,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"34":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"75":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3}}],["提供了一些工具",{"2":{"0":1}}],["モジュール",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexja.RtIw4HCL.js b/assets/chunks/@localSearchIndexja.RtIw4HCL.js
new file mode 100644
index 0000000..5e0e872
--- /dev/null
+++ b/assets/chunks/@localSearchIndexja.RtIw4HCL.js
@@ -0,0 +1 @@
+const t='{"documentCount":160,"nextId":160,"documentIds":{"0":"/ja/api/#モジュール-mbcp","1":"/ja/api/mp_math/angle.html#モジュール-mbcp-mp-math-angle","2":"/ja/api/mp_math/angle.html#class-angle","3":"/ja/api/mp_math/angle.html#class-anyangle-angle","4":"/ja/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/ja/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/ja/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/ja/api/mp_math/angle.html#method-degree-self-float","8":"/ja/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/ja/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/ja/api/mp_math/angle.html#method-sin-self-float","11":"/ja/api/mp_math/angle.html#method-cos-self-float","12":"/ja/api/mp_math/angle.html#method-tan-self-float","13":"/ja/api/mp_math/angle.html#method-cot-self-float","14":"/ja/api/mp_math/angle.html#method-sec-self-float","15":"/ja/api/mp_math/angle.html#method-csc-self-float","16":"/ja/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/ja/api/mp_math/angle.html#method-eq-self-other","18":"/ja/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/ja/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/ja/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/ja/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/ja/api/mp_math/angle.html#method-self-other","23":"/ja/api/mp_math/const.html#モジュール-mbcp-mp-math-const","24":"/ja/api/mp_math/const.html#var-pi","25":"/ja/api/mp_math/const.html#var-e","26":"/ja/api/mp_math/const.html#var-golden-ratio","27":"/ja/api/mp_math/const.html#var-gamma","28":"/ja/api/mp_math/const.html#var-epsilon","29":"/ja/api/mp_math/const.html#var-approx","30":"/ja/api/mp_math/equation.html#モジュール-mbcp-mp-math-equation","31":"/ja/api/mp_math/equation.html#class-curveequation","32":"/ja/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","33":"/ja/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","34":"/ja/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","35":"/ja/api/mp_math/function.html#モジュール-mbcp-mp-math-function","36":"/ja/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/ja/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/ja/api/mp_math/#モジュール-mbcp-mp-math","39":"/ja/api/mp_math/line.html#モジュール-mbcp-mp-math-line","40":"/ja/api/mp_math/line.html#class-line3","41":"/ja/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/ja/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/ja/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/ja/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/ja/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/ja/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/ja/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/ja/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/ja/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/ja/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/ja/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/ja/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/ja/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/ja/api/mp_math/line.html#method-simplify-self","55":"/ja/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/ja/api/mp_math/line.html#method-self-other-line3-line3-point3-none","57":"/ja/api/mp_math/line.html#method-eq-self-other-bool","58":"/ja/api/mp_math/mp_math_typing.html#モジュール-mbcp-mp-math-mp-math-typing","59":"/ja/api/mp_math/mp_math_typing.html#var-realnumber","60":"/ja/api/mp_math/mp_math_typing.html#var-number","61":"/ja/api/mp_math/mp_math_typing.html#var-singlevar","62":"/ja/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/ja/api/mp_math/mp_math_typing.html#var-var","64":"/ja/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/ja/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/ja/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/ja/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/ja/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/ja/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/ja/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/ja/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/ja/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/ja/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/ja/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/ja/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/ja/api/mp_math/plane.html#モジュール-mbcp-mp-math-plane","77":"/ja/api/mp_math/plane.html#class-plane3","78":"/ja/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/ja/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/ja/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/ja/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/ja/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/ja/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/ja/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/ja/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/ja/api/mp_math/plane.html#method-normal-self-vector3","87":"/ja/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/ja/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/ja/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/ja/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/ja/api/mp_math/plane.html#method-self-other-line3-point3-none","92":"/ja/api/mp_math/plane.html#method-self-other-plane3-line3-none","93":"/ja/api/mp_math/plane.html#method-self-other","94":"/ja/api/mp_math/plane.html#method-eq-self-other-bool","95":"/ja/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/ja/api/mp_math/point.html#モジュール-mbcp-mp-math-point","97":"/ja/api/mp_math/point.html#class-point3","98":"/ja/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/ja/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/ja/api/mp_math/point.html#method-self-other-vector3-point3","101":"/ja/api/mp_math/point.html#method-self-other-point3-point3","102":"/ja/api/mp_math/point.html#method-self-other","103":"/ja/api/mp_math/point.html#method-eq-self-other","104":"/ja/api/mp_math/point.html#method-self-other-point3-vector3","105":"/ja/api/mp_math/segment.html#モジュール-mbcp-mp-math-segment","106":"/ja/api/mp_math/segment.html#class-segment3","107":"/ja/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/ja/api/mp_math/utils.html#モジュール-mbcp-mp-math-utils","109":"/ja/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/ja/api/mp_math/utils.html#class-approx","111":"/ja/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/ja/api/mp_math/utils.html#method-eq-self-other","113":"/ja/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/ja/api/mp_math/utils.html#method-ne-self-other","115":"/ja/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/ja/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/ja/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/ja/api/mp_math/vector.html#モジュール-mbcp-mp-math-vector","119":"/ja/api/mp_math/vector.html#class-vector3","120":"/ja/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/ja/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/ja/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/ja/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/ja/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/ja/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/ja/api/mp_math/vector.html#method-normalize-self","127":"/ja/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/ja/api/mp_math/vector.html#method-length-self-float","129":"/ja/api/mp_math/vector.html#method-unit-self-vector3","130":"/ja/api/mp_math/vector.html#method-abs-self","131":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/ja/api/mp_math/vector.html#method-self-other-point3-point3","133":"/ja/api/mp_math/vector.html#method-self-other","134":"/ja/api/mp_math/vector.html#method-eq-self-other","135":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/ja/api/mp_math/vector.html#method-self-other-1","139":"/ja/api/mp_math/vector.html#method-self-other-point3","140":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/ja/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/ja/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/ja/api/mp_math/vector.html#method-self-vector3","147":"/ja/api/mp_math/vector.html#var-zero-vector3","148":"/ja/api/mp_math/vector.html#var-x-axis","149":"/ja/api/mp_math/vector.html#var-y-axis","150":"/ja/api/mp_math/vector.html#var-z-axis","151":"/ja/api/particle/#モジュール-mbcp-particle","152":"/ja/api/presets/#モジュール-mbcp-presets","153":"/ja/api/presets/model/#モジュール-mbcp-presets-model","154":"/ja/api/presets/model/#class-geometricmodels","155":"/ja/api/presets/model/#method-sphere-radius-float-density-float","156":"/ja/demo/best-practice.html#ベストプラクティス","157":"/ja/demo/best-practice.html#作品","158":"/ja/guide/#开始不了一点","159":"/ja/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,24],"5":[5,9,23],"6":[5,9,22],"7":[5,9,19],"8":[6,9,20],"9":[6,9,22],"10":[5,9,17],"11":[5,9,17],"12":[5,9,17],"13":[5,9,19],"14":[5,9,19],"15":[5,9,19],"16":[7,9,15],"17":[5,9,11],"18":[6,9,14],"19":[7,9,16],"20":[7,9,13],"21":[7,9,13],"22":[3,9,15],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[2,5,1],"32":[9,7,19],"33":[10,7,33],"34":[14,5,60],"35":[5,1,2],"36":[13,5,45],"37":[7,5,40],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,18],"42":[11,7,27],"43":[8,7,20],"44":[10,7,42],"45":[8,7,40],"46":[8,7,21],"47":[8,7,24],"48":[9,7,25],"49":[14,7,26],"50":[8,7,20],"51":[8,7,23],"52":[8,7,21],"53":[8,7,26],"54":[4,7,27],"55":[10,7,27],"56":[10,7,34],"57":[6,7,28],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,25],"79":[7,7,30],"80":[10,7,55],"81":[10,7,44],"82":[9,7,64],"83":[9,7,52],"84":[9,7,23],"85":[8,7,21],"86":[5,7,20],"87":[10,7,34],"88":[11,7,34],"89":[10,7,38],"90":[10,7,28],"91":[10,7,15],"92":[10,7,15],"93":[4,7,47],"94":[6,7,19],"95":[7,7,15],"96":[5,1,2],"97":[2,5,1],"98":[8,7,16],"99":[11,7,29],"100":[8,7,13],"101":[7,7,12],"102":[4,7,24],"103":[5,7,22],"104":[7,7,28],"105":[5,1,2],"106":[2,5,1],"107":[7,7,27],"108":[5,1,2],"109":[7,5,20],"110":[2,5,1],"111":[6,7,14],"112":[5,7,31],"113":[7,7,15],"114":[5,7,11],"115":[11,5,28],"116":[11,5,30],"117":[12,5,36],"118":[5,1,3],"119":[2,5,1],"120":[8,7,18],"121":[11,7,28],"122":[8,7,28],"123":[6,7,33],"124":[13,7,27],"125":[8,7,23],"126":[4,7,17],"127":[6,7,18],"128":[5,7,23],"129":[5,7,17],"130":[4,7,10],"131":[7,7,12],"132":[7,7,12],"133":[4,7,37],"134":[5,7,22],"135":[7,7,25],"136":[6,7,12],"137":[6,7,12],"138":[3,7,36],"139":[4,7,35],"140":[6,7,12],"141":[7,7,13],"142":[9,7,39],"143":[7,7,13],"144":[7,7,23],"145":[7,7,15],"146":[5,7,17],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,46],"156":[1,1,1],"157":[1,1,25],"158":[1,1,2],"159":[1,1,7]},"averageFieldLength":[5.75625,5.924999999999998,17.88750000000001],"storedFields":{"0":{"title":"モジュール mbcp","titles":[]},"1":{"title":"モジュール mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["モジュール mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["モジュール mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"モジュール mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["モジュール mbcp.mp_math.const"]},"25":{"title":"var E","titles":["モジュール mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["モジュール mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["モジュール mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["モジュール mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["モジュール mbcp.mp_math.const"]},"30":{"title":"モジュール mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["モジュール mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["モジュール mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["モジュール mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["モジュール mbcp.mp_math.equation"]},"35":{"title":"モジュール mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["モジュール mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["モジュール mbcp.mp_math.function"]},"38":{"title":"モジュール mbcp.mp_math","titles":[]},"39":{"title":"モジュール mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["モジュール mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["モジュール mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["モジュール mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["モジュール mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["モジュール mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["モジュール mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["モジュール mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"58":{"title":"モジュール mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"76":{"title":"モジュール mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["モジュール mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"96":{"title":"モジュール mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["モジュール mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["モジュール mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["モジュール mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"105":{"title":"モジュール mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["モジュール mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["モジュール mbcp.mp_math.segment","class Segment3"]},"108":{"title":"モジュール mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["モジュール mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["モジュール mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["モジュール mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["モジュール mbcp.mp_math.utils"]},"118":{"title":"モジュール mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["モジュール mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["モジュール mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["モジュール mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["モジュール mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["モジュール mbcp.mp_math.vector"]},"151":{"title":"モジュール mbcp.particle","titles":[]},"152":{"title":"モジュール mbcp.presets","titles":[]},"153":{"title":"モジュール mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["モジュール mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["モジュール mbcp.presets.model","class GeometricModels"]},"156":{"title":"ベストプラクティス","titles":[]},"157":{"title":"作品","titles":["ベストプラクティス"]},"158":{"title":"开始不了一点","titles":[]},"159":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"158":1}}],["开始不了一点",{"0":{"158":1}}],["红石音乐",{"2":{"157":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["作品",{"0":{"157":1}}],["ベストプラクティス",{"0":{"156":1},"1":{"157":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"34":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"159":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"104":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"104":1,"138":1}}],["新的点",{"2":{"102":1,"135":1,"139":1}}],["已在",{"2":{"104":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"98":3}}],["笛卡尔坐标系中的点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"159":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"82":1}}],["high",{"2":{"34":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"34":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"34":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["タイプ",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"103":1}}],["判断两个点是否近似相等",{"2":{"99":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"103":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"99":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中点的类",{"2":{"96":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"30":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"157":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"99":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["例",{"2":{"37":1}}],["例外",{"2":{"34":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"159":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"107":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"34":1},"2":{"34":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"34":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"33":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"100":1,"102":1,"104":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"102":1,"104":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"155":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["偏导函数",{"2":{"34":1}}],["偏移量",{"2":{"34":1,"36":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"34":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"34":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"34":1}}],["目标点",{"2":{"33":1}}],["warning",{"2":{"34":1}}],["慎用",{"2":{"34":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"155":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"33":1,"37":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"98":1,"120":1,"150":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"98":1,"115":1,"120":1,"149":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"99":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"98":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"33":3,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"81":1}}],["黄金分割比",{"2":{"26":1}}],["デフォルト",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["π",{"2":{"24":1}}],["to",{"2":{"159":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"83":2,"159":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1}}],["tuple",{"0":{"33":1,"34":1,"48":1},"2":{"33":2,"34":2,"48":2}}],["t",{"0":{"33":1,"47":1},"2":{"33":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["or",{"2":{"56":1,"83":1}}],["order",{"2":{"34":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"52":1},"2":{"52":1}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"37":1,"66":1},"2":{"32":6,"37":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"99":5,"100":1,"101":1,"102":5,"103":5,"104":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"42":1,"49":1,"99":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"42":4,"49":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["exp",{"2":{"25":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"134":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"155":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"155":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"29":1,"42":2,"49":1,"79":1,"99":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1}}],["and",{"0":{"87":1,"90":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"103":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"26":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"104":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"32":4,"33":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":4,"99":4,"100":1,"101":1,"102":4,"103":4,"104":4,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"128":3,"155":2}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"159":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"34":4}}],["return",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"22":2,"33":2,"34":4,"36":1,"37":3,"42":1,"43":1,"44":5,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":3,"57":1,"79":4,"80":2,"81":2,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":4,"94":1,"95":1,"99":1,"102":1,"103":1,"104":1,"109":1,"112":2,"114":1,"115":1,"116":3,"117":3,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"130":1,"133":2,"134":1,"135":1,"138":2,"139":1,"142":2,"143":1,"144":1,"145":1,"146":1,"155":1}}],["range",{"2":{"155":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["ratio",{"0":{"26":1}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["戻り値",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"99":1,"102":1,"103":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"155":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"102":2,"104":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["githubで表示",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"33":1},"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"97":1,"106":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["または",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["ソースコード",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["默认为否",{"2":{"4":1}}],["引数",{"2":{"4":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["任意角度",{"2":{"4":1,"38":1}}],["説明",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"32":3,"34":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"99":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"33":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"34":1,"36":1,"42":1,"49":1,"56":1,"91":1,"92":1,"99":1,"100":1,"101":1,"104":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":3,"107":5,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"159":1}}],["import",{"2":{"104":1}}],["i",{"2":{"155":4,"157":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"142":1},"2":{"34":3,"37":4,"59":1,"112":2,"142":2,"155":1}}],["in",{"2":{"33":1,"34":1,"155":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"107":1},"2":{"55":3,"57":1,"88":3,"107":8}}],["p1",{"0":{"55":1,"88":1,"107":1},"2":{"55":4,"57":1,"88":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"34":3}}],["p",{"0":{"36":1},"2":{"36":20,"102":5,"104":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"96":1},"1":{"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"97":1,"99":1,"100":1,"101":2,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"33":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"99":2,"100":1,"101":2,"102":3,"103":1,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"34":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"75":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3}}],["提供了一些工具",{"2":{"0":1}}],["モジュール",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexroot.C4Y9aF6Z.js b/assets/chunks/@localSearchIndexroot.C4Y9aF6Z.js
new file mode 100644
index 0000000..5c4501f
--- /dev/null
+++ b/assets/chunks/@localSearchIndexroot.C4Y9aF6Z.js
@@ -0,0 +1 @@
+const t='{"documentCount":163,"nextId":163,"documentIds":{"0":"/api/#模块-mbcp","1":"/api/mp_math/angle.html#模块-mbcp-mp-math-angle","2":"/api/mp_math/angle.html#class-angle","3":"/api/mp_math/angle.html#class-anyangle-angle","4":"/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/api/mp_math/angle.html#method-degree-self-float","8":"/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/api/mp_math/angle.html#method-sin-self-float","11":"/api/mp_math/angle.html#method-cos-self-float","12":"/api/mp_math/angle.html#method-tan-self-float","13":"/api/mp_math/angle.html#method-cot-self-float","14":"/api/mp_math/angle.html#method-sec-self-float","15":"/api/mp_math/angle.html#method-csc-self-float","16":"/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/api/mp_math/angle.html#method-eq-self-other","18":"/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/api/mp_math/angle.html#method-self-other","23":"/api/mp_math/equation.html#模块-mbcp-mp-math-equation","24":"/api/mp_math/equation.html#class-curveequation","25":"/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","26":"/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","27":"/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","28":"/api/mp_math/const.html#模块-mbcp-mp-math-const","29":"/api/mp_math/const.html#var-pi","30":"/api/mp_math/const.html#var-e","31":"/api/mp_math/const.html#var-golden-ratio","32":"/api/mp_math/const.html#var-gamma","33":"/api/mp_math/const.html#var-epsilon","34":"/api/mp_math/const.html#var-approx","35":"/api/mp_math/function.html#模块-mbcp-mp-math-function","36":"/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/api/mp_math/#模块-mbcp-mp-math","39":"/api/mp_math/line.html#模块-mbcp-mp-math-line","40":"/api/mp_math/line.html#class-line3","41":"/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/api/mp_math/line.html#method-simplify-self","55":"/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/api/mp_math/line.html#method-self-other-line3-line3-point3-none","57":"/api/mp_math/line.html#method-eq-self-other-bool","58":"/api/mp_math/mp_math_typing.html#模块-mbcp-mp-math-mp-math-typing","59":"/api/mp_math/mp_math_typing.html#var-realnumber","60":"/api/mp_math/mp_math_typing.html#var-number","61":"/api/mp_math/mp_math_typing.html#var-singlevar","62":"/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/api/mp_math/mp_math_typing.html#var-var","64":"/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/api/mp_math/plane.html#模块-mbcp-mp-math-plane","77":"/api/mp_math/plane.html#class-plane3","78":"/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/api/mp_math/plane.html#method-normal-self-vector3","87":"/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/api/mp_math/plane.html#method-self-other-line3-point3-none","92":"/api/mp_math/plane.html#method-self-other-plane3-line3-none","93":"/api/mp_math/plane.html#method-self-other","94":"/api/mp_math/plane.html#method-eq-self-other-bool","95":"/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/api/mp_math/point.html#模块-mbcp-mp-math-point","97":"/api/mp_math/point.html#class-point3","98":"/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/api/mp_math/point.html#method-self-other-vector3-point3","101":"/api/mp_math/point.html#method-self-other-point3-point3","102":"/api/mp_math/point.html#method-self-other","103":"/api/mp_math/point.html#method-eq-self-other","104":"/api/mp_math/point.html#method-self-other-point3-vector3","105":"/api/mp_math/segment.html#模块-mbcp-mp-math-segment","106":"/api/mp_math/segment.html#class-segment3","107":"/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/api/mp_math/utils.html#模块-mbcp-mp-math-utils","109":"/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/api/mp_math/utils.html#class-approx","111":"/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/api/mp_math/utils.html#method-eq-self-other","113":"/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/api/mp_math/utils.html#method-ne-self-other","115":"/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/api/mp_math/vector.html#模块-mbcp-mp-math-vector","119":"/api/mp_math/vector.html#class-vector3","120":"/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/api/mp_math/vector.html#method-normalize-self","127":"/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/api/mp_math/vector.html#method-length-self-float","129":"/api/mp_math/vector.html#method-unit-self-vector3","130":"/api/mp_math/vector.html#method-abs-self","131":"/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/api/mp_math/vector.html#method-self-other-point3-point3","133":"/api/mp_math/vector.html#method-self-other","134":"/api/mp_math/vector.html#method-eq-self-other","135":"/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/api/mp_math/vector.html#method-self-other-1","139":"/api/mp_math/vector.html#method-self-other-point3","140":"/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/api/mp_math/vector.html#method-self-vector3","147":"/api/mp_math/vector.html#var-zero-vector3","148":"/api/mp_math/vector.html#var-x-axis","149":"/api/mp_math/vector.html#var-y-axis","150":"/api/mp_math/vector.html#var-z-axis","151":"/api/particle/#模块-mbcp-particle","152":"/api/presets/#模块-mbcp-presets","153":"/api/presets/model/#模块-mbcp-presets-model","154":"/api/presets/model/#class-geometricmodels","155":"/api/presets/model/#method-sphere-radius-float-density-float","156":"/demo/best-practice.html#最佳实践","157":"/demo/best-practice.html#作品","158":"/demo/#demo","159":"/guide/#快速开始","160":"/guide/#安装","161":"/refer/7-differential-euqtion/#微分方程","162":"/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,24],"5":[5,9,23],"6":[5,9,22],"7":[5,9,19],"8":[6,9,20],"9":[6,9,22],"10":[5,9,17],"11":[5,9,17],"12":[5,9,17],"13":[5,9,19],"14":[5,9,19],"15":[5,9,19],"16":[7,9,15],"17":[5,9,11],"18":[6,9,14],"19":[7,9,16],"20":[7,9,13],"21":[7,9,13],"22":[3,9,15],"23":[5,1,2],"24":[2,5,1],"25":[9,7,19],"26":[10,7,32],"27":[14,5,60],"28":[5,1,2],"29":[2,5,7],"30":[2,5,8],"31":[3,5,10],"32":[2,5,6],"33":[2,5,6],"34":[2,5,6],"35":[5,1,2],"36":[13,5,45],"37":[7,5,39],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,18],"42":[11,7,27],"43":[8,7,20],"44":[10,7,42],"45":[8,7,40],"46":[8,7,21],"47":[8,7,24],"48":[9,7,25],"49":[14,7,26],"50":[8,7,20],"51":[8,7,23],"52":[8,7,21],"53":[8,7,26],"54":[4,7,27],"55":[10,7,27],"56":[10,7,34],"57":[6,7,28],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,25],"79":[7,7,30],"80":[10,7,55],"81":[10,7,44],"82":[9,7,64],"83":[9,7,52],"84":[9,7,23],"85":[8,7,21],"86":[5,7,20],"87":[10,7,34],"88":[11,7,34],"89":[10,7,38],"90":[10,7,28],"91":[10,7,15],"92":[10,7,15],"93":[4,7,47],"94":[6,7,19],"95":[7,7,15],"96":[5,1,2],"97":[2,5,1],"98":[8,7,16],"99":[11,7,29],"100":[8,7,13],"101":[7,7,12],"102":[4,7,24],"103":[5,7,22],"104":[7,7,28],"105":[5,1,2],"106":[2,5,1],"107":[7,7,27],"108":[5,1,2],"109":[7,5,20],"110":[2,5,1],"111":[6,7,14],"112":[5,7,31],"113":[7,7,15],"114":[5,7,11],"115":[11,5,28],"116":[11,5,30],"117":[12,5,36],"118":[5,1,3],"119":[2,5,1],"120":[8,7,18],"121":[11,7,28],"122":[8,7,28],"123":[6,7,33],"124":[13,7,27],"125":[8,7,23],"126":[4,7,17],"127":[6,7,18],"128":[5,7,23],"129":[5,7,17],"130":[4,7,10],"131":[7,7,12],"132":[7,7,12],"133":[4,7,37],"134":[5,7,22],"135":[7,7,25],"136":[6,7,12],"137":[6,7,12],"138":[3,7,36],"139":[4,7,35],"140":[6,7,12],"141":[7,7,13],"142":[9,7,39],"143":[7,7,13],"144":[7,7,23],"145":[7,7,15],"146":[5,7,17],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,46],"156":[1,1,1],"157":[1,1,25],"158":[1,1,1],"159":[1,1,6],"160":[1,1,4],"161":[1,1,1],"162":[1,1,7]},"averageFieldLength":[5.668711656441718,5.834355828220857,17.607361963190193],"storedFields":{"0":{"title":"模块 mbcp","titles":[]},"1":{"title":"模块 mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["模块 mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["模块 mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"模块 mbcp.mp_math.equation","titles":[]},"24":{"title":"class CurveEquation","titles":["模块 mbcp.mp_math.equation"]},"25":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"26":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"27":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模块 mbcp.mp_math.equation"]},"28":{"title":"模块 mbcp.mp_math.const","titles":[]},"29":{"title":"var PI","titles":["模块 mbcp.mp_math.const"]},"30":{"title":"var E","titles":["模块 mbcp.mp_math.const"]},"31":{"title":"var GOLDEN_RATIO","titles":["模块 mbcp.mp_math.const"]},"32":{"title":"var GAMMA","titles":["模块 mbcp.mp_math.const"]},"33":{"title":"var EPSILON","titles":["模块 mbcp.mp_math.const"]},"34":{"title":"var APPROX","titles":["模块 mbcp.mp_math.const"]},"35":{"title":"模块 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模块 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模块 mbcp.mp_math.function"]},"38":{"title":"模块 mbcp.mp_math","titles":[]},"39":{"title":"模块 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模块 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模块 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模块 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模块 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模块 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模块 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"58":{"title":"模块 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模块 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模块 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模块 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模块 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模块 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模块 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模块 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模块 mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模块 mbcp.mp_math.point","class Point3"]},"105":{"title":"模块 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模块 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模块 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模块 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模块 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模块 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"118":{"title":"模块 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模块 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["模块 mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["模块 mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["模块 mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["模块 mbcp.mp_math.vector"]},"151":{"title":"模块 mbcp.particle","titles":[]},"152":{"title":"模块 mbcp.presets","titles":[]},"153":{"title":"模块 mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["模块 mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["模块 mbcp.presets.model","class GeometricModels"]},"156":{"title":"最佳实践","titles":[]},"157":{"title":"作品","titles":["最佳实践"]},"158":{"title":"demo","titles":[]},"159":{"title":"快速开始","titles":[]},"160":{"title":"安装","titles":["快速开始"]},"161":{"title":"微分方程","titles":[]},"162":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["微分方程",{"0":{"161":1}}],["安装",{"0":{"160":1}}],["兼容性优先",{"2":{"159":1}}],["把你项目所使用的python换成pypy",{"2":{"159":1}}],["建议",{"2":{"159":1}}],["快速开始",{"0":{"159":1},"1":{"160":1}}],["红石音乐",{"2":{"157":1}}],["这样可以提高性能",{"2":{"159":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"27":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["作品",{"0":{"157":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["模块",{"0":{"0":1,"1":1,"23":1,"28":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"162":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"104":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"104":1,"138":1}}],["新的点",{"2":{"102":1,"135":1,"139":1}}],["已在",{"2":{"104":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"98":3}}],["笛卡尔坐标系中的点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"162":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"82":1}}],["high",{"2":{"27":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"27":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"29":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"27":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"27":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["类型",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"30":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"103":1}}],["判断两个点是否近似相等",{"2":{"99":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"103":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"99":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"28":1}}],["本模块定义了三维空间中点的类",{"2":{"96":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"23":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"157":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"99":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["示例",{"2":{"37":1}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"162":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"107":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["demo",{"0":{"158":1}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"27":1},"2":{"27":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"27":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"26":1}}],["约等于判定误差",{"2":{"34":1}}],["精度误差",{"2":{"33":1}}],["欧拉常数",{"2":{"32":1}}],["5772156649015329",{"2":{"32":1}}],["5",{"2":{"31":1,"81":1}}],["黄金分割比",{"2":{"31":1}}],["默认值",{"2":{"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"29":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"100":1,"102":1,"104":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"27":2,"102":1,"104":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"26":1,"27":1,"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"26":1,"27":12,"37":4}}],["valueerror",{"2":{"27":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"27":8,"155":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"26":1}}],["无效变量类型",{"2":{"27":1}}],["引发",{"2":{"27":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["偏导函数",{"2":{"27":1}}],["偏移量",{"2":{"27":1,"36":1}}],["高阶偏导",{"2":{"27":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"27":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"27":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"27":1}}],["目标点",{"2":{"26":1}}],["warning",{"2":{"27":1}}],["慎用",{"2":{"27":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"27":1}}],["number",{"0":{"27":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"155":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"27":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"27":1,"47":1,"48":1},"2":{"27":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"32":1}}],["golden",{"0":{"31":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"26":1,"27":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"102":2,"104":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"34":1}}],["0001",{"2":{"33":1}}],["0",{"0":{"115":2},"2":{"26":3,"32":1,"33":1,"34":1,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["|",{"0":{"26":1,"27":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"26":1,"27":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"25":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"26":1}}],["z函数",{"2":{"25":1}}],["z",{"0":{"25":1,"98":1,"120":1,"150":1},"2":{"25":4,"26":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"25":1}}],["y",{"0":{"25":1,"98":1,"115":1,"120":1,"149":1},"2":{"25":4,"26":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"99":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"25":1}}],["x",{"0":{"25":1,"98":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"25":4,"26":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["to",{"2":{"162":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"83":2,"162":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"27":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1,"159":1}}],["tuple",{"0":{"26":1,"27":1,"48":1},"2":{"26":2,"27":2,"48":2}}],["t",{"0":{"26":1,"47":1},"2":{"26":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["or",{"2":{"56":1,"83":1}}],["order",{"2":{"27":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"52":1},"2":{"52":1}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"25":3,"37":1,"66":1},"2":{"25":6,"37":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"99":5,"100":1,"101":1,"102":5,"103":5,"104":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"27":2,"33":1,"36":2,"42":1,"49":1,"99":1,"115":1,"121":1,"124":1},"2":{"27":6,"36":11,"42":4,"49":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["exp",{"2":{"30":1}}],["e",{"0":{"30":1},"2":{"30":1}}],["elif",{"2":{"27":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"26":1,"27":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"134":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"155":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"155":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"27":11,"37":3}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"34":1,"42":2,"49":1,"79":1,"99":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1}}],["and",{"0":{"87":1,"90":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"103":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"27":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"31":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"26":1,"30":1,"31":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最佳实践",{"0":{"156":1},"1":{"157":1}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["shellpip",{"2":{"160":1}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"31":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"104":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"25":1,"26":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"25":4,"26":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":4,"99":4,"100":1,"101":1,"102":4,"103":4,"104":4,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"27":1,"31":1,"36":3,"37":1,"45":1,"81":3,"107":3,"128":3,"155":2}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["range",{"2":{"155":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["ratio",{"0":{"31":1}}],["raise",{"0":{"113":1},"2":{"27":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["reference",{"0":{"162":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"27":4}}],["return",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"22":2,"26":2,"27":4,"36":1,"37":3,"42":1,"43":1,"44":5,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":3,"57":1,"79":4,"80":2,"81":2,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":4,"94":1,"95":1,"99":1,"102":1,"103":1,"104":1,"109":1,"112":2,"114":1,"115":1,"116":3,"117":3,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"130":1,"133":2,"134":1,"135":1,"138":2,"139":1,"142":2,"143":1,"144":1,"145":1,"146":1,"155":1}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"26":1,"27":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["返回",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"26":1,"27":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"99":1,"102":1,"103":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"26":1},"2":{"26":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"24":1,"40":1,"77":1,"97":1,"106":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"25":1,"26":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"24":1},"1":{"25":1,"26":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"28":1},"1":{"29":1,"30":1,"31":1,"32":1,"33":1,"34":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["在github上查看",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"25":1,"26":1,"27":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"27":1}}],["或",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"25":1,"26":1,"27":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["源代码",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"25":1,"26":1,"27":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"4":1,"25":1,"26":2,"27":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["任意角度",{"2":{"4":1,"38":1}}],["说明",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"25":1,"26":1,"27":1,"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"26":1,"27":1,"93":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"25":3,"27":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"25":12,"26":6,"27":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"99":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"26":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"27":1,"36":1,"42":1,"49":1,"56":1,"91":1,"92":1,"99":1,"100":1,"101":1,"104":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"25":3,"27":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":3,"107":5,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"162":1}}],["import",{"2":{"104":1}}],["i",{"2":{"155":4,"157":1}}],["install",{"2":{"160":1}}],["invalid",{"2":{"27":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"27":2,"142":1},"2":{"27":3,"37":4,"59":1,"112":2,"142":2,"155":1}}],["in",{"2":{"26":1,"27":1,"155":2}}],["init",{"0":{"4":1,"25":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"25":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"26":1,"27":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"27":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"107":1},"2":{"55":3,"57":1,"88":3,"107":8}}],["p1",{"0":{"55":1,"88":1,"107":1},"2":{"55":4,"57":1,"88":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"27":1},"2":{"27":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"27":3}}],["p",{"0":{"36":1},"2":{"36":20,"102":5,"104":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"96":1},"1":{"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"26":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"97":1,"99":1,"100":1,"101":2,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"26":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"99":2,"100":1,"101":2,"102":3,"103":1,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"25":1,"26":1,"27":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"29":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"29":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"27":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"27":2,"37":1,"75":1},"2":{"27":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"28":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"29":1,"30":1,"31":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"25":1,"26":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"28":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"28":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"29":1,"30":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3,"160":1}}],["提供了一些工具",{"2":{"0":1}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexroot.DH9jnGhe.js b/assets/chunks/@localSearchIndexroot.DH9jnGhe.js
deleted file mode 100644
index c5d420a..0000000
--- a/assets/chunks/@localSearchIndexroot.DH9jnGhe.js
+++ /dev/null
@@ -1 +0,0 @@
-const t='{"documentCount":163,"nextId":163,"documentIds":{"0":"/api/#模块-mbcp","1":"/api/mp_math/angle.html#模块-mbcp-mp-math-angle","2":"/api/mp_math/angle.html#class-angle","3":"/api/mp_math/angle.html#class-anyangle-angle","4":"/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/api/mp_math/angle.html#method-degree-self-float","8":"/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/api/mp_math/angle.html#method-sin-self-float","11":"/api/mp_math/angle.html#method-cos-self-float","12":"/api/mp_math/angle.html#method-tan-self-float","13":"/api/mp_math/angle.html#method-cot-self-float","14":"/api/mp_math/angle.html#method-sec-self-float","15":"/api/mp_math/angle.html#method-csc-self-float","16":"/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/api/mp_math/angle.html#method-eq-self-other","18":"/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/api/mp_math/angle.html#method-self-other","23":"/api/mp_math/const.html#模块-mbcp-mp-math-const","24":"/api/mp_math/const.html#var-pi","25":"/api/mp_math/const.html#var-e","26":"/api/mp_math/const.html#var-golden-ratio","27":"/api/mp_math/const.html#var-gamma","28":"/api/mp_math/const.html#var-epsilon","29":"/api/mp_math/const.html#var-approx","30":"/api/mp_math/equation.html#模块-mbcp-mp-math-equation","31":"/api/mp_math/equation.html#class-curveequation","32":"/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","33":"/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","34":"/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","35":"/api/mp_math/function.html#模块-mbcp-mp-math-function","36":"/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/api/mp_math/#模块-mbcp-mp-math","39":"/api/mp_math/line.html#模块-mbcp-mp-math-line","40":"/api/mp_math/line.html#class-line3","41":"/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/api/mp_math/line.html#method-simplify-self","55":"/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/api/mp_math/line.html#method-and-self-other-line3-line3-point3-none","57":"/api/mp_math/line.html#method-eq-self-other-bool","58":"/api/mp_math/mp_math_typing.html#模块-mbcp-mp-math-mp-math-typing","59":"/api/mp_math/mp_math_typing.html#var-realnumber","60":"/api/mp_math/mp_math_typing.html#var-number","61":"/api/mp_math/mp_math_typing.html#var-singlevar","62":"/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/api/mp_math/mp_math_typing.html#var-var","64":"/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/api/mp_math/plane.html#模块-mbcp-mp-math-plane","77":"/api/mp_math/plane.html#class-plane3","78":"/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/api/mp_math/plane.html#method-normal-self-vector3","87":"/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/api/mp_math/plane.html#method-and-self-other-line3-point3-none","92":"/api/mp_math/plane.html#method-and-self-other-plane3-line3-none","93":"/api/mp_math/plane.html#method-and-self-other","94":"/api/mp_math/plane.html#method-eq-self-other-bool","95":"/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/api/mp_math/point.html#模块-mbcp-mp-math-point","97":"/api/mp_math/point.html#class-point3","98":"/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/api/mp_math/point.html#method-self-other-vector3-point3","101":"/api/mp_math/point.html#method-self-other-point3-point3","102":"/api/mp_math/point.html#method-self-other","103":"/api/mp_math/point.html#method-eq-self-other","104":"/api/mp_math/point.html#method-self-other-point3-vector3","105":"/api/mp_math/segment.html#模块-mbcp-mp-math-segment","106":"/api/mp_math/segment.html#class-segment3","107":"/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/api/mp_math/utils.html#模块-mbcp-mp-math-utils","109":"/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/api/mp_math/utils.html#class-approx","111":"/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/api/mp_math/utils.html#method-eq-self-other","113":"/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/api/mp_math/utils.html#method-ne-self-other","115":"/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/api/mp_math/vector.html#模块-mbcp-mp-math-vector","119":"/api/mp_math/vector.html#class-vector3","120":"/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/api/mp_math/vector.html#method-normalize-self","127":"/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/api/mp_math/vector.html#method-length-self-float","129":"/api/mp_math/vector.html#method-unit-self-vector3","130":"/api/mp_math/vector.html#method-abs-self","131":"/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/api/mp_math/vector.html#method-self-other-point3-point3","133":"/api/mp_math/vector.html#method-self-other","134":"/api/mp_math/vector.html#method-eq-self-other","135":"/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/api/mp_math/vector.html#method-self-other-1","139":"/api/mp_math/vector.html#method-self-other-point3","140":"/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/api/mp_math/vector.html#method-self-vector3","147":"/api/mp_math/vector.html#var-zero-vector3","148":"/api/mp_math/vector.html#var-x-axis","149":"/api/mp_math/vector.html#var-y-axis","150":"/api/mp_math/vector.html#var-z-axis","151":"/api/particle/#模块-mbcp-particle","152":"/api/presets/#模块-mbcp-presets","153":"/demo/best-practice.html#最佳实践","154":"/demo/best-practice.html#作品","155":"/api/presets/model/#模块-mbcp-presets-model","156":"/api/presets/model/#class-geometricmodels","157":"/api/presets/model/#method-sphere-radius-float-density-float","158":"/demo/#demo","159":"/guide/#快速开始","160":"/guide/#安装","161":"/refer/7-differential-euqtion/#微分方程","162":"/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,24],"5":[5,9,23],"6":[5,9,22],"7":[5,9,19],"8":[6,9,20],"9":[6,9,22],"10":[5,9,17],"11":[5,9,17],"12":[5,9,17],"13":[5,9,19],"14":[5,9,19],"15":[5,9,19],"16":[7,9,15],"17":[5,9,11],"18":[6,9,14],"19":[7,9,16],"20":[7,9,13],"21":[7,9,13],"22":[3,9,15],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[2,5,1],"32":[9,7,19],"33":[10,7,32],"34":[14,5,60],"35":[5,1,2],"36":[13,5,45],"37":[7,5,39],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,18],"42":[11,7,27],"43":[8,7,20],"44":[10,7,42],"45":[8,7,40],"46":[8,7,21],"47":[8,7,24],"48":[9,7,25],"49":[14,7,26],"50":[8,7,20],"51":[8,7,23],"52":[8,7,21],"53":[8,7,26],"54":[4,7,27],"55":[10,7,27],"56":[9,7,34],"57":[6,7,28],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,25],"79":[7,7,30],"80":[10,7,55],"81":[10,7,44],"82":[9,7,64],"83":[9,7,52],"84":[9,7,23],"85":[8,7,21],"86":[5,7,20],"87":[10,7,34],"88":[11,7,34],"89":[10,7,38],"90":[10,7,28],"91":[9,7,15],"92":[9,7,15],"93":[5,7,47],"94":[6,7,19],"95":[7,7,15],"96":[5,1,2],"97":[2,5,1],"98":[8,7,16],"99":[11,7,29],"100":[8,7,13],"101":[7,7,12],"102":[4,7,24],"103":[5,7,22],"104":[7,7,28],"105":[5,1,2],"106":[2,5,1],"107":[7,7,27],"108":[5,1,2],"109":[7,5,20],"110":[2,5,1],"111":[6,7,14],"112":[5,7,31],"113":[7,7,15],"114":[5,7,11],"115":[11,5,28],"116":[11,5,30],"117":[12,5,36],"118":[5,1,3],"119":[2,5,1],"120":[8,7,18],"121":[11,7,28],"122":[8,7,28],"123":[6,7,33],"124":[13,7,27],"125":[8,7,23],"126":[4,7,17],"127":[6,7,18],"128":[5,7,23],"129":[5,7,17],"130":[4,7,10],"131":[7,7,12],"132":[7,7,12],"133":[4,7,37],"134":[5,7,22],"135":[7,7,25],"136":[6,7,12],"137":[6,7,12],"138":[3,7,36],"139":[4,7,35],"140":[6,7,12],"141":[7,7,13],"142":[9,7,39],"143":[7,7,13],"144":[7,7,23],"145":[7,7,15],"146":[5,7,17],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[1,1,1],"154":[1,1,25],"155":[4,1,2],"156":[2,4,2],"157":[6,6,46],"158":[1,1,1],"159":[1,1,6],"160":[1,1,4],"161":[1,1,1],"162":[1,1,7]},"averageFieldLength":[5.656441717791411,5.834355828220857,17.607361963190193],"storedFields":{"0":{"title":"模块 mbcp","titles":[]},"1":{"title":"模块 mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["模块 mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["模块 mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"模块 mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["模块 mbcp.mp_math.const"]},"25":{"title":"var E","titles":["模块 mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["模块 mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["模块 mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["模块 mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["模块 mbcp.mp_math.const"]},"30":{"title":"模块 mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["模块 mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模块 mbcp.mp_math.equation"]},"35":{"title":"模块 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模块 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模块 mbcp.mp_math.function"]},"38":{"title":"模块 mbcp.mp_math","titles":[]},"39":{"title":"模块 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模块 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模块 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模块 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模块 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模块 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模块 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"56":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"58":{"title":"模块 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模块 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模块 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模块 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模块 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模块 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method __and__(self, other)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模块 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模块 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模块 mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模块 mbcp.mp_math.point","class Point3"]},"105":{"title":"模块 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模块 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模块 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模块 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模块 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模块 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"118":{"title":"模块 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模块 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["模块 mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["模块 mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["模块 mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["模块 mbcp.mp_math.vector"]},"151":{"title":"模块 mbcp.particle","titles":[]},"152":{"title":"模块 mbcp.presets","titles":[]},"153":{"title":"最佳实践","titles":[]},"154":{"title":"作品","titles":["最佳实践"]},"155":{"title":"模块 mbcp.presets.model","titles":[]},"156":{"title":"class GeometricModels","titles":["模块 mbcp.presets.model"]},"157":{"title":"method sphere(radius: float, density: float)","titles":["模块 mbcp.presets.model","class GeometricModels"]},"158":{"title":"demo","titles":[]},"159":{"title":"快速开始","titles":[]},"160":{"title":"安装","titles":["快速开始"]},"161":{"title":"微分方程","titles":[]},"162":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["微分方程",{"0":{"161":1}}],["安装",{"0":{"160":1}}],["兼容性优先",{"2":{"159":1}}],["把你项目所使用的python换成pypy",{"2":{"159":1}}],["建议",{"2":{"159":1}}],["快速开始",{"0":{"159":1},"1":{"160":1}}],["4",{"2":{"157":1}}],["球体上的点集",{"2":{"157":1}}],["生成球体上的点集",{"2":{"157":1}}],["几何模型点集",{"2":{"155":1}}],["红石音乐",{"2":{"154":1}}],["这样可以提高性能",{"2":{"159":1}}],["这么可爱真是抱歉",{"2":{"154":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"154":1}}],["芙宁娜pv曲",{"2":{"154":1}}],["有点甜~",{"2":{"154":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"154":1}}],["崩坏",{"2":{"154":1}}],["使一颗心免于哀伤",{"2":{"154":1}}],["总有一条蜿蜒在童话镇里",{"2":{"154":1}}],["童话镇~",{"2":{"154":1}}],["特效红石音乐",{"2":{"154":2}}],["作品",{"0":{"154":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["模块",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"155":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"156":1,"157":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"162":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"104":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"104":1,"138":1}}],["新的点",{"2":{"102":1,"135":1,"139":1}}],["已在",{"2":{"104":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"98":3}}],["笛卡尔坐标系中的点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"162":1}}],["heart",{"2":{"154":1}}],["have",{"2":{"82":1}}],["high",{"2":{"34":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"34":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"34":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["类型",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"103":1}}],["判断两个点是否近似相等",{"2":{"99":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"103":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"99":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中点的类",{"2":{"96":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"30":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"154":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"99":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["示例",{"2":{"37":1}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"162":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"107":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["demo",{"0":{"158":1}}],["density",{"0":{"157":1},"2":{"157":3}}],["derivative",{"0":{"34":1},"2":{"34":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"34":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"157":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"33":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"100":1,"102":1,"104":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"102":1,"104":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"157":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["引发",{"2":{"34":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["偏导函数",{"2":{"34":1}}],["偏移量",{"2":{"34":1,"36":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"154":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"34":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"34":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"34":1}}],["目标点",{"2":{"33":1}}],["warning",{"2":{"34":1}}],["慎用",{"2":{"34":1}}],["num",{"2":{"157":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"157":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"98":1,"120":1,"150":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"157":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"98":1,"115":1,"120":1,"149":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"157":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"99":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"98":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":5,"99":2,"102":2,"103":2,"104":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"157":2}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"33":3,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"157":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"81":1}}],["黄金分割比",{"2":{"26":1}}],["geometricmodels",{"0":{"156":1},"1":{"157":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"102":2,"104":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["默认值",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"162":1}}],["theta",{"2":{"157":3}}],["the",{"2":{"83":2,"162":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1,"159":1}}],["tuple",{"0":{"33":1,"34":1,"48":1},"2":{"33":2,"34":2,"48":2}}],["t",{"0":{"33":1,"47":1},"2":{"33":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["or",{"2":{"56":1,"83":1}}],["order",{"2":{"34":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"52":1},"2":{"52":1}}],["one",{"2":{"154":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"37":1,"66":1},"2":{"32":6,"37":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"99":5,"100":1,"101":1,"102":5,"103":5,"104":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["ep",{"2":{"154":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"42":1,"49":1,"99":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"42":4,"49":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["exp",{"2":{"25":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"134":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["arccos",{"2":{"157":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"157":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"157":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"29":1,"42":2,"49":1,"79":1,"99":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1}}],["and",{"0":{"56":1,"87":1,"90":1,"91":1,"92":1,"93":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"103":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"157":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"157":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最佳实践",{"0":{"153":1},"1":{"154":1}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["shellpip",{"2":{"160":1}}],["sphere",{"0":{"157":1},"2":{"157":1}}],["staticmethod",{"2":{"156":1,"157":1}}],["stop",{"2":{"154":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"157":3}}],["sqrt",{"2":{"26":1,"128":1,"157":1}}],["sub",{"2":{"18":1,"104":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"32":4,"33":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":4,"99":4,"100":1,"101":1,"102":4,"103":4,"104":4,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["255万个粒子",{"2":{"154":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"128":3,"157":2}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"162":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"34":4}}],["return",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"22":2,"33":2,"34":4,"36":1,"37":3,"42":1,"43":1,"44":5,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":3,"57":1,"79":4,"80":2,"81":2,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":4,"94":1,"95":1,"99":1,"102":1,"103":1,"104":1,"109":1,"112":2,"114":1,"115":1,"116":3,"117":3,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"130":1,"133":2,"134":1,"135":1,"138":2,"139":1,"142":2,"143":1,"144":1,"145":1,"146":1,"157":1}}],["range",{"2":{"157":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"157":1},"2":{"157":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["ratio",{"0":{"26":1}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["返回",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"99":1,"102":1,"103":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"157":1}}],["can",{"2":{"154":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"33":1},"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"157":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"97":1,"106":1,"110":1,"119":1,"156":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"157":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"157":2}}],["在github上查看",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"157":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"34":1}}],["或",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"157":1}}],["源代码",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"157":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"4":1,"32":1,"33":2,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"157":1}}],["任意角度",{"2":{"4":1,"38":1}}],["说明",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"157":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"154":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"133":1,"138":1,"139":1,"142":1,"157":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"32":3,"34":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"99":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"157":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"157":2}}],["==",{"2":{"33":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"34":1,"36":1,"42":1,"49":1,"99":1,"100":1,"101":1,"104":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":3,"107":5,"111":1,"120":3,"126":4,"157":7}}],["improve",{"2":{"162":1}}],["import",{"2":{"104":1}}],["i",{"2":{"154":1,"157":4}}],["install",{"2":{"160":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"142":1},"2":{"34":3,"37":4,"59":1,"112":2,"142":2,"157":1}}],["in",{"2":{"33":1,"34":1,"157":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"154":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"157":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"107":1},"2":{"55":3,"57":1,"88":3,"107":8}}],["p1",{"0":{"55":1,"88":1,"107":1},"2":{"55":4,"57":1,"88":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"34":3}}],["p",{"0":{"36":1},"2":{"36":20,"102":5,"104":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"96":1},"1":{"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"97":1,"99":1,"100":1,"101":2,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"33":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"99":2,"100":1,"101":2,"102":3,"103":1,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"157":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"157":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"99":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"155":1},"1":{"156":1,"157":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"157":2}}],["粒子生成工具",{"2":{"0":1}}],["model",{"0":{"155":1},"1":{"156":1,"157":1}}],["mc特效红石音乐",{"2":{"154":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"154":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"34":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"75":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"157":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"105":1,"108":1,"118":1,"151":1,"152":1,"155":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"156":1,"157":1},"2":{"0":3,"160":1}}],["提供了一些工具",{"2":{"0":1}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexzht.BOVgxEGY.js b/assets/chunks/@localSearchIndexzht.BOVgxEGY.js
new file mode 100644
index 0000000..ae4a0e1
--- /dev/null
+++ b/assets/chunks/@localSearchIndexzht.BOVgxEGY.js
@@ -0,0 +1 @@
+const t='{"documentCount":160,"nextId":160,"documentIds":{"0":"/zht/api/#模組-mbcp","1":"/zht/api/mp_math/angle.html#模組-mbcp-mp-math-angle","2":"/zht/api/mp_math/angle.html#class-angle","3":"/zht/api/mp_math/angle.html#class-anyangle-angle","4":"/zht/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/zht/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/zht/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/zht/api/mp_math/angle.html#method-degree-self-float","8":"/zht/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/zht/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/zht/api/mp_math/angle.html#method-sin-self-float","11":"/zht/api/mp_math/angle.html#method-cos-self-float","12":"/zht/api/mp_math/angle.html#method-tan-self-float","13":"/zht/api/mp_math/angle.html#method-cot-self-float","14":"/zht/api/mp_math/angle.html#method-sec-self-float","15":"/zht/api/mp_math/angle.html#method-csc-self-float","16":"/zht/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/zht/api/mp_math/angle.html#method-eq-self-other","18":"/zht/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/zht/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/zht/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/zht/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/zht/api/mp_math/angle.html#method-self-other","23":"/zht/api/mp_math/const.html#模組-mbcp-mp-math-const","24":"/zht/api/mp_math/const.html#var-pi","25":"/zht/api/mp_math/const.html#var-e","26":"/zht/api/mp_math/const.html#var-golden-ratio","27":"/zht/api/mp_math/const.html#var-gamma","28":"/zht/api/mp_math/const.html#var-epsilon","29":"/zht/api/mp_math/const.html#var-approx","30":"/zht/api/mp_math/equation.html#模組-mbcp-mp-math-equation","31":"/zht/api/mp_math/equation.html#class-curveequation","32":"/zht/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","33":"/zht/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","34":"/zht/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","35":"/zht/api/mp_math/function.html#模組-mbcp-mp-math-function","36":"/zht/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","37":"/zht/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","38":"/zht/api/mp_math/#模組-mbcp-mp-math","39":"/zht/api/mp_math/line.html#模組-mbcp-mp-math-line","40":"/zht/api/mp_math/line.html#class-line3","41":"/zht/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","42":"/zht/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","43":"/zht/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","44":"/zht/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","45":"/zht/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","46":"/zht/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","47":"/zht/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","48":"/zht/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","49":"/zht/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","50":"/zht/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","51":"/zht/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","52":"/zht/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","53":"/zht/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","54":"/zht/api/mp_math/line.html#method-simplify-self","55":"/zht/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","56":"/zht/api/mp_math/line.html#method-self-other-line3-line3-point3-none","57":"/zht/api/mp_math/line.html#method-eq-self-other-bool","58":"/zht/api/mp_math/mp_math_typing.html#模組-mbcp-mp-math-mp-math-typing","59":"/zht/api/mp_math/mp_math_typing.html#var-realnumber","60":"/zht/api/mp_math/mp_math_typing.html#var-number","61":"/zht/api/mp_math/mp_math_typing.html#var-singlevar","62":"/zht/api/mp_math/mp_math_typing.html#var-arrayvar","63":"/zht/api/mp_math/mp_math_typing.html#var-var","64":"/zht/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","65":"/zht/api/mp_math/mp_math_typing.html#var-onearrayfunc","66":"/zht/api/mp_math/mp_math_typing.html#var-onevarfunc","67":"/zht/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","68":"/zht/api/mp_math/mp_math_typing.html#var-twoarraysfunc","69":"/zht/api/mp_math/mp_math_typing.html#var-twovarsfunc","70":"/zht/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","71":"/zht/api/mp_math/mp_math_typing.html#var-threearraysfunc","72":"/zht/api/mp_math/mp_math_typing.html#var-threevarsfunc","73":"/zht/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","74":"/zht/api/mp_math/mp_math_typing.html#var-multiarraysfunc","75":"/zht/api/mp_math/mp_math_typing.html#var-multivarsfunc","76":"/zht/api/mp_math/plane.html#模組-mbcp-mp-math-plane","77":"/zht/api/mp_math/plane.html#class-plane3","78":"/zht/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","79":"/zht/api/mp_math/plane.html#method-approx-self-other-plane3-bool","80":"/zht/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","81":"/zht/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","82":"/zht/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","83":"/zht/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","84":"/zht/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","85":"/zht/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","86":"/zht/api/mp_math/plane.html#method-normal-self-vector3","87":"/zht/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","88":"/zht/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","89":"/zht/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","90":"/zht/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","91":"/zht/api/mp_math/plane.html#method-self-other-line3-point3-none","92":"/zht/api/mp_math/plane.html#method-self-other-plane3-line3-none","93":"/zht/api/mp_math/plane.html#method-self-other","94":"/zht/api/mp_math/plane.html#method-eq-self-other-bool","95":"/zht/api/mp_math/plane.html#method-rand-self-other-line3-point3","96":"/zht/api/mp_math/segment.html#模組-mbcp-mp-math-segment","97":"/zht/api/mp_math/segment.html#class-segment3","98":"/zht/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","99":"/zht/api/mp_math/point.html#模組-mbcp-mp-math-point","100":"/zht/api/mp_math/point.html#class-point3","101":"/zht/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","102":"/zht/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","103":"/zht/api/mp_math/point.html#method-self-other-vector3-point3","104":"/zht/api/mp_math/point.html#method-self-other-point3-point3","105":"/zht/api/mp_math/point.html#method-self-other","106":"/zht/api/mp_math/point.html#method-eq-self-other","107":"/zht/api/mp_math/point.html#method-self-other-point3-vector3","108":"/zht/api/mp_math/utils.html#模組-mbcp-mp-math-utils","109":"/zht/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/zht/api/mp_math/utils.html#class-approx","111":"/zht/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/zht/api/mp_math/utils.html#method-eq-self-other","113":"/zht/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/zht/api/mp_math/utils.html#method-ne-self-other","115":"/zht/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/zht/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/zht/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/zht/api/mp_math/vector.html#模組-mbcp-mp-math-vector","119":"/zht/api/mp_math/vector.html#class-vector3","120":"/zht/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/zht/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/zht/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/zht/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/zht/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/zht/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/zht/api/mp_math/vector.html#method-normalize-self","127":"/zht/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/zht/api/mp_math/vector.html#method-length-self-float","129":"/zht/api/mp_math/vector.html#method-unit-self-vector3","130":"/zht/api/mp_math/vector.html#method-abs-self","131":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/zht/api/mp_math/vector.html#method-self-other-point3-point3","133":"/zht/api/mp_math/vector.html#method-self-other","134":"/zht/api/mp_math/vector.html#method-eq-self-other","135":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/zht/api/mp_math/vector.html#method-self-other-1","139":"/zht/api/mp_math/vector.html#method-self-other-point3","140":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/zht/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/zht/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/zht/api/mp_math/vector.html#method-self-vector3","147":"/zht/api/mp_math/vector.html#var-zero-vector3","148":"/zht/api/mp_math/vector.html#var-x-axis","149":"/zht/api/mp_math/vector.html#var-y-axis","150":"/zht/api/mp_math/vector.html#var-z-axis","151":"/zht/api/particle/#模組-mbcp-particle","152":"/zht/api/presets/#模組-mbcp-presets","153":"/zht/api/presets/model/#模組-mbcp-presets-model","154":"/zht/api/presets/model/#class-geometricmodels","155":"/zht/api/presets/model/#method-sphere-radius-float-density-float","156":"/zht/demo/best-practice.html#最佳實踐","157":"/zht/demo/best-practice.html#作品","158":"/zht/guide/#开始不了一点","159":"/zht/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,24],"5":[5,9,23],"6":[5,9,22],"7":[5,9,19],"8":[6,9,20],"9":[6,9,22],"10":[5,9,17],"11":[5,9,17],"12":[5,9,17],"13":[5,9,19],"14":[5,9,19],"15":[5,9,19],"16":[7,9,15],"17":[5,9,11],"18":[6,9,14],"19":[7,9,16],"20":[7,9,13],"21":[7,9,13],"22":[3,9,15],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[2,5,1],"32":[9,7,19],"33":[10,7,33],"34":[14,5,60],"35":[5,1,2],"36":[13,5,45],"37":[7,5,40],"38":[4,1,20],"39":[5,1,2],"40":[2,5,1],"41":[8,7,18],"42":[11,7,27],"43":[8,7,20],"44":[10,7,42],"45":[8,7,40],"46":[8,7,21],"47":[8,7,24],"48":[9,7,25],"49":[14,7,26],"50":[8,7,20],"51":[8,7,23],"52":[8,7,21],"53":[8,7,26],"54":[4,7,27],"55":[10,7,27],"56":[10,7,34],"57":[6,7,28],"58":[5,1,2],"59":[2,5,9],"60":[2,5,9],"61":[2,5,7],"62":[2,5,8],"63":[2,5,9],"64":[2,5,8],"65":[2,5,8],"66":[2,5,9],"67":[2,5,8],"68":[2,5,8],"69":[2,5,9],"70":[2,5,8],"71":[2,5,8],"72":[2,5,9],"73":[2,5,8],"74":[2,5,8],"75":[2,5,9],"76":[5,1,2],"77":[2,5,1],"78":[9,7,25],"79":[7,7,30],"80":[10,7,55],"81":[10,7,44],"82":[9,7,64],"83":[9,7,52],"84":[9,7,23],"85":[8,7,21],"86":[5,7,20],"87":[10,7,34],"88":[11,7,34],"89":[10,7,38],"90":[10,7,28],"91":[10,7,15],"92":[10,7,15],"93":[4,7,47],"94":[6,7,19],"95":[7,7,15],"96":[5,1,2],"97":[2,5,1],"98":[7,7,27],"99":[5,1,2],"100":[2,5,1],"101":[8,7,16],"102":[11,7,29],"103":[8,7,13],"104":[7,7,12],"105":[4,7,24],"106":[5,7,22],"107":[7,7,28],"108":[5,1,2],"109":[7,5,20],"110":[2,5,1],"111":[6,7,14],"112":[5,7,31],"113":[7,7,15],"114":[5,7,11],"115":[11,5,28],"116":[11,5,30],"117":[12,5,36],"118":[5,1,3],"119":[2,5,1],"120":[8,7,18],"121":[11,7,28],"122":[8,7,28],"123":[6,7,33],"124":[13,7,27],"125":[8,7,23],"126":[4,7,17],"127":[6,7,18],"128":[5,7,23],"129":[5,7,17],"130":[4,7,10],"131":[7,7,12],"132":[7,7,12],"133":[4,7,37],"134":[5,7,22],"135":[7,7,25],"136":[6,7,12],"137":[6,7,12],"138":[3,7,36],"139":[4,7,35],"140":[6,7,12],"141":[7,7,13],"142":[9,7,39],"143":[7,7,13],"144":[7,7,23],"145":[7,7,15],"146":[5,7,17],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,46],"156":[1,1,1],"157":[1,1,25],"158":[1,1,2],"159":[1,1,7]},"averageFieldLength":[5.75625,5.924999999999998,17.88750000000001],"storedFields":{"0":{"title":"模組 mbcp","titles":[]},"1":{"title":"模組 mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["模組 mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["模組 mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"模組 mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["模組 mbcp.mp_math.const"]},"25":{"title":"var E","titles":["模組 mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["模組 mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["模組 mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["模組 mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["模組 mbcp.mp_math.const"]},"30":{"title":"模組 mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["模組 mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模組 mbcp.mp_math.equation"]},"35":{"title":"模組 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模組 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模組 mbcp.mp_math.function"]},"38":{"title":"模組 mbcp.mp_math","titles":[]},"39":{"title":"模組 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模組 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模組 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模組 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模組 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模組 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模組 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"56":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模組 mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"58":{"title":"模組 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模組 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模組 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模組 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method self & other: Line3 => Point3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method self & other: Plane3 => Line3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method self & other","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模組 mbcp.mp_math.segment","titles":[]},"97":{"title":"class Segment3","titles":["模組 mbcp.mp_math.segment"]},"98":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模組 mbcp.mp_math.segment","class Segment3"]},"99":{"title":"模組 mbcp.mp_math.point","titles":[]},"100":{"title":"class Point3","titles":["模組 mbcp.mp_math.point"]},"101":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.point","class Point3"]},"102":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self + other: Vector3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"105":{"title":"method self + other","titles":["模組 mbcp.mp_math.point","class Point3"]},"106":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.point","class Point3"]},"107":{"title":"method self - other: Point3 => Vector3","titles":["模組 mbcp.mp_math.point","class Point3"]},"108":{"title":"模組 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模組 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模組 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"118":{"title":"模組 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模組 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["模組 mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["模組 mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["模組 mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["模組 mbcp.mp_math.vector"]},"151":{"title":"模組 mbcp.particle","titles":[]},"152":{"title":"模組 mbcp.presets","titles":[]},"153":{"title":"模組 mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["模組 mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["模組 mbcp.presets.model","class GeometricModels"]},"156":{"title":"最佳實踐","titles":[]},"157":{"title":"作品","titles":["最佳實踐"]},"158":{"title":"开始不了一点","titles":[]},"159":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"158":1}}],["开始不了一点",{"0":{"158":1}}],["红石音乐",{"2":{"157":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["作品",{"0":{"157":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"128":1}}],["模組",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"99":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"100":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"48":1}}],["获取直线上的点",{"2":{"47":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"159":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"107":1,"138":1}}],["新的点",{"2":{"105":1,"135":1,"139":1}}],["中实现",{"2":{"107":1}}],["中心点",{"2":{"98":1}}],["已在",{"2":{"107":1}}],["已知一个函数f",{"2":{"36":1}}],["坐标",{"2":{"101":3}}],["笛卡尔坐标系中的点",{"2":{"101":1}}],["长度",{"2":{"98":1}}],["线段的另一个端点",{"2":{"98":1}}],["线段的一个端点",{"2":{"98":1}}],["人话",{"2":{"93":1}}],["法向量",{"2":{"86":1,"87":1}}],["help",{"2":{"159":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"82":1}}],["high",{"2":{"34":2}}],["并代入两平面方程求出合适的点",{"2":{"82":1}}],["并对向量单位化",{"2":{"54":1}}],["依次假设x=0",{"2":{"82":1}}],["寻找直线上的一点",{"2":{"82":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"82":1}}],["求n元函数一阶偏导函数",{"2":{"34":1}}],["为直线的方向向量",{"2":{"80":1}}],["为平面的法向量",{"2":{"80":1}}],["分别为两个平面的法向量",{"2":{"80":1}}],["和",{"2":{"80":1}}],["其中",{"2":{"80":2}}],["θ=arccos⁡",{"2":{"80":2,"122":1}}],["k",{"2":{"79":12}}],["常数项",{"2":{"78":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"87":1,"90":1}}],["平面的法向量",{"2":{"86":1}}],["平面",{"2":{"84":1,"87":1,"88":1,"89":1,"90":1}}],["平面与直线平行或重合",{"2":{"83":1}}],["平面与直线夹角计算公式",{"2":{"80":1}}],["平面平行且无交线",{"2":{"82":1}}],["平面间夹角计算公式",{"2":{"80":1}}],["平面方程",{"2":{"78":1}}],["平行线返回none",{"2":{"56":1}}],["多元函数",{"2":{"75":1}}],["多元数组函数",{"2":{"74":1}}],["多元单变量函数",{"2":{"73":1}}],["二元函数",{"2":{"69":1}}],["二元数组函数",{"2":{"68":1}}],["二元单变量函数",{"2":{"67":1}}],["一元函数",{"2":{"66":1}}],["一元数组函数",{"2":{"65":1}}],["一元单变量函数",{"2":{"64":1}}],["一阶偏导",{"2":{"34":1}}],["变量",{"2":{"63":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"62":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"60":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["類型",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["实数",{"2":{"59":1,"111":1}}],["∧",{"2":{"57":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"93":1}}],["交点",{"2":{"45":1,"83":1}}],["重合线返回自身",{"2":{"56":1}}],["由点和直线构造平面",{"2":{"90":1}}],["由点和法向量构造平面",{"2":{"87":1}}],["由两直线构造平面",{"2":{"89":1}}],["由两点构造直线",{"2":{"55":1}}],["由三点构造平面",{"2":{"88":1}}],["由一个点和一个方向向量确定",{"2":{"41":1}}],["工厂函数",{"2":{"55":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"36":1}}],["化",{"2":{"54":1}}],["按照可行性一次对x",{"2":{"54":1}}],["不返回值",{"2":{"54":1,"126":1}}],["不支持的类型",{"2":{"44":1,"80":1,"81":1,"93":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"54":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"54":1}}],["简化直线方程",{"2":{"54":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"53":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"53":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个点是否相等",{"2":{"106":1}}],["判断两个点是否近似相等",{"2":{"102":1}}],["判断两个平面是否等价",{"2":{"94":1}}],["判断两个平面是否平行",{"2":{"85":1}}],["判断两个平面是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"57":1}}],["判断两条直线是否共面",{"2":{"53":1}}],["判断两条直线是否共线",{"2":{"51":1}}],["判断两条直线是否平行",{"2":{"50":1}}],["判断两条直线是否近似平行",{"2":{"49":1}}],["判断两条直线是否近似相等",{"2":{"42":1}}],["判断点是否在直线上",{"2":{"52":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个点或向量",{"2":{"105":1}}],["另一个点",{"2":{"102":1,"106":1,"107":1,"135":1,"139":1}}],["另一个平面或点",{"2":{"81":1}}],["另一个平面或直线",{"2":{"80":1,"93":1}}],["另一个平面",{"2":{"79":1,"82":1,"85":1,"94":1}}],["另一",{"2":{"50":1,"51":1,"53":1}}],["另一条直线或点",{"2":{"44":1}}],["另一条直线",{"2":{"42":1,"43":1,"45":1,"49":1,"56":1,"57":1}}],["则同一个t对应的点不同",{"2":{"47":1}}],["则其在点",{"2":{"36":1}}],["但起始点和方向向量不同",{"2":{"47":1}}],["同一条直线",{"2":{"47":1}}],["垂线",{"2":{"46":1}}],["指定点",{"2":{"46":1,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"55":1,"83":1,"89":2,"90":1}}],["直线不共面",{"2":{"45":1}}],["直线平行",{"2":{"45":1}}],["直线上的一点",{"2":{"41":1}}],["距离",{"2":{"44":1,"81":1}}],["夹角",{"2":{"43":1,"80":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"106":1,"134":1}}],["是否等价",{"2":{"57":1,"94":1}}],["是否共面",{"2":{"53":1}}],["是否共线",{"2":{"51":1}}],["是否在直线上",{"2":{"52":1}}],["是否平行",{"2":{"50":1,"85":1,"125":1}}],["是否近似平行",{"2":{"49":1,"124":1}}],["是否近似相等",{"2":{"42":1,"79":1,"102":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"102":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"98":1}}],["三元数组函数",{"2":{"71":1}}],["三元单变量函数",{"2":{"70":1}}],["三元函数",{"2":{"36":1,"72":1}}],["三维空间中的线段",{"2":{"98":1}}],["三维空间中的直线",{"2":{"41":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"58":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中点的类",{"2":{"99":1}}],["本模块定义了三维空间中的线段类",{"2":{"96":1}}],["本模块定义了三维空间中的平面类",{"2":{"76":1}}],["本模块定义了三维空间中的直线类",{"2":{"39":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"30":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["6",{"2":{"37":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"37":1}}],["3vf",{"0":{"36":1},"2":{"36":1}}],["breaking",{"2":{"157":1}}],["by",{"2":{"78":1}}],["bound=iterable",{"2":{"62":1}}],["bound=number",{"2":{"61":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"42":1,"49":1,"50":1,"51":1,"52":1,"53":1,"57":1,"79":1,"85":1,"94":1,"102":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"42":2,"49":2,"50":2,"51":2,"52":2,"53":2,"57":2,"79":2,"85":2,"94":2,"102":2,"106":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["範例",{"2":{"37":1}}],["柯里化后的函数",{"2":{"37":1}}],["柯理化",{"2":{"37":1}}],["函数",{"2":{"37":1}}],["对多参数函数进行柯里化",{"2":{"37":1}}],["d=n1×n2",{"2":{"82":1}}],["d",{"0":{"78":1},"2":{"78":5,"79":6,"80":1,"81":1,"82":6,"83":1,"87":2}}],["documentation",{"2":{"159":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"81":1},"2":{"44":1,"81":1}}],["direction",{"0":{"41":1},"2":{"41":4,"42":1,"43":2,"44":8,"45":6,"46":1,"47":1,"48":3,"49":2,"50":2,"51":1,"52":1,"53":2,"54":4,"55":2,"57":3,"80":1,"82":2,"83":4,"89":1,"90":1,"93":1,"98":2}}],["dz",{"2":{"36":2}}],["dy",{"2":{"36":2}}],["dx",{"2":{"36":2}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"34":1},"2":{"34":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"34":2,"37":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"103":1,"104":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"55":1,"88":1}}],["点1",{"2":{"55":1,"88":1}}],["点",{"2":{"36":1,"47":1,"52":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算平行于该平面且过指定点的平面",{"2":{"84":1}}],["计算平面与直线的交点",{"2":{"83":1}}],["计算平面与平面或点之间的距离",{"2":{"81":1}}],["计算平面与平面之间的夹角",{"2":{"80":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"82":1}}],["计算两平面的交线",{"2":{"82":1}}],["计算两条直线点集合的交集",{"2":{"56":1}}],["计算两条直线的交点",{"2":{"45":1}}],["计算直线经过指定点p的垂线",{"2":{"46":1}}],["计算直线和直线或点之间的距离",{"2":{"44":1}}],["计算直线和直线之间的夹角",{"2":{"43":1}}],["计算三元函数在某点的梯度向量",{"2":{"36":1}}],["计算曲线上的点",{"2":{"33":1}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"107":1}}],["vector3",{"0":{"36":1,"41":1,"86":1,"87":1,"103":1,"107":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"36":2,"38":1,"41":2,"86":3,"87":2,"89":1,"103":1,"105":1,"107":5,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"57":1,"88":2,"89":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"57":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"105":1,"107":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":2,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"45":4,"82":2,"83":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["l2",{"0":{"89":1},"2":{"89":4}}],["l1",{"0":{"89":1},"2":{"89":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"45":2,"89":1}}],["line",{"0":{"39":1,"90":2},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"83":1,"90":4}}],["line3",{"0":{"40":1,"42":1,"43":1,"44":1,"45":1,"46":1,"49":1,"50":1,"51":1,"53":1,"55":1,"56":2,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":1},"1":{"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1},"2":{"38":1,"42":2,"43":2,"44":3,"45":2,"46":3,"49":2,"50":2,"51":2,"53":2,"55":2,"56":4,"57":1,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"155":9}}],["length",{"0":{"128":1},"2":{"44":5,"45":1,"80":2,"98":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["抛出",{"2":{"34":1,"44":1,"45":1,"80":1,"81":1,"82":1,"83":1,"93":1}}],["偏导函数",{"2":{"34":1}}],["偏移量",{"2":{"34":1,"36":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可参考函数式编程",{"2":{"37":1}}],["可为整数",{"2":{"34":1}}],["可导入",{"2":{"0":1}}],["因此该函数的稳定性有待提升",{"2":{"34":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"34":1}}],["目标点",{"2":{"33":1}}],["warning",{"2":{"34":1}}],["慎用",{"2":{"34":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"82":9,"127":4,"155":9}}],["n",{"2":{"80":1}}],["n⋅d|n|⋅|d|",{"2":{"80":1}}],["n2",{"2":{"80":1}}],["n1",{"2":{"80":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"80":1}}],["no",{"2":{"82":1}}],["normal",{"0":{"86":1,"87":2},"2":{"80":5,"82":4,"83":1,"84":2,"85":2,"86":1,"87":6,"88":3,"89":1,"90":1,"93":3}}],["normalize",{"0":{"126":1},"2":{"54":1,"126":1}}],["none",{"0":{"56":1,"91":1,"92":1},"2":{"56":3,"91":1,"92":1,"93":3}}],["not",{"2":{"44":1,"45":4,"56":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["参数方程",{"2":{"48":1}}],["参数t",{"2":{"47":1}}],["参数",{"2":{"33":1,"37":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"80":1,"81":1,"91":1,"92":1,"142":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"80":2,"81":2,"91":1,"92":1,"93":3,"105":1,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"89":1,"125":1}}],["z=0",{"2":{"82":1}}],["z系数",{"2":{"78":1}}],["z0",{"2":{"36":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"101":1,"120":1,"150":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":2,"101":5,"102":2,"105":2,"106":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"82":1}}],["y系数",{"2":{"78":1}}],["y0",{"2":{"36":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"101":1,"115":1,"120":1,"149":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":3,"81":1,"82":4,"83":4,"87":2,"98":2,"101":5,"102":2,"105":2,"106":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x3c",{"2":{"102":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x26",{"2":{"93":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"82":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"82":1}}],["x系数",{"2":{"78":1}}],["x0",{"2":{"36":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"101":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"32":4,"33":4,"36":7,"48":2,"54":2,"81":1,"82":4,"83":4,"87":2,"98":2,"101":5,"102":2,"105":2,"106":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"49":1},"2":{"49":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"33":3,"44":2,"53":1,"54":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"81":1}}],["黄金分割比",{"2":{"26":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"83":1,"89":1}}],["gradient",{"0":{"36":1},"2":{"36":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"102":1,"103":1,"104":1,"107":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"105":2,"107":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["默認值",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"147":1,"148":1,"149":1,"150":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"159":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"83":2,"159":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"36":1,"70":1},"2":{"36":2,"72":1}}],["typing",{"0":{"58":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typevar",{"2":{"61":1,"62":1}}],["typealias",{"2":{"59":1,"60":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1}}],["typeerror",{"2":{"44":2,"80":2,"81":2,"93":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"89":1},"2":{"55":1,"89":1}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1}}],["tuple",{"0":{"33":1,"34":1,"48":1},"2":{"33":2,"34":2,"48":2}}],["t",{"0":{"33":1,"47":1},"2":{"33":9,"47":3,"48":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["or",{"2":{"56":1,"83":1}}],["order",{"2":{"34":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"52":1},"2":{"52":1}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"37":1,"66":1},"2":{"32":6,"37":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"102":1,"103":2,"104":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"42":1,"43":1,"44":1,"45":1,"49":1,"50":1,"51":1,"53":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"85":1,"91":1,"92":1,"93":1,"94":1,"95":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"42":4,"43":3,"44":12,"45":8,"49":3,"50":3,"51":4,"53":4,"56":6,"57":4,"79":14,"80":8,"81":8,"82":16,"83":10,"85":3,"91":1,"92":1,"93":9,"94":3,"95":2,"102":5,"103":1,"104":1,"105":5,"106":5,"107":5,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"42":1,"49":1,"102":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"42":4,"49":3,"102":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["exp",{"2":{"25":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"0":{"17":1,"57":1,"94":1,"106":1,"112":1,"134":1},"2":{"17":1,"57":1,"94":1,"106":1,"112":1,"114":1,"134":1}}],["all",{"2":{"102":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"82":6,"127":2,"155":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"155":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"130":1},"2":{"44":1,"81":1,"102":3,"112":1,"115":1,"117":1,"121":3,"130":1}}],["a",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":12,"83":2,"86":1,"87":3}}],["aaa",{"2":{"35":1}}],["approx",{"0":{"29":1,"42":2,"49":1,"79":1,"102":2,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"42":3,"49":2,"79":10,"94":1,"102":1,"106":3,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"37":4,"103":1,"104":1,"105":1,"131":1,"132":1,"133":1}}],["and",{"0":{"87":1,"90":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":1,"79":6,"82":4,"83":1,"84":1,"87":1,"88":1,"89":1,"90":2,"91":1,"92":1,"93":2,"106":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"43":1,"80":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"43":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":1,"80":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"43":2,"80":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"103":1,"104":1,"105":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"36":3,"37":2,"45":1,"47":1,"48":3,"78":3,"81":5,"83":5,"98":3,"105":5,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最佳實踐",{"0":{"156":1},"1":{"157":1}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"82":3}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"54":1},"2":{"54":1}}],["singlevar",{"0":{"61":1},"2":{"61":1,"63":1,"64":2,"67":3,"70":4,"73":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"26":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"107":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"96":1},"1":{"97":1,"98":1}}],["segment3",{"0":{"97":1},"1":{"98":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"32":4,"33":7,"41":3,"42":4,"43":2,"44":13,"45":8,"46":3,"47":3,"48":7,"49":2,"50":2,"51":4,"52":3,"53":3,"54":8,"56":6,"57":4,"78":5,"79":16,"80":4,"81":8,"82":15,"83":9,"84":2,"85":2,"86":4,"91":1,"92":1,"93":5,"94":2,"95":2,"98":15,"101":4,"102":4,"103":1,"104":1,"105":4,"106":4,"107":4,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"98":3,"128":3,"155":2}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"159":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"47":2,"60":1,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"34":4}}],["return",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"22":2,"33":2,"34":4,"36":1,"37":3,"42":1,"43":1,"44":5,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":3,"57":1,"79":4,"80":2,"81":2,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":4,"94":1,"95":1,"102":1,"105":1,"106":1,"107":1,"109":1,"112":2,"114":1,"115":1,"116":3,"117":3,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"130":1,"133":2,"134":1,"135":1,"138":2,"139":1,"142":2,"143":1,"144":1,"145":1,"146":1,"155":1}}],["range",{"2":{"155":2}}],["rand",{"0":{"95":1},"2":{"95":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"80":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["ratio",{"0":{"26":1}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":3,"36":1,"37":3,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"95":1,"102":1,"103":1,"104":1,"107":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["返回",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"33":1,"34":1,"36":1,"37":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"102":1,"105":1,"106":1,"107":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["cal",{"0":{"36":1,"43":1,"44":1,"45":1,"46":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"43":2,"44":1,"45":1,"46":1,"56":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"0":{"33":1},"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"54":1,"55":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"97":1,"100":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"82":1,"88":1,"89":1,"123":1,"124":1,"125":1}}],["c",{"0":{"78":1},"2":{"37":2,"78":4,"79":7,"81":2,"82":6,"83":2,"86":1,"87":3}}],["curried",{"2":{"37":4}}],["currying",{"2":{"37":1}}],["curry",{"0":{"37":1},"2":{"37":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"38":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"83":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"80":1}}],["collinear",{"0":{"51":1},"2":{"51":1,"56":1}}],["coplanar",{"0":{"53":1},"2":{"44":1,"45":2,"53":1,"56":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["於github上查看",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"34":1}}],["或",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["源碼",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["變數説明",{"2":{"4":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"49":1,"50":1,"51":1,"52":1,"53":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"101":1,"102":1,"105":1,"106":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["任意角度",{"2":{"4":1,"38":1}}],["説明",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"33":1,"34":1,"36":1,"37":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"93":1,"94":1,"98":1,"101":1,"102":1,"105":1,"106":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"55":1,"87":1,"88":1,"89":1,"90":1},"2":{"55":1,"84":1,"87":1,"88":2,"89":2,"90":2,"107":1,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["function",{"0":{"35":1},"1":{"36":1,"37":1}}],["func",{"0":{"32":3,"34":3,"36":2,"37":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"36":8,"37":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"79":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"102":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"36":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"36":1,"42":1,"44":1,"49":1,"78":4,"81":1,"101":3,"102":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"42":1,"44":2,"49":1,"59":1,"78":8,"81":2,"101":6,"102":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"33":1,"44":1,"53":1,"54":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"34":1,"36":1,"42":1,"49":1,"56":1,"91":1,"92":1,"102":1,"103":1,"104":1,"107":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"41":2,"54":3,"55":1,"78":5,"79":6,"82":17,"83":2,"87":2,"88":3,"89":3,"98":5,"101":3,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"159":1}}],["import",{"2":{"107":1}}],["i",{"2":{"155":4,"157":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"82":1,"83":1},"2":{"45":1,"56":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"142":1},"2":{"34":3,"37":4,"59":1,"112":2,"142":2,"155":1}}],["in",{"2":{"33":1,"34":1,"155":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"98":1,"101":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"98":1,"101":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"44":2,"45":2,"54":3,"56":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"85":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"42":2,"44":2,"45":2,"49":2,"50":2,"51":3,"52":2,"53":1,"56":3,"57":2,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"55":1,"88":1,"98":1},"2":{"55":3,"57":1,"88":3,"98":8}}],["p1",{"0":{"55":1,"88":1,"98":1},"2":{"55":4,"57":1,"88":5,"98":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"83":1}}],["parallel",{"0":{"49":1,"50":1,"84":1,"85":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"82":1}}],["plane",{"0":{"76":1},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"83":1}}],["plane3",{"0":{"77":1,"79":1,"80":1,"81":1,"82":1,"84":2,"85":1,"87":1,"88":1,"89":1,"90":1,"92":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1},"2":{"38":1,"79":2,"80":3,"81":3,"82":2,"84":4,"85":2,"87":2,"88":1,"89":1,"90":1,"92":1,"93":3,"94":1,"112":1}}],["plus",{"2":{"34":3}}],["p",{"0":{"36":1},"2":{"36":20,"105":5,"107":4,"133":2,"135":2,"138":2,"139":2}}],["points",{"0":{"55":1,"88":1},"2":{"55":1,"88":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":2,"84":1,"87":2,"90":2,"99":1},"1":{"100":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1},"2":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":1,"81":1,"83":2,"84":1,"87":1,"88":3,"90":1,"91":1,"95":1,"98":2,"100":1,"102":1,"103":1,"104":2,"107":1,"132":2,"135":2,"137":2,"139":1},"1":{"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1},"2":{"33":4,"36":2,"38":1,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":2,"81":3,"82":1,"83":4,"84":2,"87":2,"88":6,"90":2,"91":1,"93":2,"95":2,"98":5,"102":2,"103":1,"104":2,"105":3,"106":1,"107":2,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"55":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"103":1,"104":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"36":1,"37":2,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"105":1,"106":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"85":1,"86":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["midpoint",{"2":{"98":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"34":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"74":1},"2":{"75":1}}],["multisinglevarsfunc",{"0":{"73":1},"2":{"75":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"75":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"99":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"100":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"80":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"32":1,"33":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"98":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":2,"76":1,"96":1,"99":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":2,"60":2,"61":2,"62":2,"63":2,"64":2,"65":2,"66":2,"67":2,"68":2,"69":2,"70":2,"71":2,"72":2,"73":2,"74":2,"75":2,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"100":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"58":1,"76":1,"96":1,"99":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"33":1,"34":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"57":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"85":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"97":1,"98":1,"100":1,"101":1,"102":1,"103":1,"104":1,"105":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3}}],["提供了一些工具",{"2":{"0":1}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/@localSearchIndexzht.DIej9wva.js b/assets/chunks/@localSearchIndexzht.DIej9wva.js
deleted file mode 100644
index 2dec3bc..0000000
--- a/assets/chunks/@localSearchIndexzht.DIej9wva.js
+++ /dev/null
@@ -1 +0,0 @@
-const t='{"documentCount":160,"nextId":160,"documentIds":{"0":"/zht/api/#模組-mbcp","1":"/zht/api/mp_math/angle.html#模組-mbcp-mp-math-angle","2":"/zht/api/mp_math/angle.html#class-angle","3":"/zht/api/mp_math/angle.html#class-anyangle-angle","4":"/zht/api/mp_math/angle.html#method-init-self-value-float-is-radian-bool-false","5":"/zht/api/mp_math/angle.html#method-complementary-self-anyangle","6":"/zht/api/mp_math/angle.html#method-supplementary-self-anyangle","7":"/zht/api/mp_math/angle.html#method-degree-self-float","8":"/zht/api/mp_math/angle.html#method-minimum-positive-self-anyangle","9":"/zht/api/mp_math/angle.html#method-maximum-negative-self-anyangle","10":"/zht/api/mp_math/angle.html#method-sin-self-float","11":"/zht/api/mp_math/angle.html#method-cos-self-float","12":"/zht/api/mp_math/angle.html#method-tan-self-float","13":"/zht/api/mp_math/angle.html#method-cot-self-float","14":"/zht/api/mp_math/angle.html#method-sec-self-float","15":"/zht/api/mp_math/angle.html#method-csc-self-float","16":"/zht/api/mp_math/angle.html#method-self-other-anyangle-anyangle","17":"/zht/api/mp_math/angle.html#method-eq-self-other","18":"/zht/api/mp_math/angle.html#method-self-other-anyangle-anyangle-1","19":"/zht/api/mp_math/angle.html#method-self-other-float-anyangle","20":"/zht/api/mp_math/angle.html#method-self-other-float-anyangle-1","21":"/zht/api/mp_math/angle.html#method-self-other-anyangle-float","22":"/zht/api/mp_math/angle.html#method-self-other","23":"/zht/api/mp_math/const.html#模組-mbcp-mp-math-const","24":"/zht/api/mp_math/const.html#var-pi","25":"/zht/api/mp_math/const.html#var-e","26":"/zht/api/mp_math/const.html#var-golden-ratio","27":"/zht/api/mp_math/const.html#var-gamma","28":"/zht/api/mp_math/const.html#var-epsilon","29":"/zht/api/mp_math/const.html#var-approx","30":"/zht/api/mp_math/function.html#模組-mbcp-mp-math-function","31":"/zht/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","32":"/zht/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","33":"/zht/api/mp_math/equation.html#模組-mbcp-mp-math-equation","34":"/zht/api/mp_math/equation.html#class-curveequation","35":"/zht/api/mp_math/equation.html#method-init-self-x-func-onevarfunc-y-func-onevarfunc-z-func-onevarfunc","36":"/zht/api/mp_math/equation.html#method-call-self-t-var-point3-tuple-point3","37":"/zht/api/mp_math/equation.html#func-get-partial-derivative-func-func-multivarsfunc-var-int-tuple-int-epsilon-number-epsilon-multivarsfunc","38":"/zht/api/mp_math/#模組-mbcp-mp-math","39":"/zht/api/mp_math/mp_math_typing.html#模組-mbcp-mp-math-mp-math-typing","40":"/zht/api/mp_math/mp_math_typing.html#var-realnumber","41":"/zht/api/mp_math/mp_math_typing.html#var-number","42":"/zht/api/mp_math/mp_math_typing.html#var-singlevar","43":"/zht/api/mp_math/mp_math_typing.html#var-arrayvar","44":"/zht/api/mp_math/mp_math_typing.html#var-var","45":"/zht/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","46":"/zht/api/mp_math/mp_math_typing.html#var-onearrayfunc","47":"/zht/api/mp_math/mp_math_typing.html#var-onevarfunc","48":"/zht/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","49":"/zht/api/mp_math/mp_math_typing.html#var-twoarraysfunc","50":"/zht/api/mp_math/mp_math_typing.html#var-twovarsfunc","51":"/zht/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","52":"/zht/api/mp_math/mp_math_typing.html#var-threearraysfunc","53":"/zht/api/mp_math/mp_math_typing.html#var-threevarsfunc","54":"/zht/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","55":"/zht/api/mp_math/mp_math_typing.html#var-multiarraysfunc","56":"/zht/api/mp_math/mp_math_typing.html#var-multivarsfunc","57":"/zht/api/mp_math/line.html#模組-mbcp-mp-math-line","58":"/zht/api/mp_math/line.html#class-line3","59":"/zht/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","60":"/zht/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","61":"/zht/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","62":"/zht/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","63":"/zht/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","64":"/zht/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","65":"/zht/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","66":"/zht/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","67":"/zht/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","68":"/zht/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","69":"/zht/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","70":"/zht/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","71":"/zht/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","72":"/zht/api/mp_math/line.html#method-simplify-self","73":"/zht/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","74":"/zht/api/mp_math/line.html#method-and-self-other-line3-line3-point3-none","75":"/zht/api/mp_math/line.html#method-eq-self-other-bool","76":"/zht/api/mp_math/point.html#模組-mbcp-mp-math-point","77":"/zht/api/mp_math/point.html#class-point3","78":"/zht/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","79":"/zht/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","80":"/zht/api/mp_math/point.html#method-self-other-vector3-point3","81":"/zht/api/mp_math/point.html#method-self-other-point3-point3","82":"/zht/api/mp_math/point.html#method-self-other","83":"/zht/api/mp_math/point.html#method-eq-self-other","84":"/zht/api/mp_math/point.html#method-self-other-point3-vector3","85":"/zht/api/mp_math/plane.html#模組-mbcp-mp-math-plane","86":"/zht/api/mp_math/plane.html#class-plane3","87":"/zht/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","88":"/zht/api/mp_math/plane.html#method-approx-self-other-plane3-bool","89":"/zht/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","90":"/zht/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","91":"/zht/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","92":"/zht/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","93":"/zht/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","94":"/zht/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","95":"/zht/api/mp_math/plane.html#method-normal-self-vector3","96":"/zht/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","97":"/zht/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","98":"/zht/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","99":"/zht/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","100":"/zht/api/mp_math/plane.html#method-and-self-other-line3-point3-none","101":"/zht/api/mp_math/plane.html#method-and-self-other-plane3-line3-none","102":"/zht/api/mp_math/plane.html#method-and-self-other","103":"/zht/api/mp_math/plane.html#method-eq-self-other-bool","104":"/zht/api/mp_math/plane.html#method-rand-self-other-line3-point3","105":"/zht/api/mp_math/segment.html#模組-mbcp-mp-math-segment","106":"/zht/api/mp_math/segment.html#class-segment3","107":"/zht/api/mp_math/segment.html#method-init-self-p1-point3-p2-point3","108":"/zht/api/mp_math/utils.html#模組-mbcp-mp-math-utils","109":"/zht/api/mp_math/utils.html#func-clamp-x-float-min-float-max-float-float","110":"/zht/api/mp_math/utils.html#class-approx","111":"/zht/api/mp_math/utils.html#method-init-self-value-realnumber","112":"/zht/api/mp_math/utils.html#method-eq-self-other","113":"/zht/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/zht/api/mp_math/utils.html#method-ne-self-other","115":"/zht/api/mp_math/utils.html#func-approx-x-float-y-float-0-0-epsilon-float-approx-bool","116":"/zht/api/mp_math/utils.html#func-sign-x-float-only-neg-bool-false-str","117":"/zht/api/mp_math/utils.html#func-sign-format-x-float-only-neg-bool-false-str","118":"/zht/api/mp_math/vector.html#模組-mbcp-mp-math-vector","119":"/zht/api/mp_math/vector.html#class-vector3","120":"/zht/api/mp_math/vector.html#method-init-self-x-float-y-float-z-float","121":"/zht/api/mp_math/vector.html#method-approx-self-other-vector3-epsilon-float-approx-bool","122":"/zht/api/mp_math/vector.html#method-cal-angle-self-other-vector3-anyangle","123":"/zht/api/mp_math/vector.html#method-cross-self-other-vector3-vector3","124":"/zht/api/mp_math/vector.html#method-is-approx-parallel-self-other-vector3-epsilon-float-approx-bool","125":"/zht/api/mp_math/vector.html#method-is-parallel-self-other-vector3-bool","126":"/zht/api/mp_math/vector.html#method-normalize-self","127":"/zht/api/mp_math/vector.html#method-np-array-self-np-ndarray","128":"/zht/api/mp_math/vector.html#method-length-self-float","129":"/zht/api/mp_math/vector.html#method-unit-self-vector3","130":"/zht/api/mp_math/vector.html#method-abs-self","131":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3","132":"/zht/api/mp_math/vector.html#method-self-other-point3-point3","133":"/zht/api/mp_math/vector.html#method-self-other","134":"/zht/api/mp_math/vector.html#method-eq-self-other","135":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-1","136":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-1","137":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-2","138":"/zht/api/mp_math/vector.html#method-self-other-1","139":"/zht/api/mp_math/vector.html#method-self-other-point3","140":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-2","141":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3","142":"/zht/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","143":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","144":"/zht/api/mp_math/vector.html#method-self-other-vector3-realnumber","145":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","146":"/zht/api/mp_math/vector.html#method-self-vector3","147":"/zht/api/mp_math/vector.html#var-zero-vector3","148":"/zht/api/mp_math/vector.html#var-x-axis","149":"/zht/api/mp_math/vector.html#var-y-axis","150":"/zht/api/mp_math/vector.html#var-z-axis","151":"/zht/api/particle/#模組-mbcp-particle","152":"/zht/api/presets/#模組-mbcp-presets","153":"/zht/api/presets/model/#模組-mbcp-presets-model","154":"/zht/api/presets/model/#class-geometricmodels","155":"/zht/api/presets/model/#method-sphere-radius-float-density-float","156":"/zht/demo/best-practice.html#最佳實踐","157":"/zht/demo/best-practice.html#作品","158":"/zht/guide/#开始不了一点","159":"/zht/refer/#reference"},"fieldIds":{"title":0,"titles":1,"text":2},"fieldLength":{"0":[2,1,12],"1":[5,1,2],"2":[2,5,1],"3":[4,5,1],"4":[11,9,24],"5":[5,9,23],"6":[5,9,22],"7":[5,9,19],"8":[6,9,20],"9":[6,9,22],"10":[5,9,17],"11":[5,9,17],"12":[5,9,17],"13":[5,9,19],"14":[5,9,19],"15":[5,9,19],"16":[7,9,15],"17":[5,9,11],"18":[6,9,14],"19":[7,9,16],"20":[7,9,13],"21":[7,9,13],"22":[3,9,15],"23":[5,1,2],"24":[2,5,7],"25":[2,5,8],"26":[3,5,10],"27":[2,5,6],"28":[2,5,6],"29":[2,5,6],"30":[5,1,2],"31":[13,5,45],"32":[7,5,40],"33":[5,1,2],"34":[2,5,1],"35":[9,7,19],"36":[10,7,33],"37":[14,5,60],"38":[4,1,20],"39":[5,1,2],"40":[2,5,9],"41":[2,5,9],"42":[2,5,7],"43":[2,5,8],"44":[2,5,9],"45":[2,5,8],"46":[2,5,8],"47":[2,5,9],"48":[2,5,8],"49":[2,5,8],"50":[2,5,9],"51":[2,5,8],"52":[2,5,8],"53":[2,5,9],"54":[2,5,8],"55":[2,5,8],"56":[2,5,9],"57":[5,1,2],"58":[2,5,1],"59":[8,7,18],"60":[11,7,27],"61":[8,7,20],"62":[10,7,42],"63":[8,7,40],"64":[8,7,21],"65":[8,7,24],"66":[9,7,25],"67":[14,7,26],"68":[8,7,20],"69":[8,7,23],"70":[8,7,21],"71":[8,7,26],"72":[4,7,27],"73":[10,7,27],"74":[9,7,34],"75":[6,7,28],"76":[5,1,2],"77":[2,5,1],"78":[8,7,16],"79":[11,7,29],"80":[8,7,13],"81":[7,7,12],"82":[4,7,24],"83":[5,7,22],"84":[7,7,28],"85":[5,1,2],"86":[2,5,1],"87":[9,7,25],"88":[7,7,30],"89":[10,7,55],"90":[10,7,44],"91":[9,7,64],"92":[9,7,52],"93":[9,7,23],"94":[8,7,21],"95":[5,7,20],"96":[10,7,34],"97":[11,7,34],"98":[10,7,38],"99":[10,7,28],"100":[9,7,15],"101":[9,7,15],"102":[5,7,47],"103":[6,7,19],"104":[7,7,15],"105":[5,1,2],"106":[2,5,1],"107":[7,7,27],"108":[5,1,2],"109":[7,5,20],"110":[2,5,1],"111":[6,7,14],"112":[5,7,31],"113":[7,7,15],"114":[5,7,11],"115":[11,5,28],"116":[11,5,30],"117":[12,5,36],"118":[5,1,3],"119":[2,5,1],"120":[8,7,18],"121":[11,7,28],"122":[8,7,28],"123":[6,7,33],"124":[13,7,27],"125":[8,7,23],"126":[4,7,17],"127":[6,7,18],"128":[5,7,23],"129":[5,7,17],"130":[4,7,10],"131":[7,7,12],"132":[7,7,12],"133":[4,7,37],"134":[5,7,22],"135":[7,7,25],"136":[6,7,12],"137":[6,7,12],"138":[3,7,36],"139":[4,7,35],"140":[6,7,12],"141":[7,7,13],"142":[9,7,39],"143":[7,7,13],"144":[7,7,23],"145":[7,7,15],"146":[5,7,17],"147":[3,5,7],"148":[3,5,8],"149":[3,5,8],"150":[3,5,8],"151":[3,1,2],"152":[3,1,2],"153":[4,1,2],"154":[2,4,2],"155":[6,6,46],"156":[1,1,1],"157":[1,1,25],"158":[1,1,2],"159":[1,1,7]},"averageFieldLength":[5.743749999999997,5.924999999999998,17.887500000000003],"storedFields":{"0":{"title":"模組 mbcp","titles":[]},"1":{"title":"模組 mbcp.mp_math.angle","titles":[]},"2":{"title":"class Angle","titles":["模組 mbcp.mp_math.angle"]},"3":{"title":"class AnyAngle(Angle)","titles":["模組 mbcp.mp_math.angle"]},"4":{"title":"method __init__(self, value: float, is_radian: bool = False)","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"5":{"title":"method complementary(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"6":{"title":"method supplementary(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"7":{"title":"method degree(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"8":{"title":"method minimum_positive(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"9":{"title":"method maximum_negative(self) -> AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"10":{"title":"method sin(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"11":{"title":"method cos(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"12":{"title":"method tan(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"13":{"title":"method cot(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"14":{"title":"method sec(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"15":{"title":"method csc(self) -> float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"16":{"title":"method self + other: AnyAngle => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"17":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"18":{"title":"method self - other: AnyAngle => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"19":{"title":"method self * other: float => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["模組 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"模組 mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["模組 mbcp.mp_math.const"]},"25":{"title":"var E","titles":["模組 mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["模組 mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["模組 mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["模組 mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["模組 mbcp.mp_math.const"]},"30":{"title":"模組 mbcp.mp_math.function","titles":[]},"31":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模組 mbcp.mp_math.function"]},"32":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模組 mbcp.mp_math.function"]},"33":{"title":"模組 mbcp.mp_math.equation","titles":[]},"34":{"title":"class CurveEquation","titles":["模組 mbcp.mp_math.equation"]},"35":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"36":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"37":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模組 mbcp.mp_math.equation"]},"38":{"title":"模組 mbcp.mp_math","titles":[]},"39":{"title":"模組 mbcp.mp_math.mp_math_typing","titles":[]},"40":{"title":"var RealNumber","titles":["模組 mbcp.mp_math.mp_math_typing"]},"41":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"42":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"43":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"44":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"45":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"46":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"47":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"48":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"49":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"50":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"51":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"52":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"53":{"title":"var ThreeVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"54":{"title":"var MultiSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"55":{"title":"var MultiArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"56":{"title":"var MultiVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"57":{"title":"模組 mbcp.mp_math.line","titles":[]},"58":{"title":"class Line3","titles":["模組 mbcp.mp_math.line"]},"59":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模組 mbcp.mp_math.line","class Line3"]},"60":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"61":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模組 mbcp.mp_math.line","class Line3"]},"62":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模組 mbcp.mp_math.line","class Line3"]},"63":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"64":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"65":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"66":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模組 mbcp.mp_math.line","class Line3"]},"67":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"68":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"69":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"70":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"71":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"72":{"title":"method simplify(self)","titles":["模組 mbcp.mp_math.line","class Line3"]},"73":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"74":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["模組 mbcp.mp_math.line","class Line3"]},"75":{"title":"method __eq__(self, other) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"76":{"title":"模組 mbcp.mp_math.point","titles":[]},"77":{"title":"class Point3","titles":["模組 mbcp.mp_math.point"]},"78":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.point","class Point3"]},"79":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.point","class Point3"]},"80":{"title":"method self + other: Vector3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"81":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"82":{"title":"method self + other","titles":["模組 mbcp.mp_math.point","class Point3"]},"83":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.point","class Point3"]},"84":{"title":"method self - other: Point3 => Vector3","titles":["模組 mbcp.mp_math.point","class Point3"]},"85":{"title":"模組 mbcp.mp_math.plane","titles":[]},"86":{"title":"class Plane3","titles":["模組 mbcp.mp_math.plane"]},"87":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method approx(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method normal(self) -> Vector3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"97":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"98":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"99":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"100":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"101":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"102":{"title":"method __and__(self, other)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"103":{"title":"method __eq__(self, other) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"104":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"105":{"title":"模組 mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["模組 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模組 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模組 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模組 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模組 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"118":{"title":"模組 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模組 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other: Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self * other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self @ other: Vector3 => RealNumber","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self / other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method - self => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"var zero_vector3","titles":["模組 mbcp.mp_math.vector"]},"148":{"title":"var x_axis","titles":["模組 mbcp.mp_math.vector"]},"149":{"title":"var y_axis","titles":["模組 mbcp.mp_math.vector"]},"150":{"title":"var z_axis","titles":["模組 mbcp.mp_math.vector"]},"151":{"title":"模組 mbcp.particle","titles":[]},"152":{"title":"模組 mbcp.presets","titles":[]},"153":{"title":"模組 mbcp.presets.model","titles":[]},"154":{"title":"class GeometricModels","titles":["模組 mbcp.presets.model"]},"155":{"title":"method sphere(radius: float, density: float)","titles":["模組 mbcp.presets.model","class GeometricModels"]},"156":{"title":"最佳實踐","titles":[]},"157":{"title":"作品","titles":["最佳實踐"]},"158":{"title":"开始不了一点","titles":[]},"159":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"158":1}}],["开始不了一点",{"0":{"158":1}}],["红石音乐",{"2":{"157":1}}],["这么可爱真是抱歉",{"2":{"157":1}}],["这玩意不太稳定",{"2":{"37":1}}],["轻涟",{"2":{"157":1}}],["芙宁娜pv曲",{"2":{"157":1}}],["有点甜~",{"2":{"157":1}}],["有关函数柯里化",{"2":{"32":1}}],["星穹铁道",{"2":{"157":1}}],["崩坏",{"2":{"157":1}}],["使一颗心免于哀伤",{"2":{"157":1}}],["总有一条蜿蜒在童话镇里",{"2":{"157":1}}],["童话镇~",{"2":{"157":1}}],["特效红石音乐",{"2":{"157":2}}],["作品",{"0":{"157":1}}],["4",{"2":{"155":1}}],["球体上的点集",{"2":{"155":1}}],["生成球体上的点集",{"2":{"155":1}}],["几何模型点集",{"2":{"153":1}}],["零向量",{"2":{"147":1}}],["负向量",{"2":{"146":1}}],["取负",{"2":{"146":1}}],["取两平面的交集",{"2":{"102":1}}],["非点乘",{"2":{"142":1}}],["别去点那边实现了",{"2":{"135":1}}],["单位向量",{"2":{"129":1}}],["单变量",{"2":{"42":1}}],["模",{"2":{"128":1}}],["模組",{"0":{"0":1,"1":1,"23":1,"30":1,"33":1,"38":1,"39":1,"57":1,"76":1,"85":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"34":1,"35":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"58":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1}}],["将向量归一化",{"2":{"126":1}}],["转换为行列式形式",{"2":{"123":1}}],["叉乘使用cross",{"2":{"142":1}}],["叉乘结果",{"2":{"123":1}}],["叉乘运算法则为",{"2":{"123":1}}],["叉乘",{"2":{"123":1}}],["向量的模",{"2":{"128":1}}],["向量积",{"2":{"123":1}}],["向量夹角计算公式",{"2":{"122":1}}],["以及一些常用的向量",{"2":{"118":1}}],["格式化符号数",{"2":{"117":1}}],["quot",{"2":{"116":2,"117":4}}],["符号",{"2":{"116":1,"117":1}}],["获取该向量的单位向量",{"2":{"129":1}}],["获取数的符号",{"2":{"116":1}}],["获取直线的参数方程",{"2":{"66":1}}],["获取直线上的点",{"2":{"65":1}}],["用于判断是否近似于0",{"2":{"115":1}}],["用于近似比较对象",{"2":{"111":1}}],["限定在区间内的值",{"2":{"109":1}}],["值",{"2":{"109":1}}],["区间限定函数",{"2":{"109":1}}],["us",{"2":{"159":1}}],["unit",{"0":{"129":1},"2":{"129":1}}],["unsupported",{"2":{"62":1,"89":1,"90":1,"102":1,"113":1,"133":1,"138":1,"139":1,"142":1}}],["utils",{"0":{"108":1},"1":{"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1}}],["中心点",{"2":{"107":1}}],["中实现",{"2":{"84":1}}],["长度",{"2":{"107":1}}],["线段的另一个端点",{"2":{"107":1}}],["线段的一个端点",{"2":{"107":1}}],["人话",{"2":{"102":1}}],["法向量",{"2":{"95":1,"96":1}}],["help",{"2":{"159":1}}],["heart",{"2":{"157":1}}],["have",{"2":{"91":1}}],["high",{"2":{"37":2}}],["并代入两平面方程求出合适的点",{"2":{"91":1}}],["并对向量单位化",{"2":{"72":1}}],["依次假设x=0",{"2":{"91":1}}],["寻找直线上的一点",{"2":{"91":1}}],["求两平面的法向量的叉乘得到方向向量",{"2":{"91":1}}],["求n元函数一阶偏导函数",{"2":{"37":1}}],["为直线的方向向量",{"2":{"89":1}}],["为平面的法向量",{"2":{"89":1}}],["分别为两个平面的法向量",{"2":{"89":1}}],["和",{"2":{"89":1}}],["其中",{"2":{"89":2}}],["θ=arccos⁡",{"2":{"89":2,"122":1}}],["k",{"2":{"88":12}}],["常数项",{"2":{"87":1}}],["常量",{"2":{"24":1}}],["平面上一点",{"2":{"96":1,"99":1}}],["平面的法向量",{"2":{"95":1}}],["平面",{"2":{"93":1,"96":1,"97":1,"98":1,"99":1}}],["平面与直线平行或重合",{"2":{"92":1}}],["平面与直线夹角计算公式",{"2":{"89":1}}],["平面平行且无交线",{"2":{"91":1}}],["平面间夹角计算公式",{"2":{"89":1}}],["平面方程",{"2":{"87":1}}],["平行线返回none",{"2":{"74":1}}],["新的向量或点",{"2":{"133":1}}],["新的向量",{"2":{"84":1,"138":1}}],["新的点",{"2":{"82":1,"135":1,"139":1}}],["已在",{"2":{"84":1}}],["已知一个函数f",{"2":{"31":1}}],["坐标",{"2":{"78":3}}],["笛卡尔坐标系中的点",{"2":{"78":1}}],["∧",{"2":{"75":1}}],["交线",{"2":{"91":1,"102":1}}],["交线返回交点",{"2":{"74":1}}],["交集",{"2":{"74":1,"102":1}}],["交点",{"2":{"63":1,"92":1}}],["重合线返回自身",{"2":{"74":1}}],["由点和直线构造平面",{"2":{"99":1}}],["由点和法向量构造平面",{"2":{"96":1}}],["由两直线构造平面",{"2":{"98":1}}],["由两点构造直线",{"2":{"73":1}}],["由三点构造平面",{"2":{"97":1}}],["由一个点和一个方向向量确定",{"2":{"59":1}}],["工厂函数",{"2":{"73":1,"96":1,"97":1,"98":1,"99":1}}],["处理",{"2":{"72":1}}],["处的梯度向量为",{"2":{"31":1}}],["化",{"2":{"72":1}}],["按照可行性一次对x",{"2":{"72":1}}],["不返回值",{"2":{"72":1,"126":1}}],["不支持的类型",{"2":{"62":1,"89":1,"90":1,"102":1}}],["自体归一化",{"2":{"126":1}}],["自体简化",{"2":{"72":1}}],["自然对数的底",{"2":{"25":1}}],["等价相等",{"2":{"72":1}}],["简化直线方程",{"2":{"72":1}}],["两直线方向向量的叉乘与两直线上任意一点的向量的点积为0",{"2":{"71":1}}],["两角的和为180°",{"2":{"6":1}}],["两角的和为90°",{"2":{"5":1}}],["充要条件",{"2":{"71":1}}],["判断两个向量是否相等",{"2":{"134":1}}],["判断两个向量是否平行",{"2":{"125":1}}],["判断两个向量是否近似平行",{"2":{"124":1}}],["判断两个向量是否近似相等",{"2":{"121":1}}],["判断两个数是否近似相等",{"2":{"115":1}}],["判断两个平面是否等价",{"2":{"103":1}}],["判断两个平面是否平行",{"2":{"94":1}}],["判断两个平面是否近似相等",{"2":{"88":1}}],["判断两个点是否相等",{"2":{"83":1}}],["判断两个点是否近似相等",{"2":{"79":1}}],["判断两条直线是否等价",{"2":{"75":1}}],["判断两条直线是否共面",{"2":{"71":1}}],["判断两条直线是否共线",{"2":{"69":1}}],["判断两条直线是否平行",{"2":{"68":1}}],["判断两条直线是否近似平行",{"2":{"67":1}}],["判断两条直线是否近似相等",{"2":{"60":1}}],["判断点是否在直线上",{"2":{"70":1}}],["另一个向量或数",{"2":{"142":1}}],["另一个向量或点",{"2":{"133":1,"138":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"134":1,"144":1}}],["另一个平面或点",{"2":{"90":1}}],["另一个平面或直线",{"2":{"89":1,"102":1}}],["另一个平面",{"2":{"88":1,"91":1,"94":1,"103":1}}],["另一个点或向量",{"2":{"82":1}}],["另一个点",{"2":{"79":1,"83":1,"84":1,"135":1,"139":1}}],["另一",{"2":{"68":1,"69":1,"71":1}}],["另一条直线或点",{"2":{"62":1}}],["另一条直线",{"2":{"60":1,"61":1,"63":1,"67":1,"74":1,"75":1}}],["则同一个t对应的点不同",{"2":{"65":1}}],["则其在点",{"2":{"31":1}}],["但起始点和方向向量不同",{"2":{"65":1}}],["同一条直线",{"2":{"65":1}}],["垂线",{"2":{"64":1}}],["指定点",{"2":{"64":1,"93":1}}],["直线最终可用参数方程或点向式表示",{"2":{"91":1}}],["直线",{"2":{"73":1,"92":1,"98":2,"99":1}}],["直线不共面",{"2":{"63":1}}],["直线平行",{"2":{"63":1}}],["直线上的一点",{"2":{"59":1}}],["距离",{"2":{"62":1,"90":1}}],["夹角",{"2":{"61":1,"89":1,"122":1}}],["是否只返回负数的符号",{"2":{"116":1,"117":1}}],["是否相等",{"2":{"83":1,"134":1}}],["是否等价",{"2":{"75":1,"103":1}}],["是否共面",{"2":{"71":1}}],["是否共线",{"2":{"69":1}}],["是否在直线上",{"2":{"70":1}}],["是否平行",{"2":{"68":1,"94":1,"125":1}}],["是否近似平行",{"2":{"67":1,"124":1}}],["是否近似相等",{"2":{"60":1,"79":1,"88":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"60":1,"67":1,"79":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"59":1,"107":1}}],["多元函数",{"2":{"56":1}}],["多元数组函数",{"2":{"55":1}}],["多元单变量函数",{"2":{"54":1}}],["二元函数",{"2":{"50":1}}],["二元数组函数",{"2":{"49":1}}],["二元单变量函数",{"2":{"48":1}}],["一元函数",{"2":{"47":1}}],["一元数组函数",{"2":{"46":1}}],["一元单变量函数",{"2":{"45":1}}],["一阶偏导",{"2":{"37":1}}],["变量",{"2":{"44":1}}],["变量位置",{"2":{"37":1}}],["数组运算结果",{"2":{"142":1}}],["数组运算",{"2":{"142":1}}],["数组变量",{"2":{"43":1}}],["数2",{"2":{"115":1}}],["数1",{"2":{"115":1}}],["数",{"2":{"41":1,"116":1,"117":1}}],["数学工具",{"2":{"0":1}}],["類型",{"2":{"40":1,"41":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"147":1,"148":1,"149":1,"150":1}}],["实数",{"2":{"40":1,"111":1}}],["三元数组函数",{"2":{"52":1}}],["三元单变量函数",{"2":{"51":1}}],["三元函数",{"2":{"31":1,"53":1}}],["三维空间中的线段",{"2":{"107":1}}],["三维空间中的直线",{"2":{"59":1}}],["三维向量",{"2":{"38":1}}],["三维线段",{"2":{"38":1}}],["三维点",{"2":{"38":1}}],["三维平面",{"2":{"38":1}}],["三维直线",{"2":{"38":1}}],["导入的类有",{"2":{"38":1}}],["本包定义了一些常用的导入",{"2":{"38":1}}],["本模块塞了一些预设",{"2":{"152":1}}],["本模块用于内部类型提示",{"2":{"39":1}}],["本模块定义了粒子生成相关的工具",{"2":{"151":1}}],["本模块定义了3维向量的类vector3",{"2":{"118":1}}],["本模块定义了一些常用的工具函数",{"2":{"108":1}}],["本模块定义了一些常用的常量",{"2":{"23":1}}],["本模块定义了三维空间中的线段类",{"2":{"105":1}}],["本模块定义了三维空间中的平面类",{"2":{"85":1}}],["本模块定义了三维空间中的直线类",{"2":{"57":1}}],["本模块定义了三维空间中点的类",{"2":{"76":1}}],["本模块定义了方程相关的类和函数以及一些常用的数学函数",{"2":{"33":1}}],["本模块定义了角度相关的类",{"2":{"1":1}}],["本模块是主模块",{"2":{"0":1}}],["l2",{"0":{"98":1},"2":{"98":4}}],["l1",{"0":{"98":1},"2":{"98":6}}],["lambda",{"2":{"66":3}}],["linalg",{"2":{"91":3}}],["lines",{"0":{"98":1},"2":{"63":2,"98":1}}],["line",{"0":{"57":1,"99":2},"1":{"58":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1},"2":{"92":1,"99":4}}],["line3",{"0":{"58":1,"60":1,"61":1,"62":1,"63":1,"64":1,"67":1,"68":1,"69":1,"71":1,"73":1,"74":2,"89":1,"91":2,"92":1,"98":2,"99":1,"100":1,"101":1,"104":1},"1":{"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1},"2":{"38":1,"60":2,"61":2,"62":3,"63":2,"64":3,"67":2,"68":2,"69":2,"71":2,"73":2,"74":4,"75":1,"89":3,"91":4,"92":2,"98":4,"99":2,"100":1,"101":1,"102":4,"104":1,"112":1}}],["list",{"2":{"37":8,"155":9}}],["length",{"0":{"128":1},"2":{"62":5,"63":1,"89":2,"107":2,"122":2,"124":1,"126":5,"128":1,"129":1,"130":1}}],["len",{"2":{"36":1}}],["无效变量类型",{"2":{"37":1}}],["抛出",{"2":{"37":1,"62":1,"63":1,"89":1,"90":1,"91":1,"92":1,"102":1}}],["偏导函数",{"2":{"37":1}}],["偏移量",{"2":{"31":1,"37":1}}],["高阶偏导",{"2":{"37":1}}],["因此该函数的稳定性有待提升",{"2":{"37":1}}],["目前数学界对于一个函数的导函数并没有通解的说法",{"2":{"37":1}}],["目标点",{"2":{"36":1}}],["warning",{"2":{"37":1}}],["慎用",{"2":{"37":1}}],["num",{"2":{"155":5}}],["numpy数组",{"2":{"127":1}}],["number=epsilon",{"2":{"37":1}}],["number",{"0":{"37":1,"41":1},"2":{"43":1}}],["ndarray",{"0":{"127":1},"2":{"127":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"146":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"0":{"114":1},"2":{"114":1}}],["np",{"0":{"127":2},"2":{"91":9,"127":4,"155":9}}],["n",{"2":{"89":1}}],["n⋅d|n|⋅|d|",{"2":{"89":1}}],["n2",{"2":{"89":1}}],["n1",{"2":{"89":1}}],["n1⋅n2|n1|⋅|n2|",{"2":{"89":1}}],["no",{"2":{"91":1}}],["normal",{"0":{"95":1,"96":2},"2":{"89":5,"91":4,"92":1,"93":2,"94":2,"95":1,"96":6,"97":3,"98":1,"99":1,"102":3}}],["normalize",{"0":{"126":1},"2":{"72":1,"126":1}}],["none",{"0":{"74":1,"100":1,"101":1},"2":{"74":3,"100":1,"101":1,"102":3}}],["not",{"2":{"62":1,"63":4,"74":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"37":1}}],["计算平行于该平面且过指定点的平面",{"2":{"93":1}}],["计算平面与直线的交点",{"2":{"92":1}}],["计算平面与平面或点之间的距离",{"2":{"90":1}}],["计算平面与平面之间的夹角",{"2":{"89":1}}],["计算两个向量之间的夹角",{"2":{"122":1}}],["计算两平面交线的一般步骤",{"2":{"91":1}}],["计算两平面的交线",{"2":{"91":1}}],["计算两条直线点集合的交集",{"2":{"74":1}}],["计算两条直线的交点",{"2":{"63":1}}],["计算直线经过指定点p的垂线",{"2":{"64":1}}],["计算直线和直线或点之间的距离",{"2":{"62":1}}],["计算直线和直线之间的夹角",{"2":{"61":1}}],["计算曲线上的点",{"2":{"36":1}}],["计算三元函数在某点的梯度向量",{"2":{"31":1}}],["|",{"0":{"36":1,"37":1,"62":1,"74":2,"89":1,"90":1,"100":1,"101":1,"142":2},"2":{"36":1,"37":1,"40":1,"41":1,"44":1,"47":1,"50":1,"53":1,"56":1,"62":2,"74":4,"82":1,"89":2,"90":2,"100":1,"101":1,"102":3,"133":2,"138":2,"142":3}}],["曲线方程",{"2":{"35":1,"38":1}}],["6",{"2":{"32":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"32":1}}],["3vf",{"0":{"31":1},"2":{"31":1}}],["breaking",{"2":{"157":1}}],["by",{"2":{"87":1}}],["bound=iterable",{"2":{"43":1}}],["bound=number",{"2":{"42":1}}],["bool=false",{"2":{"4":1,"116":1,"117":1}}],["bool",{"0":{"4":1,"60":1,"67":1,"68":1,"69":1,"70":1,"71":1,"75":1,"79":1,"88":1,"94":1,"103":1,"115":1,"116":1,"117":1,"121":1,"124":1,"125":1},"2":{"60":2,"67":2,"68":2,"69":2,"70":2,"71":2,"75":2,"79":2,"83":1,"88":2,"94":2,"103":2,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"134":1}}],["b",{"0":{"87":1},"2":{"32":2,"87":4,"88":7,"90":2,"91":12,"92":2,"95":1,"96":3}}],["範例",{"2":{"32":1}}],["柯里化后的函数",{"2":{"32":1}}],["柯理化",{"2":{"32":1}}],["参数方程",{"2":{"66":1}}],["参数t",{"2":{"65":1}}],["参数",{"2":{"32":1,"36":1}}],["函数",{"2":{"32":1}}],["可愛くてごめん",{"2":{"157":1}}],["可直接从mbcp",{"2":{"38":1}}],["可为整数",{"2":{"37":1}}],["可参考函数式编程",{"2":{"32":1}}],["可导入",{"2":{"0":1}}],["对多参数函数进行柯里化",{"2":{"32":1}}],["d=n1×n2",{"2":{"91":1}}],["d",{"0":{"87":1},"2":{"87":5,"88":6,"89":1,"90":1,"91":6,"92":1,"96":2}}],["documentation",{"2":{"159":1}}],["do",{"2":{"63":2}}],["distance",{"0":{"62":1,"90":1},"2":{"62":1,"90":1}}],["direction",{"0":{"59":1},"2":{"59":4,"60":1,"61":2,"62":8,"63":6,"64":1,"65":1,"66":3,"67":2,"68":2,"69":1,"70":1,"71":2,"72":4,"73":2,"75":3,"89":1,"91":2,"92":4,"98":1,"99":1,"102":1,"107":2}}],["dz",{"2":{"31":2}}],["dy",{"2":{"31":2}}],["dx",{"2":{"31":2}}],["density",{"0":{"155":1},"2":{"155":3}}],["derivative",{"0":{"37":1},"2":{"37":6}}],["degree",{"0":{"7":1},"2":{"7":1}}],["def",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"32":1,"37":2,"73":1,"80":1,"81":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["梯度",{"2":{"31":1}}],["点乘结果",{"2":{"144":1}}],["点乘",{"2":{"144":1}}],["点乘使用",{"2":{"142":1}}],["点3",{"2":{"97":1}}],["点法式构造",{"2":{"96":1}}],["点2",{"2":{"73":1,"97":1}}],["点1",{"2":{"73":1,"97":1}}],["点",{"2":{"31":1,"65":1,"70":1}}],["∂f∂z",{"2":{"31":1}}],["∂f∂y",{"2":{"31":1}}],["∂f∂x",{"2":{"31":1}}],["∇f",{"2":{"31":1}}],["z轴单位向量",{"2":{"150":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"147":1},"2":{"98":1,"125":1}}],["z=0",{"2":{"91":1}}],["z系数",{"2":{"87":1}}],["zip",{"2":{"36":1}}],["z函数",{"2":{"35":1}}],["z0",{"2":{"31":2}}],["z",{"0":{"35":1,"78":1,"120":1,"150":1},"2":{"31":7,"35":4,"36":4,"66":2,"72":3,"78":5,"79":2,"82":2,"83":2,"84":2,"90":1,"91":4,"92":4,"96":2,"107":2,"112":2,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["y轴单位向量",{"2":{"149":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"91":1}}],["y系数",{"2":{"87":1}}],["y函数",{"2":{"35":1}}],["y0",{"2":{"31":2}}],["y",{"0":{"35":1,"78":1,"115":1,"120":1,"149":1},"2":{"31":7,"35":4,"36":4,"66":2,"72":3,"78":5,"79":2,"82":2,"83":2,"84":2,"90":1,"91":4,"92":4,"96":2,"107":2,"112":2,"115":3,"120":4,"121":2,"123":4,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["x轴单位向量",{"2":{"148":1}}],["x轴分量",{"2":{"120":1}}],["x26",{"2":{"102":1}}],["x−x0m=y−y0n=z−z0p",{"2":{"91":1}}],["x=x0+dty=y0+dtz=z0+dt或",{"2":{"91":1}}],["x系数",{"2":{"87":1}}],["x3c",{"2":{"79":3,"112":1,"115":1,"116":1,"117":1,"121":3,"124":1}}],["x函数",{"2":{"35":1}}],["x0",{"2":{"31":2}}],["x",{"0":{"35":1,"78":1,"109":1,"115":1,"116":1,"117":1,"120":1,"148":1},"2":{"31":7,"35":4,"36":4,"66":2,"72":2,"78":5,"79":2,"82":2,"83":2,"84":2,"90":1,"91":4,"92":4,"96":2,"107":2,"109":3,"112":2,"115":3,"116":4,"117":7,"120":4,"121":2,"123":5,"126":1,"127":1,"128":1,"133":4,"134":2,"135":2,"138":4,"139":2,"142":3,"144":2,"145":1,"146":1,"155":2}}],["v3",{"2":{"123":1}}],["vector",{"0":{"118":1},"1":{"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"84":1}}],["vector3",{"0":{"31":1,"59":1,"80":1,"84":1,"95":1,"96":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"129":1,"131":2,"136":2,"140":2,"141":1,"142":2,"143":1,"144":1,"145":1,"146":1,"147":1},"1":{"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"31":2,"38":1,"59":2,"80":1,"82":1,"84":5,"95":3,"96":2,"98":1,"112":2,"121":2,"122":2,"123":5,"124":2,"125":3,"129":2,"131":2,"133":5,"134":1,"136":2,"138":5,"139":1,"140":2,"141":1,"142":8,"143":1,"144":2,"145":2,"146":3,"147":2,"148":2,"149":2,"150":2}}],["v2",{"2":{"75":1,"97":2,"98":4,"123":1}}],["v1x⋅v2y−v1y⋅v2x",{"2":{"123":1}}],["v1z⋅v2x−v1x⋅v2z",{"2":{"123":1}}],["v1y⋅v2z−v1z⋅v2y",{"2":{"123":1}}],["v1×v2=|ijkv1xv1yv1zv2xv2yv2z|",{"2":{"123":1}}],["v1×v2=",{"2":{"123":1}}],["v1⋅v2|v1|⋅|v2|",{"2":{"122":1}}],["v1",{"2":{"75":2,"97":2,"98":2,"123":1}}],["v",{"2":{"37":2,"82":1,"84":2,"133":4,"135":1,"138":4,"139":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"32":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":2,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"147":1,"148":1,"149":1,"150":1},"2":{"32":4,"36":1,"37":12}}],["valueerror",{"2":{"37":2,"63":4,"91":2,"92":2}}],["value",{"0":{"4":1,"111":1},"2":{"4":4,"111":4,"112":6,"113":1}}],["约等于判定误差",{"2":{"29":1}}],["精度误差",{"2":{"28":1}}],["06",{"0":{"67":1},"2":{"67":1}}],["001",{"2":{"29":1}}],["0001",{"2":{"28":1}}],["0",{"0":{"115":2},"2":{"27":1,"28":1,"29":1,"36":3,"62":2,"71":1,"72":7,"87":1,"88":3,"90":2,"91":9,"92":1,"102":1,"115":1,"116":2,"117":3,"147":3,"148":2,"149":2,"150":2,"155":2}}],["欧拉常数",{"2":{"27":1}}],["5772156649015329",{"2":{"27":1}}],["5",{"2":{"26":1,"90":1}}],["黄金分割比",{"2":{"26":1}}],["geometricmodels",{"0":{"154":1},"1":{"155":1}}],["get",{"0":{"37":1,"65":1,"66":1},"2":{"37":2,"65":1,"66":1,"92":1,"98":1}}],["gradient",{"0":{"31":1},"2":{"31":1}}],["gamma",{"0":{"27":1}}],["golden",{"0":{"26":1}}],["gt",{"0":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"31":1,"32":1,"36":1,"37":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"73":1,"74":1,"75":1,"79":1,"80":1,"81":1,"84":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"103":1,"104":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"82":2,"84":2,"117":3,"123":1,"133":2,"135":1,"138":2,"139":1}}],["默認值",{"2":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"147":1,"148":1,"149":1,"150":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"159":1}}],["theta",{"2":{"155":3}}],["the",{"2":{"92":2,"159":1}}],["three",{"0":{"97":1},"2":{"97":1}}],["threevarsfunc",{"0":{"53":1}}],["threearraysfunc",{"0":{"52":1},"2":{"53":1}}],["threesinglevarsfunc",{"0":{"31":1,"51":1},"2":{"31":2,"53":1}}],["two",{"0":{"73":1,"98":1},"2":{"73":1,"98":1}}],["twovarsfunc",{"0":{"50":1}}],["twoarraysfunc",{"0":{"49":1},"2":{"50":1}}],["twosinglevarsfunc",{"0":{"48":1},"2":{"50":1}}],["typing",{"0":{"39":1},"1":{"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1}}],["typeerror",{"2":{"62":2,"89":2,"90":2,"102":2,"113":1,"133":1,"138":1,"139":1,"142":1}}],["typevar",{"2":{"42":1,"43":1}}],["typealias",{"2":{"40":1,"41":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1}}],["type",{"0":{"113":1},"2":{"37":1,"62":1,"89":2,"90":2,"102":2,"112":2,"113":4,"133":2,"138":2,"139":2,"142":2}}],["tuple",{"0":{"36":1,"37":1,"66":1},"2":{"36":2,"37":2,"66":2}}],["t",{"0":{"36":1,"65":1},"2":{"36":9,"65":3,"66":6,"92":4}}],["tip",{"2":{"31":1,"32":1,"89":2,"91":1,"122":1,"123":1}}],["truediv",{"2":{"20":1,"21":1,"22":1,"145":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"102":1,"133":1,"138":1,"139":1,"142":1}}],["or",{"2":{"74":1,"92":1}}],["order",{"2":{"37":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"70":1},"2":{"70":1}}],["one",{"2":{"157":1}}],["onearrayfunc",{"0":{"46":1},"2":{"47":1}}],["onesinglevarfunc",{"0":{"45":1,"66":3},"2":{"47":1,"66":6}}],["onevarfunc",{"0":{"32":1,"35":3,"47":1},"2":{"32":1,"35":6}}],["overload",{"2":{"19":1,"20":2,"21":1,"79":1,"80":2,"81":1,"99":1,"100":2,"101":1,"130":1,"131":2,"132":1,"135":1,"136":2,"137":1,"139":1,"140":2,"141":1}}],["other",{"0":{"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"60":1,"61":1,"62":1,"63":1,"67":1,"68":1,"69":1,"71":1,"74":1,"75":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"88":1,"89":1,"90":1,"91":1,"92":1,"94":1,"100":1,"101":1,"102":1,"103":1,"104":1,"112":1,"113":1,"114":1,"121":1,"122":1,"123":1,"124":1,"125":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1},"2":{"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":4,"60":4,"61":3,"62":12,"63":8,"67":3,"68":3,"69":4,"71":4,"74":6,"75":4,"79":5,"80":1,"81":1,"82":5,"83":5,"84":5,"88":14,"89":8,"90":8,"91":16,"92":10,"94":3,"100":1,"101":1,"102":9,"103":3,"104":2,"112":9,"113":2,"114":2,"121":5,"122":4,"123":8,"124":3,"125":3,"131":1,"132":1,"133":11,"134":5,"135":5,"136":1,"137":1,"138":11,"139":7,"140":1,"141":1,"142":11,"143":2,"144":5,"145":4}}],["ep",{"2":{"157":1}}],["epsilon",{"0":{"28":1,"31":2,"37":2,"60":1,"67":1,"79":1,"115":1,"121":1,"124":1},"2":{"31":11,"37":6,"60":4,"67":3,"79":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["elif",{"2":{"37":1,"62":3,"74":1,"88":2,"89":1,"90":1,"91":2,"102":1,"112":1,"116":1,"117":1,"133":1,"138":1,"142":1}}],["else",{"2":{"4":1,"36":1,"37":1,"62":2,"74":1,"88":1,"89":1,"90":1,"102":1,"112":2,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1}}],["exp",{"2":{"25":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"66":1},"2":{"66":1,"92":1}}],["equation",{"0":{"33":1},"1":{"34":1,"35":1,"36":1,"37":1}}],["eq",{"0":{"17":1,"75":1,"83":1,"103":1,"112":1,"134":1},"2":{"17":1,"75":1,"83":1,"103":1,"112":1,"114":1,"134":1}}],["acos",{"2":{"89":1,"122":1}}],["axis",{"0":{"148":1,"149":1,"150":1}}],["ax",{"2":{"87":1}}],["all",{"2":{"79":1,"112":1,"121":1}}],["abs",{"0":{"130":1},"2":{"62":1,"79":3,"90":1,"112":1,"115":1,"117":1,"121":3,"130":1}}],["arccos",{"2":{"155":1}}],["array",{"0":{"127":1},"2":{"91":6,"127":2,"155":6}}],["arrayvar",{"0":{"43":1},"2":{"43":1,"44":1,"46":2,"49":3,"52":4,"55":1}}],["area",{"2":{"155":2}}],["are",{"2":{"63":2,"91":1,"92":1}}],["args2",{"2":{"32":2}}],["args",{"0":{"32":1},"2":{"32":3,"37":11}}],["a",{"0":{"87":1},"2":{"32":2,"87":4,"88":7,"90":2,"91":12,"92":2,"95":1,"96":3}}],["aaa",{"2":{"30":1}}],["approx",{"0":{"29":1,"60":2,"67":1,"79":2,"88":1,"110":1,"115":2,"121":2,"124":2},"1":{"111":1,"112":1,"113":1,"114":1},"2":{"17":1,"60":3,"67":2,"79":1,"83":3,"88":10,"103":1,"112":4,"115":1,"121":1,"124":1,"125":1,"134":3}}],["add",{"2":{"16":1,"32":4,"80":1,"81":1,"82":1,"131":1,"132":1,"133":1}}],["and",{"0":{"74":1,"96":1,"99":1,"100":1,"101":1,"102":1},"2":{"60":1,"63":2,"69":1,"74":1,"75":1,"83":2,"88":6,"91":4,"92":1,"93":1,"96":1,"97":1,"98":1,"99":2,"100":1,"101":1,"102":2,"113":1,"133":1,"134":2,"138":1,"139":1,"142":1}}],["anyangle",{"0":{"3":1,"5":1,"6":1,"8":1,"9":1,"16":2,"18":2,"19":1,"20":1,"21":1,"61":1,"89":1,"122":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1},"2":{"5":2,"6":2,"8":2,"9":2,"16":3,"18":3,"19":2,"20":1,"21":1,"22":2,"38":1,"61":2,"89":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"61":1,"89":1,"122":1},"1":{"2":1,"3":1,"4":2,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":2,"21":2,"22":2},"2":{"61":2,"89":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"37":1}}],["+",{"0":{"16":1,"80":1,"81":1,"82":1,"131":1,"132":1,"133":1,"135":1},"2":{"16":1,"26":1,"31":3,"32":2,"63":1,"65":1,"66":3,"82":5,"87":3,"90":5,"92":5,"107":3,"116":2,"117":2,"128":2,"133":9,"135":4,"144":2,"155":1}}],["1e",{"0":{"67":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"32":1,"36":1,"98":1,"117":3,"148":1,"149":1,"150":1,"155":4}}],["180",{"2":{"4":1,"7":1}}],["正割值",{"2":{"14":2}}],["正切值",{"2":{"12":2}}],["正弦值",{"2":{"10":2}}],["余割值",{"2":{"15":2}}],["余切值",{"2":{"13":2}}],["余弦值",{"2":{"11":2}}],["余角",{"2":{"5":2}}],["最佳實踐",{"0":{"156":1},"1":{"157":1}}],["最大值",{"2":{"109":1}}],["最大负角度",{"2":{"9":1}}],["最大负角",{"2":{"9":1}}],["最小值",{"2":{"109":1}}],["最小正角度",{"2":{"8":1}}],["最小正角",{"2":{"8":1}}],["弧度",{"2":{"7":1}}],["角度",{"2":{"7":1}}],["角度或弧度值",{"2":{"4":1}}],["补角",{"2":{"6":2}}],["sphere",{"0":{"155":1},"2":{"155":1}}],["stop",{"2":{"157":1}}],["staticmethod",{"2":{"154":1,"155":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"102":1,"133":1,"138":1,"139":1,"142":1}}],["solve",{"2":{"91":3}}],["sign",{"0":{"116":1,"117":1},"2":{"116":1,"117":1}}],["simplify",{"0":{"72":1},"2":{"72":1}}],["singlevar",{"0":{"42":1},"2":{"42":1,"44":1,"45":2,"48":3,"51":4,"54":1}}],["sin",{"0":{"10":1},"2":{"10":2,"15":1,"155":3}}],["sqrt",{"2":{"26":1,"128":1,"155":1}}],["sub",{"2":{"18":1,"84":1,"136":1,"137":1,"138":1}}],["supplementary",{"0":{"6":1},"2":{"6":1}}],["segment",{"0":{"105":1},"1":{"106":1,"107":1}}],["segment3",{"0":{"106":1},"1":{"107":1},"2":{"38":1}}],["sec",{"0":{"14":1},"2":{"14":1}}],["self",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"35":1,"36":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":3,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":2,"16":2,"17":2,"18":2,"19":2,"20":1,"21":1,"22":3,"35":4,"36":7,"59":3,"60":4,"61":2,"62":13,"63":8,"64":3,"65":3,"66":7,"67":2,"68":2,"69":4,"70":3,"71":3,"72":8,"74":6,"75":4,"78":4,"79":4,"80":1,"81":1,"82":4,"83":4,"84":4,"87":5,"88":16,"89":4,"90":8,"91":15,"92":9,"93":2,"94":2,"95":4,"100":1,"101":1,"102":5,"103":2,"104":2,"107":15,"111":2,"112":9,"113":2,"114":2,"120":4,"121":4,"122":3,"123":7,"124":2,"125":2,"126":5,"127":4,"128":4,"129":3,"130":2,"131":1,"132":1,"133":7,"134":4,"135":4,"136":1,"137":1,"138":7,"139":4,"140":1,"141":1,"142":7,"143":2,"144":4,"145":4,"146":4}}],["255万个粒子",{"2":{"157":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"31":3,"32":1,"37":1,"63":1,"90":3,"107":3,"128":3,"155":2}}],["rmul",{"2":{"143":1}}],["rsub",{"2":{"139":1}}],["reference",{"0":{"159":1}}],["realnumber",{"0":{"40":1,"65":1,"111":1,"141":1,"143":1,"144":1,"145":1},"2":{"41":1,"65":2,"111":2,"141":1,"143":1,"144":1,"145":1}}],["result",{"2":{"37":4}}],["return",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"22":2,"31":1,"32":3,"36":2,"37":4,"60":1,"61":1,"62":5,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"73":1,"74":3,"75":1,"79":1,"82":1,"83":1,"84":1,"88":4,"89":2,"90":2,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"102":4,"103":1,"104":1,"109":1,"112":2,"114":1,"115":1,"116":3,"117":3,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"130":1,"133":2,"134":1,"135":1,"138":2,"139":1,"142":2,"143":1,"144":1,"145":1,"146":1,"155":1}}],["range",{"2":{"155":2}}],["rand",{"0":{"104":1},"2":{"104":1}}],["radius",{"0":{"155":1},"2":{"155":6}}],["radian=true",{"2":{"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"89":1,"122":1}}],["radian",{"0":{"4":1},"2":{"4":5,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":2,"17":2,"18":2,"19":1,"22":3}}],["radd",{"2":{"135":1}}],["raise",{"0":{"113":1},"2":{"37":1,"62":1,"63":2,"89":1,"90":1,"91":1,"92":1,"102":1,"112":2,"113":2,"133":1,"138":1,"139":1,"142":1}}],["ratio",{"0":{"26":1}}],[">",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"18":1,"19":1,"20":1,"21":1,"31":1,"32":3,"36":1,"37":3,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"73":1,"74":1,"75":1,"79":1,"80":1,"81":1,"84":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"103":1,"104":1,"109":1,"115":1,"116":2,"117":2,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["返回",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"31":1,"32":1,"36":1,"37":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"73":1,"74":1,"75":1,"79":1,"82":1,"83":1,"84":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"102":1,"103":1,"109":1,"115":1,"116":1,"117":1,"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"155":1}}],["can",{"2":{"157":1}}],["callable",{"2":{"45":1,"46":1,"48":1,"49":1,"51":1,"52":1,"54":1,"55":1}}],["call",{"0":{"36":1},"2":{"36":1}}],["cal",{"0":{"31":1,"61":1,"62":1,"63":1,"64":1,"89":1,"90":1,"91":1,"92":1,"93":1,"122":1},"2":{"31":1,"61":2,"62":1,"63":1,"64":1,"74":1,"89":2,"90":1,"91":1,"92":1,"93":1,"102":2,"104":1,"122":1}}],["cz",{"2":{"87":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"155":1}}],["classmethod",{"2":{"72":1,"73":1,"95":1,"96":2,"97":2,"98":2,"99":1}}],["class",{"0":{"2":1,"3":1,"34":1,"58":1,"77":1,"86":1,"106":1,"110":1,"119":1,"154":1},"1":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"35":1,"36":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["cls",{"0":{"73":1,"96":1,"97":1,"98":1,"99":1},"2":{"73":2,"96":2,"97":2,"98":2,"99":2}}],["cross",{"0":{"123":1},"2":{"62":4,"63":3,"64":1,"71":1,"91":1,"97":1,"98":1,"123":1,"124":1,"125":1}}],["curveequation",{"0":{"34":1},"1":{"35":1,"36":1},"2":{"38":1}}],["curried",{"2":{"32":4}}],["currying",{"2":{"32":1}}],["curry",{"0":{"32":1},"2":{"32":2}}],["c",{"0":{"87":1},"2":{"32":2,"87":4,"88":7,"90":2,"91":6,"92":2,"95":1,"96":3}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"92":1}}],["collinear",{"0":{"69":1},"2":{"69":1,"74":1}}],["coplanar",{"0":{"71":1},"2":{"62":1,"63":2,"71":1,"74":1}}],["complex",{"2":{"41":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"89":1}}],["const",{"0":{"23":1},"1":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1}}],["cot",{"0":{"13":1},"2":{"13":1}}],["cos",{"0":{"11":1},"2":{"11":2,"14":1,"155":2}}],["於github上查看",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"31":1,"32":1,"35":1,"36":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["或包装一个实数",{"2":{"115":1}}],["或整数元组",{"2":{"37":1}}],["或",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"31":1,"32":1,"35":1,"36":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["源碼",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"31":1,"32":1,"35":1,"36":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["變數説明",{"2":{"4":1,"31":1,"32":1,"35":1,"36":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"67":1,"68":1,"69":1,"70":1,"71":1,"73":1,"74":1,"75":1,"78":1,"79":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"96":1,"97":1,"98":1,"99":1,"102":1,"103":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"155":1}}],["任意角度",{"2":{"4":1,"38":1}}],["説明",{"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"35":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"102":1,"103":1,"107":1,"109":1,"111":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"128":1,"129":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"144":1,"146":1,"147":1,"148":1,"149":1,"150":1,"155":1}}],["f",{"2":{"89":1,"90":1,"102":1,"113":1,"117":3,"133":1,"138":1,"139":1,"142":1}}],["from",{"0":{"73":1,"96":1,"97":1,"98":1,"99":1},"2":{"73":1,"84":1,"93":1,"96":1,"97":2,"98":2,"99":2,"157":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"36":1,"37":1,"102":1,"133":1,"138":1,"139":1,"142":1,"155":2}}],["func",{"0":{"31":2,"32":2,"35":3,"37":3,"109":1,"115":1,"116":1,"117":1},"2":{"31":8,"32":5,"35":12,"36":6,"37":15}}],["function",{"0":{"30":1},"1":{"31":1,"32":1}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"88":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"67":1}}],["float=approx",{"2":{"60":1,"79":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"31":1}}],["float",{"0":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"31":1,"60":1,"62":1,"67":1,"78":3,"79":1,"87":4,"90":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"128":1,"142":1,"155":2},"2":{"4":1,"7":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"19":1,"20":1,"21":1,"40":1,"60":1,"62":2,"67":1,"78":6,"79":1,"87":8,"90":2,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"128":2,"142":3,"144":1,"155":2}}],["==",{"2":{"36":1,"62":1,"71":1,"72":3,"92":1,"98":1,"102":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"31":1,"37":1,"60":1,"67":1,"79":1,"80":1,"81":1,"84":1,"115":2,"116":1,"117":1,"121":1,"124":1,"131":1,"132":1,"135":1,"136":1,"137":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1},"2":{"4":2,"31":4,"32":1,"35":3,"37":5,"59":2,"72":3,"73":1,"78":3,"87":5,"88":6,"91":17,"92":2,"96":2,"97":3,"98":3,"107":5,"111":1,"120":3,"126":4,"155":7}}],["improve",{"2":{"159":1}}],["import",{"2":{"84":1}}],["i",{"2":{"155":4,"157":1}}],["invalid",{"2":{"37":1}}],["in",{"2":{"36":1,"37":1,"155":2}}],["intersect",{"2":{"63":2}}],["intersection",{"0":{"63":1,"91":1,"92":1},"2":{"63":1,"74":1,"91":2,"92":1,"102":2,"104":1}}],["int",{"0":{"37":2,"142":1},"2":{"32":4,"37":3,"40":1,"112":2,"142":2,"155":1}}],["init",{"0":{"4":1,"35":1,"59":1,"78":1,"87":1,"107":1,"111":1,"120":1},"2":{"4":1,"35":1,"59":1,"78":1,"87":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"36":1,"37":1,"62":2,"63":2,"72":3,"74":1,"88":1,"89":1,"90":1,"91":2,"92":1,"98":1,"102":3,"112":3,"116":2,"117":2,"133":1,"138":1,"139":1,"142":1,"157":1}}],["isinstance",{"2":{"22":1,"37":2,"62":2,"89":2,"90":2,"102":2,"112":4,"133":2,"138":2,"139":1,"142":2}}],["is",{"0":{"4":1,"67":1,"68":1,"69":1,"70":1,"71":1,"94":1,"124":1,"125":1},"2":{"4":3,"5":1,"6":1,"9":1,"16":1,"18":1,"19":1,"22":1,"60":2,"62":2,"63":2,"67":2,"68":2,"69":3,"70":2,"71":1,"74":3,"75":2,"89":1,"91":1,"94":2,"102":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"155":5}}],["p3",{"0":{"97":1},"2":{"97":3}}],["p2",{"0":{"73":1,"97":1,"107":1},"2":{"73":3,"75":1,"97":3,"107":8}}],["p1",{"0":{"73":1,"97":1,"107":1},"2":{"73":4,"75":1,"97":5,"107":8}}],["perpendicular",{"0":{"64":1},"2":{"64":1}}],["parametric",{"0":{"66":1},"2":{"66":1,"92":1}}],["parallel",{"0":{"67":1,"68":1,"93":1,"94":1,"124":1,"125":1},"2":{"60":2,"62":1,"63":2,"67":2,"68":2,"69":2,"70":1,"74":1,"75":2,"91":2,"92":1,"93":1,"94":2,"102":1,"124":1,"125":1}}],["partial",{"0":{"37":1},"2":{"37":6}}],["particle",{"0":{"151":1},"2":{"0":1}}],["planes",{"2":{"91":1}}],["plane",{"0":{"85":1},"1":{"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"92":1}}],["plane3",{"0":{"86":1,"88":1,"89":1,"90":1,"91":1,"93":2,"94":1,"96":1,"97":1,"98":1,"99":1,"101":1},"1":{"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"38":1,"88":2,"89":3,"90":3,"91":2,"93":4,"94":2,"96":2,"97":1,"98":1,"99":1,"101":1,"102":3,"103":1,"112":1}}],["plus",{"2":{"37":3}}],["points",{"0":{"73":1,"97":1},"2":{"73":1,"97":1}}],["point",{"0":{"59":1,"64":1,"65":1,"70":2,"76":1,"93":1,"96":2,"99":2},"1":{"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1},"2":{"59":4,"60":2,"62":5,"63":3,"64":5,"65":2,"66":3,"69":2,"70":5,"71":2,"72":3,"75":2,"92":3,"93":4,"96":6,"97":1,"98":6,"99":5}}],["point3",{"0":{"31":1,"36":2,"59":1,"62":1,"63":1,"64":1,"65":1,"70":1,"73":2,"74":1,"77":1,"79":1,"80":1,"81":2,"84":1,"90":1,"92":2,"93":1,"96":1,"97":3,"99":1,"100":1,"104":1,"107":2,"132":2,"135":2,"137":2,"139":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1},"2":{"31":2,"36":4,"38":1,"59":2,"62":3,"63":2,"64":2,"65":2,"70":2,"73":4,"74":2,"79":2,"80":1,"81":2,"82":3,"83":1,"84":2,"90":3,"91":1,"92":4,"93":2,"96":2,"97":6,"99":2,"100":1,"102":2,"104":2,"107":5,"112":1,"132":2,"133":4,"135":5,"137":2,"138":4,"139":5,"155":2}}],["positive",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["p",{"0":{"31":1},"2":{"31":20,"82":5,"84":4,"133":2,"135":2,"138":2,"139":2}}],["python",{"2":{"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"20":1,"21":1,"73":1,"80":1,"81":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"127":1,"128":1,"129":1,"131":1,"132":1,"136":1,"137":1,"140":1,"141":1,"155":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"31":1,"32":2,"35":1,"36":1,"37":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"74":1,"75":1,"78":1,"79":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"102":1,"103":1,"104":1,"107":1,"109":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"130":1,"133":1,"134":1,"135":1,"138":1,"139":1,"142":1,"143":1,"144":1,"145":1,"146":1}}],["property",{"2":{"4":1,"5":2,"6":2,"7":2,"8":2,"9":2,"10":2,"11":2,"12":2,"13":2,"14":2,"15":1,"94":1,"95":1,"126":1,"127":2,"128":2,"129":1}}],["presets",{"0":{"152":1,"153":1},"1":{"154":1,"155":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"155":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"157":1}}],["model",{"0":{"153":1},"1":{"154":1,"155":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"157":1}}],["min",{"0":{"109":1},"2":{"109":4}}],["minus",{"2":{"37":3}}],["minimum",{"0":{"8":1},"2":{"5":1,"6":1,"8":1}}],["multiarraysfunc",{"0":{"55":1},"2":{"56":1}}],["multisinglevarsfunc",{"0":{"54":1},"2":{"56":1}}],["multivarsfunc",{"0":{"32":1,"37":2,"56":1},"2":{"32":2,"37":3}}],["mul",{"2":{"19":1,"140":1,"141":1,"142":1,"143":1}}],["matmul",{"2":{"144":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"33":1,"38":1,"39":2,"57":1,"76":1,"85":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"34":1,"35":1,"36":1,"37":1,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"50":2,"51":2,"52":2,"53":2,"54":2,"55":2,"56":2,"58":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"24":1,"25":1,"26":1,"89":1,"122":1,"128":1}}],["max",{"0":{"109":1},"2":{"109":4}}],["maximum",{"0":{"9":1},"2":{"9":1}}],["method",{"0":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"35":1,"36":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"107":1,"111":1,"112":1,"113":1,"114":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"155":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"33":1,"38":1,"39":2,"57":1,"76":1,"85":1,"105":1,"108":1,"118":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"34":1,"35":1,"36":1,"37":1,"40":2,"41":2,"42":2,"43":2,"44":2,"45":2,"46":2,"47":2,"48":2,"49":2,"50":2,"51":2,"52":2,"53":2,"54":2,"55":2,"56":2,"58":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"33":1,"38":1,"39":1,"57":1,"76":1,"85":1,"105":1,"108":1,"118":1,"151":1,"152":1,"153":1},"1":{"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1,"11":1,"12":1,"13":1,"14":1,"15":1,"16":1,"17":1,"18":1,"19":1,"20":1,"21":1,"22":1,"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"31":1,"32":1,"34":1,"35":1,"36":1,"37":1,"40":1,"41":1,"42":1,"43":1,"44":1,"45":1,"46":1,"47":1,"48":1,"49":1,"50":1,"51":1,"52":1,"53":1,"54":1,"55":1,"56":1,"58":1,"59":1,"60":1,"61":1,"62":1,"63":1,"64":1,"65":1,"66":1,"67":1,"68":1,"69":1,"70":1,"71":1,"72":1,"73":1,"74":1,"75":1,"77":1,"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"93":1,"94":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1,"106":1,"107":1,"109":1,"110":1,"111":1,"112":1,"113":1,"114":1,"115":1,"116":1,"117":1,"119":1,"120":1,"121":1,"122":1,"123":1,"124":1,"125":1,"126":1,"127":1,"128":1,"129":1,"130":1,"131":1,"132":1,"133":1,"134":1,"135":1,"136":1,"137":1,"138":1,"139":1,"140":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1,"148":1,"149":1,"150":1,"154":1,"155":1},"2":{"0":3}}],["提供了一些工具",{"2":{"0":1}}]],"serializationVersion":2}';export{t as default};
diff --git a/assets/chunks/VPLocalSearchBox.Lyrn-94G.js b/assets/chunks/VPLocalSearchBox.DhHzxM_l.js
similarity index 99%
rename from assets/chunks/VPLocalSearchBox.Lyrn-94G.js
rename to assets/chunks/VPLocalSearchBox.DhHzxM_l.js
index 5c6d9fe..562f3db 100644
--- a/assets/chunks/VPLocalSearchBox.Lyrn-94G.js
+++ b/assets/chunks/VPLocalSearchBox.DhHzxM_l.js
@@ -1,4 +1,4 @@
-var Ot=Object.defineProperty;var Rt=(a,e,t)=>e in a?Ot(a,e,{enumerable:!0,configurable:!0,writable:!0,value:t}):a[e]=t;var Me=(a,e,t)=>Rt(a,typeof e!="symbol"?e+"":e,t);import{X as ye,s as ne,h as ve,aj as tt,ak as Ct,al as Mt,v as $e,am as At,d as Lt,G as we,an as st,ao as Dt,ap as zt,x as Pt,aq as Vt,y as Ae,R as de,Q as _e,ar as jt,as as $t,Y as Bt,U as Wt,a1 as Kt,o as Q,b as Jt,j as x,a2 as Ut,k as D,at as qt,au as Gt,av as Qt,c as Z,n as nt,e as xe,E as it,F as rt,a as he,t as fe,aw as Ht,p as Yt,l as Zt,ax as at,ay as Xt,a8 as es,ae as ts,az as ss,_ as ns}from"./framework.DpC1ZpOZ.js";import{u as is,c as rs}from"./theme.4Aq0plHp.js";const as={en:()=>ye(()=>import("./@localSearchIndexen.BiKPGziK.js"),[]),ja:()=>ye(()=>import("./@localSearchIndexja.NAYqQakD.js"),[]),root:()=>ye(()=>import("./@localSearchIndexroot.DH9jnGhe.js"),[]),zht:()=>ye(()=>import("./@localSearchIndexzht.DIej9wva.js"),[])};/*!
+var Ot=Object.defineProperty;var Rt=(a,e,t)=>e in a?Ot(a,e,{enumerable:!0,configurable:!0,writable:!0,value:t}):a[e]=t;var Me=(a,e,t)=>Rt(a,typeof e!="symbol"?e+"":e,t);import{X as ye,s as ne,h as ve,aj as tt,ak as Ct,al as Mt,v as $e,am as At,d as Lt,G as we,an as st,ao as Dt,ap as zt,x as Pt,aq as Vt,y as Ae,R as de,Q as _e,ar as jt,as as $t,Y as Bt,U as Wt,a1 as Kt,o as Q,b as Jt,j as x,a2 as Ut,k as D,at as qt,au as Gt,av as Qt,c as Z,n as nt,e as xe,E as it,F as rt,a as he,t as fe,aw as Ht,p as Yt,l as Zt,ax as at,ay as Xt,a8 as es,ae as ts,az as ss,_ as ns}from"./framework.DpC1ZpOZ.js";import{u as is,c as rs}from"./theme.Cq7NoE_k.js";const as={en:()=>ye(()=>import("./@localSearchIndexen.BJkPsfRt.js"),[]),ja:()=>ye(()=>import("./@localSearchIndexja.RtIw4HCL.js"),[]),root:()=>ye(()=>import("./@localSearchIndexroot.C4Y9aF6Z.js"),[]),zht:()=>ye(()=>import("./@localSearchIndexzht.BOVgxEGY.js"),[])};/*!
 * tabbable 6.2.0
 * @license MIT, https://github.com/focus-trap/tabbable/blob/master/LICENSE
 */var gt=["input:not([inert])","select:not([inert])","textarea:not([inert])","a[href]:not([inert])","button:not([inert])","[tabindex]:not(slot):not([inert])","audio[controls]:not([inert])","video[controls]:not([inert])",'[contenteditable]:not([contenteditable="false"]):not([inert])',"details>summary:first-of-type:not([inert])","details:not([inert])"],Ne=gt.join(","),bt=typeof Element>"u",re=bt?function(){}:Element.prototype.matches||Element.prototype.msMatchesSelector||Element.prototype.webkitMatchesSelector,ke=!bt&&Element.prototype.getRootNode?function(a){var e;return a==null||(e=a.getRootNode)===null||e===void 0?void 0:e.call(a)}:function(a){return a==null?void 0:a.ownerDocument},Fe=function a(e,t){var s;t===void 0&&(t=!0);var n=e==null||(s=e.getAttribute)===null||s===void 0?void 0:s.call(e,"inert"),r=n===""||n==="true",i=r||t&&e&&a(e.parentNode);return i},os=function(e){var t,s=e==null||(t=e.getAttribute)===null||t===void 0?void 0:t.call(e,"contenteditable");return s===""||s==="true"},yt=function(e,t,s){if(Fe(e))return[];var n=Array.prototype.slice.apply(e.querySelectorAll(Ne));return t&&re.call(e,Ne)&&n.unshift(e),n=n.filter(s),n},wt=function a(e,t,s){for(var n=[],r=Array.from(e);r.length;){var i=r.shift();if(!Fe(i,!1))if(i.tagName==="SLOT"){var o=i.assignedElements(),c=o.length?o:i.children,l=a(c,!0,s);s.flatten?n.push.apply(n,l):n.push({scopeParent:i,candidates:l})}else{var h=re.call(i,Ne);h&&s.filter(i)&&(t||!e.includes(i))&&n.push(i);var v=i.shadowRoot||typeof s.getShadowRoot=="function"&&s.getShadowRoot(i),f=!Fe(v,!1)&&(!s.shadowRootFilter||s.shadowRootFilter(i));if(v&&f){var b=a(v===!0?i.children:v.children,!0,s);s.flatten?n.push.apply(n,b):n.push({scopeParent:i,candidates:b})}else r.unshift.apply(r,i.children)}}return n},_t=function(e){return!isNaN(parseInt(e.getAttribute("tabindex"),10))},ie=function(e){if(!e)throw new Error("No node provided");return e.tabIndex<0&&(/^(AUDIO|VIDEO|DETAILS)$/.test(e.tagName)||os(e))&&!_t(e)?0:e.tabIndex},cs=function(e,t){var s=ie(e);return s<0&&t&&!_t(e)?0:s},ls=function(e,t){return e.tabIndex===t.tabIndex?e.documentOrder-t.documentOrder:e.tabIndex-t.tabIndex},xt=function(e){return e.tagName==="INPUT"},us=function(e){return xt(e)&&e.type==="hidden"},ds=function(e){var t=e.tagName==="DETAILS"&&Array.prototype.slice.apply(e.children).some(function(s){return s.tagName==="SUMMARY"});return t},hs=function(e,t){for(var s=0;ssummary:first-of-type"),i=r?e.parentElement:e;if(re.call(i,"details:not([open]) *"))return!0;if(!s||s==="full"||s==="legacy-full"){if(typeof n=="function"){for(var o=e;e;){var c=e.parentElement,l=ke(e);if(c&&!c.shadowRoot&&n(c)===!0)return ot(e);e.assignedSlot?e=e.assignedSlot:!c&&l!==e.ownerDocument?e=l.host:e=c}e=o}if(ms(e))return!e.getClientRects().length;if(s!=="legacy-full")return!0}else if(s==="non-zero-area")return ot(e);return!1},bs=function(e){if(/^(INPUT|BUTTON|SELECT|TEXTAREA)$/.test(e.tagName))for(var t=e.parentElement;t;){if(t.tagName==="FIELDSET"&&t.disabled){for(var s=0;s=0)},ws=function a(e){var t=[],s=[];return e.forEach(function(n,r){var i=!!n.scopeParent,o=i?n.scopeParent:n,c=cs(o,i),l=i?a(n.candidates):o;c===0?i?t.push.apply(t,l):t.push(o):s.push({documentOrder:r,tabIndex:c,item:n,isScope:i,content:l})}),s.sort(ls).reduce(function(n,r){return r.isScope?n.push.apply(n,r.content):n.push(r.content),n},[]).concat(t)},_s=function(e,t){t=t||{};var s;return t.getShadowRoot?s=wt([e],t.includeContainer,{filter:Be.bind(null,t),flatten:!1,getShadowRoot:t.getShadowRoot,shadowRootFilter:ys}):s=yt(e,t.includeContainer,Be.bind(null,t)),ws(s)},xs=function(e,t){t=t||{};var s;return t.getShadowRoot?s=wt([e],t.includeContainer,{filter:Oe.bind(null,t),flatten:!0,getShadowRoot:t.getShadowRoot}):s=yt(e,t.includeContainer,Oe.bind(null,t)),s},ae=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return re.call(e,Ne)===!1?!1:Be(t,e)},Ss=gt.concat("iframe").join(","),Le=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return re.call(e,Ss)===!1?!1:Oe(t,e)};/*!
diff --git a/assets/chunks/theme.4Aq0plHp.js b/assets/chunks/theme.Cq7NoE_k.js
similarity index 99%
rename from assets/chunks/theme.4Aq0plHp.js
rename to assets/chunks/theme.Cq7NoE_k.js
index 60774e7..1ab902d 100644
--- a/assets/chunks/theme.4Aq0plHp.js
+++ b/assets/chunks/theme.Cq7NoE_k.js
@@ -1,2 +1,2 @@
-const __vite__mapDeps=(i,m=__vite__mapDeps,d=(m.f||(m.f=["assets/chunks/VPLocalSearchBox.Lyrn-94G.js","assets/chunks/framework.DpC1ZpOZ.js"])))=>i.map(i=>d[i]);
-import{d as _,o as a,c,r as l,n as N,a as O,t as I,b as k,w as d,e as f,T as ve,_ as b,u as Ge,i as Ue,f as je,g as pe,h as y,j as v,k as r,p as C,l as H,m as K,q as ie,s as w,v as G,x as Z,y as W,z as he,A as fe,B as ze,C as qe,D as R,F as M,E,G as Pe,H as x,I as m,J as F,K as Ve,L as ee,M as q,N as te,O as Ke,P as Le,Q as le,R as We,S as Se,U as oe,V as Re,W as Je,X as Xe,Y as Te,Z as Ie,$ as Ye,a0 as Qe,a1 as Ze,a2 as xe,a3 as et}from"./framework.DpC1ZpOZ.js";const tt=_({__name:"VPBadge",props:{text:{},type:{default:"tip"}},setup(o){return(e,t)=>(a(),c("span",{class:N(["VPBadge",e.type])},[l(e.$slots,"default",{},()=>[O(I(e.text),1)])],2))}}),ot={key:0,class:"VPBackdrop"},nt=_({__name:"VPBackdrop",props:{show:{type:Boolean}},setup(o){return(e,t)=>(a(),k(ve,{name:"fade"},{default:d(()=>[e.show?(a(),c("div",ot)):f("",!0)]),_:1}))}}),st=b(nt,[["__scopeId","data-v-daa1937f"]]),P=Ge;function at(o,e){let t,s=!1;return()=>{t&&clearTimeout(t),s?t=setTimeout(o,e):(o(),(s=!0)&&setTimeout(()=>s=!1,e))}}function ce(o){return/^\//.test(o)?o:`/${o}`}function _e(o){const{pathname:e,search:t,hash:s,protocol:n}=new URL(o,"http://a.com");if(Ue(o)||o.startsWith("#")||!n.startsWith("http")||!je(e))return o;const{site:i}=P(),u=e.endsWith("/")||e.endsWith(".html")?o:o.replace(/(?:(^\.+)\/)?.*$/,`$1${e.replace(/(\.md)?$/,i.value.cleanUrls?"":".html")}${t}${s}`);return pe(u)}function X({correspondingLink:o=!1}={}){const{site:e,localeIndex:t,page:s,theme:n,hash:i}=P(),u=y(()=>{var p,g;return{label:(p=e.value.locales[t.value])==null?void 0:p.label,link:((g=e.value.locales[t.value])==null?void 0:g.link)||(t.value==="root"?"/":`/${t.value}/`)}});return{localeLinks:y(()=>Object.entries(e.value.locales).flatMap(([p,g])=>u.value.label===g.label?[]:{text:g.label,link:rt(g.link||(p==="root"?"/":`/${p}/`),n.value.i18nRouting!==!1&&o,s.value.relativePath.slice(u.value.link.length-1),!e.value.cleanUrls)+i.value})),currentLang:u}}function rt(o,e,t,s){return e?o.replace(/\/$/,"")+ce(t.replace(/(^|\/)index\.md$/,"$1").replace(/\.md$/,s?".html":"")):o}const it=o=>(C("data-v-2aa14331"),o=o(),H(),o),lt={class:"NotFound"},ct={class:"code"},ut={class:"title"},dt=it(()=>v("div",{class:"divider"},null,-1)),vt={class:"quote"},pt={class:"action"},ht=["href","aria-label"],ft=_({__name:"NotFound",setup(o){const{theme:e}=P(),{currentLang:t}=X();return(s,n)=>{var i,u,h,p,g;return a(),c("div",lt,[v("p",ct,I(((i=r(e).notFound)==null?void 0:i.code)??"404"),1),v("h1",ut,I(((u=r(e).notFound)==null?void 0:u.title)??"PAGE NOT FOUND"),1),dt,v("blockquote",vt,I(((h=r(e).notFound)==null?void 0:h.quote)??"But if you don't change your direction, and if you keep looking, you may end up where you are heading."),1),v("div",pt,[v("a",{class:"link",href:r(pe)(r(t).link),"aria-label":((p=r(e).notFound)==null?void 0:p.linkLabel)??"go to home"},I(((g=r(e).notFound)==null?void 0:g.linkText)??"Take me home"),9,ht)])])}}}),_t=b(ft,[["__scopeId","data-v-2aa14331"]]);function we(o,e){if(Array.isArray(o))return Y(o);if(o==null)return[];e=ce(e);const t=Object.keys(o).sort((n,i)=>i.split("/").length-n.split("/").length).find(n=>e.startsWith(ce(n))),s=t?o[t]:[];return Array.isArray(s)?Y(s):Y(s.items,s.base)}function mt(o){const e=[];let t=0;for(const s in o){const n=o[s];if(n.items){t=e.push(n);continue}e[t]||e.push({items:[]}),e[t].items.push(n)}return e}function kt(o){const e=[];function t(s){for(const n of s)n.text&&n.link&&e.push({text:n.text,link:n.link,docFooterText:n.docFooterText}),n.items&&t(n.items)}return t(o),e}function ue(o,e){return Array.isArray(e)?e.some(t=>ue(o,t)):K(o,e.link)?!0:e.items?ue(o,e.items):!1}function Y(o,e){return[...o].map(t=>{const s={...t},n=s.base||e;return n&&s.link&&(s.link=n+s.link),s.items&&(s.items=Y(s.items,n)),s})}function U(){const{frontmatter:o,page:e,theme:t}=P(),s=ie("(min-width: 960px)"),n=w(!1),i=y(()=>{const B=t.value.sidebar,S=e.value.relativePath;return B?we(B,S):[]}),u=w(i.value);G(i,(B,S)=>{JSON.stringify(B)!==JSON.stringify(S)&&(u.value=i.value)});const h=y(()=>o.value.sidebar!==!1&&u.value.length>0&&o.value.layout!=="home"),p=y(()=>g?o.value.aside==null?t.value.aside==="left":o.value.aside==="left":!1),g=y(()=>o.value.layout==="home"?!1:o.value.aside!=null?!!o.value.aside:t.value.aside!==!1),L=y(()=>h.value&&s.value),$=y(()=>h.value?mt(u.value):[]);function V(){n.value=!0}function T(){n.value=!1}function A(){n.value?T():V()}return{isOpen:n,sidebar:u,sidebarGroups:$,hasSidebar:h,hasAside:g,leftAside:p,isSidebarEnabled:L,open:V,close:T,toggle:A}}function $t(o,e){let t;Z(()=>{t=o.value?document.activeElement:void 0}),W(()=>{window.addEventListener("keyup",s)}),he(()=>{window.removeEventListener("keyup",s)});function s(n){n.key==="Escape"&&o.value&&(e(),t==null||t.focus())}}function bt(o){const{page:e,hash:t}=P(),s=w(!1),n=y(()=>o.value.collapsed!=null),i=y(()=>!!o.value.link),u=w(!1),h=()=>{u.value=K(e.value.relativePath,o.value.link)};G([e,o,t],h),W(h);const p=y(()=>u.value?!0:o.value.items?ue(e.value.relativePath,o.value.items):!1),g=y(()=>!!(o.value.items&&o.value.items.length));Z(()=>{s.value=!!(n.value&&o.value.collapsed)}),fe(()=>{(u.value||p.value)&&(s.value=!1)});function L(){n.value&&(s.value=!s.value)}return{collapsed:s,collapsible:n,isLink:i,isActiveLink:u,hasActiveLink:p,hasChildren:g,toggle:L}}function gt(){const{hasSidebar:o}=U(),e=ie("(min-width: 960px)"),t=ie("(min-width: 1280px)");return{isAsideEnabled:y(()=>!t.value&&!e.value?!1:o.value?t.value:e.value)}}const de=[];function Ne(o){return typeof o.outline=="object"&&!Array.isArray(o.outline)&&o.outline.label||o.outlineTitle||"On this page"}function me(o){const e=[...document.querySelectorAll(".VPDoc :where(h1,h2,h3,h4,h5,h6)")].filter(t=>t.id&&t.hasChildNodes()).map(t=>{const s=Number(t.tagName[1]);return{element:t,title:yt(t),link:"#"+t.id,level:s}});return Pt(e,o)}function yt(o){let e="";for(const t of o.childNodes)if(t.nodeType===1){if(t.classList.contains("VPBadge")||t.classList.contains("header-anchor")||t.classList.contains("ignore-header"))continue;e+=t.textContent}else t.nodeType===3&&(e+=t.textContent);return e.trim()}function Pt(o,e){if(e===!1)return[];const t=(typeof e=="object"&&!Array.isArray(e)?e.level:e)||2,[s,n]=typeof t=="number"?[t,t]:t==="deep"?[2,6]:t;o=o.filter(u=>u.level>=s&&u.level<=n),de.length=0;for(const{element:u,link:h}of o)de.push({element:u,link:h});const i=[];e:for(let u=0;u=0;p--){const g=o[p];if(g.level{requestAnimationFrame(i),window.addEventListener("scroll",s)}),ze(()=>{u(location.hash)}),he(()=>{window.removeEventListener("scroll",s)});function i(){if(!t.value)return;const h=window.scrollY,p=window.innerHeight,g=document.body.offsetHeight,L=Math.abs(h+p-g)<1,$=de.map(({element:T,link:A})=>({link:A,top:Lt(T)})).filter(({top:T})=>!Number.isNaN(T)).sort((T,A)=>T.top-A.top);if(!$.length){u(null);return}if(h<1){u(null);return}if(L){u($[$.length-1].link);return}let V=null;for(const{link:T,top:A}of $){if(A>h+qe()+4)break;V=T}u(V)}function u(h){n&&n.classList.remove("active"),h==null?n=null:n=o.value.querySelector(`a[href="${decodeURIComponent(h)}"]`);const p=n;p?(p.classList.add("active"),e.value.style.top=p.offsetTop+39+"px",e.value.style.opacity="1"):(e.value.style.top="33px",e.value.style.opacity="0")}}function Lt(o){let e=0;for(;o!==document.body;){if(o===null)return NaN;e+=o.offsetTop,o=o.offsetParent}return e}const St=["href","title"],Tt=_({__name:"VPDocOutlineItem",props:{headers:{},root:{type:Boolean}},setup(o){function e({target:t}){const s=t.href.split("#")[1],n=document.getElementById(decodeURIComponent(s));n==null||n.focus({preventScroll:!0})}return(t,s)=>{const n=R("VPDocOutlineItem",!0);return a(),c("ul",{class:N(["VPDocOutlineItem",t.root?"root":"nested"])},[(a(!0),c(M,null,E(t.headers,({children:i,link:u,title:h})=>(a(),c("li",null,[v("a",{class:"outline-link",href:u,onClick:e,title:h},I(h),9,St),i!=null&&i.length?(a(),k(n,{key:0,headers:i},null,8,["headers"])):f("",!0)]))),256))],2)}}}),Me=b(Tt,[["__scopeId","data-v-b9c884bb"]]),It={class:"content"},wt={"aria-level":"2",class:"outline-title",id:"doc-outline-aria-label",role:"heading"},Nt=_({__name:"VPDocAsideOutline",setup(o){const{frontmatter:e,theme:t}=P(),s=Pe([]);x(()=>{s.value=me(e.value.outline??t.value.outline)});const n=w(),i=w();return Vt(n,i),(u,h)=>(a(),c("nav",{"aria-labelledby":"doc-outline-aria-label",class:N(["VPDocAsideOutline",{"has-outline":s.value.length>0}]),ref_key:"container",ref:n},[v("div",It,[v("div",{class:"outline-marker",ref_key:"marker",ref:i},null,512),v("div",wt,I(r(Ne)(r(t))),1),m(Me,{headers:s.value,root:!0},null,8,["headers"])])],2))}}),Mt=b(Nt,[["__scopeId","data-v-d34649dc"]]),At={class:"VPDocAsideCarbonAds"},Bt=_({__name:"VPDocAsideCarbonAds",props:{carbonAds:{}},setup(o){const e=()=>null;return(t,s)=>(a(),c("div",At,[m(r(e),{"carbon-ads":t.carbonAds},null,8,["carbon-ads"])]))}}),Ct=o=>(C("data-v-8951c20f"),o=o(),H(),o),Ht={class:"VPDocAside"},Et=Ct(()=>v("div",{class:"spacer"},null,-1)),Ft=_({__name:"VPDocAside",setup(o){const{theme:e}=P();return(t,s)=>(a(),c("div",Ht,[l(t.$slots,"aside-top",{},void 0,!0),l(t.$slots,"aside-outline-before",{},void 0,!0),m(Mt),l(t.$slots,"aside-outline-after",{},void 0,!0),Et,l(t.$slots,"aside-ads-before",{},void 0,!0),r(e).carbonAds?(a(),k(Bt,{key:0,"carbon-ads":r(e).carbonAds},null,8,["carbon-ads"])):f("",!0),l(t.$slots,"aside-ads-after",{},void 0,!0),l(t.$slots,"aside-bottom",{},void 0,!0)]))}}),Dt=b(Ft,[["__scopeId","data-v-8951c20f"]]);function Ot(){const{theme:o,page:e}=P();return y(()=>{const{text:t="Edit this page",pattern:s=""}=o.value.editLink||{};let n;return typeof s=="function"?n=s(e.value):n=s.replace(/:path/g,e.value.filePath),{url:n,text:t}})}function Gt(){const{page:o,theme:e,frontmatter:t}=P();return y(()=>{var g,L,$,V,T,A,B,S;const s=we(e.value.sidebar,o.value.relativePath),n=kt(s),i=Ut(n,j=>j.link.replace(/[?#].*$/,"")),u=i.findIndex(j=>K(o.value.relativePath,j.link)),h=((g=e.value.docFooter)==null?void 0:g.prev)===!1&&!t.value.prev||t.value.prev===!1,p=((L=e.value.docFooter)==null?void 0:L.next)===!1&&!t.value.next||t.value.next===!1;return{prev:h?void 0:{text:(typeof t.value.prev=="string"?t.value.prev:typeof t.value.prev=="object"?t.value.prev.text:void 0)??(($=i[u-1])==null?void 0:$.docFooterText)??((V=i[u-1])==null?void 0:V.text),link:(typeof t.value.prev=="object"?t.value.prev.link:void 0)??((T=i[u-1])==null?void 0:T.link)},next:p?void 0:{text:(typeof t.value.next=="string"?t.value.next:typeof t.value.next=="object"?t.value.next.text:void 0)??((A=i[u+1])==null?void 0:A.docFooterText)??((B=i[u+1])==null?void 0:B.text),link:(typeof t.value.next=="object"?t.value.next.link:void 0)??((S=i[u+1])==null?void 0:S.link)}}})}function Ut(o,e){const t=new Set;return o.filter(s=>{const n=e(s);return t.has(n)?!1:t.add(n)})}const D=_({__name:"VPLink",props:{tag:{},href:{},noIcon:{type:Boolean},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.tag??(e.href?"a":"span")),s=y(()=>e.href&&Ve.test(e.href)||e.target==="_blank");return(n,i)=>(a(),k(F(t.value),{class:N(["VPLink",{link:n.href,"vp-external-link-icon":s.value,"no-icon":n.noIcon}]),href:n.href?r(_e)(n.href):void 0,target:n.target??(s.value?"_blank":void 0),rel:n.rel??(s.value?"noreferrer":void 0)},{default:d(()=>[l(n.$slots,"default")]),_:3},8,["class","href","target","rel"]))}}),jt={class:"VPLastUpdated"},zt=["datetime"],qt=_({__name:"VPDocFooterLastUpdated",setup(o){const{theme:e,page:t,lang:s}=P(),n=y(()=>new Date(t.value.lastUpdated)),i=y(()=>n.value.toISOString()),u=w("");return W(()=>{Z(()=>{var h,p,g;u.value=new Intl.DateTimeFormat((p=(h=e.value.lastUpdated)==null?void 0:h.formatOptions)!=null&&p.forceLocale?s.value:void 0,((g=e.value.lastUpdated)==null?void 0:g.formatOptions)??{dateStyle:"short",timeStyle:"short"}).format(n.value)})}),(h,p)=>{var g;return a(),c("p",jt,[O(I(((g=r(e).lastUpdated)==null?void 0:g.text)||r(e).lastUpdatedText||"Last updated")+": ",1),v("time",{datetime:i.value},I(u.value),9,zt)])}}}),Kt=b(qt,[["__scopeId","data-v-19bf19fb"]]),Ae=o=>(C("data-v-28deee4a"),o=o(),H(),o),Wt={key:0,class:"VPDocFooter"},Rt={key:0,class:"edit-info"},Jt={key:0,class:"edit-link"},Xt=Ae(()=>v("span",{class:"vpi-square-pen edit-link-icon"},null,-1)),Yt={key:1,class:"last-updated"},Qt={key:1,class:"prev-next","aria-labelledby":"doc-footer-aria-label"},Zt=Ae(()=>v("span",{class:"visually-hidden",id:"doc-footer-aria-label"},"Pager",-1)),xt={class:"pager"},eo=["innerHTML"],to=["innerHTML"],oo={class:"pager"},no=["innerHTML"],so=["innerHTML"],ao=_({__name:"VPDocFooter",setup(o){const{theme:e,page:t,frontmatter:s}=P(),n=Ot(),i=Gt(),u=y(()=>e.value.editLink&&s.value.editLink!==!1),h=y(()=>t.value.lastUpdated),p=y(()=>u.value||h.value||i.value.prev||i.value.next);return(g,L)=>{var $,V,T,A;return p.value?(a(),c("footer",Wt,[l(g.$slots,"doc-footer-before",{},void 0,!0),u.value||h.value?(a(),c("div",Rt,[u.value?(a(),c("div",Jt,[m(D,{class:"edit-link-button",href:r(n).url,"no-icon":!0},{default:d(()=>[Xt,O(" "+I(r(n).text),1)]),_:1},8,["href"])])):f("",!0),h.value?(a(),c("div",Yt,[m(Kt)])):f("",!0)])):f("",!0),($=r(i).prev)!=null&&$.link||(V=r(i).next)!=null&&V.link?(a(),c("nav",Qt,[Zt,v("div",xt,[(T=r(i).prev)!=null&&T.link?(a(),k(D,{key:0,class:"pager-link prev",href:r(i).prev.link},{default:d(()=>{var B;return[v("span",{class:"desc",innerHTML:((B=r(e).docFooter)==null?void 0:B.prev)||"Previous page"},null,8,eo),v("span",{class:"title",innerHTML:r(i).prev.text},null,8,to)]}),_:1},8,["href"])):f("",!0)]),v("div",oo,[(A=r(i).next)!=null&&A.link?(a(),k(D,{key:0,class:"pager-link next",href:r(i).next.link},{default:d(()=>{var B;return[v("span",{class:"desc",innerHTML:((B=r(e).docFooter)==null?void 0:B.next)||"Next page"},null,8,no),v("span",{class:"title",innerHTML:r(i).next.text},null,8,so)]}),_:1},8,["href"])):f("",!0)])])):f("",!0)])):f("",!0)}}}),ro=b(ao,[["__scopeId","data-v-28deee4a"]]),io=o=>(C("data-v-01c90815"),o=o(),H(),o),lo={class:"container"},co=io(()=>v("div",{class:"aside-curtain"},null,-1)),uo={class:"aside-container"},vo={class:"aside-content"},po={class:"content"},ho={class:"content-container"},fo={class:"main"},_o=_({__name:"VPDoc",setup(o){const{theme:e}=P(),t=ee(),{hasSidebar:s,hasAside:n,leftAside:i}=U(),u=y(()=>t.path.replace(/[./]+/g,"_").replace(/_html$/,""));return(h,p)=>{const g=R("Content");return a(),c("div",{class:N(["VPDoc",{"has-sidebar":r(s),"has-aside":r(n)}])},[l(h.$slots,"doc-top",{},void 0,!0),v("div",lo,[r(n)?(a(),c("div",{key:0,class:N(["aside",{"left-aside":r(i)}])},[co,v("div",uo,[v("div",vo,[m(Dt,null,{"aside-top":d(()=>[l(h.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":d(()=>[l(h.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":d(()=>[l(h.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":d(()=>[l(h.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":d(()=>[l(h.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":d(()=>[l(h.$slots,"aside-ads-after",{},void 0,!0)]),_:3})])])],2)):f("",!0),v("div",po,[v("div",ho,[l(h.$slots,"doc-before",{},void 0,!0),v("main",fo,[m(g,{class:N(["vp-doc",[u.value,r(e).externalLinkIcon&&"external-link-icon-enabled"]])},null,8,["class"])]),m(ro,null,{"doc-footer-before":d(()=>[l(h.$slots,"doc-footer-before",{},void 0,!0)]),_:3}),l(h.$slots,"doc-after",{},void 0,!0)])])]),l(h.$slots,"doc-bottom",{},void 0,!0)],2)}}}),mo=b(_o,[["__scopeId","data-v-01c90815"]]),ko=_({__name:"VPButton",props:{tag:{},size:{default:"medium"},theme:{default:"brand"},text:{},href:{},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.href&&Ve.test(e.href)),s=y(()=>e.tag||e.href?"a":"button");return(n,i)=>(a(),k(F(s.value),{class:N(["VPButton",[n.size,n.theme]]),href:n.href?r(_e)(n.href):void 0,target:e.target??(t.value?"_blank":void 0),rel:e.rel??(t.value?"noreferrer":void 0)},{default:d(()=>[O(I(n.text),1)]),_:1},8,["class","href","target","rel"]))}}),$o=b(ko,[["__scopeId","data-v-f549f0f3"]]),bo=["src","alt"],go=_({inheritAttrs:!1,__name:"VPImage",props:{image:{},alt:{}},setup(o){return(e,t)=>{const s=R("VPImage",!0);return e.image?(a(),c(M,{key:0},[typeof e.image=="string"||"src"in e.image?(a(),c("img",q({key:0,class:"VPImage"},typeof e.image=="string"?e.$attrs:{...e.image,...e.$attrs},{src:r(pe)(typeof e.image=="string"?e.image:e.image.src),alt:e.alt??(typeof e.image=="string"?"":e.image.alt||"")}),null,16,bo)):(a(),c(M,{key:1},[m(s,q({class:"dark",image:e.image.dark,alt:e.image.alt},e.$attrs),null,16,["image","alt"]),m(s,q({class:"light",image:e.image.light,alt:e.image.alt},e.$attrs),null,16,["image","alt"])],64))],64)):f("",!0)}}}),Q=b(go,[["__scopeId","data-v-cc63e071"]]),yo=o=>(C("data-v-e302b8ce"),o=o(),H(),o),Po={class:"container"},Vo={class:"main"},Lo={key:0,class:"name"},So=["innerHTML"],To=["innerHTML"],Io=["innerHTML"],wo={key:0,class:"actions"},No={key:0,class:"image"},Mo={class:"image-container"},Ao=yo(()=>v("div",{class:"image-bg"},null,-1)),Bo=_({__name:"VPHero",props:{name:{},text:{},tagline:{},image:{},actions:{}},setup(o){const e=te("hero-image-slot-exists");return(t,s)=>(a(),c("div",{class:N(["VPHero",{"has-image":t.image||r(e)}])},[v("div",Po,[v("div",Vo,[l(t.$slots,"home-hero-info-before",{},void 0,!0),l(t.$slots,"home-hero-info",{},()=>[t.name?(a(),c("h1",Lo,[v("span",{innerHTML:t.name,class:"clip"},null,8,So)])):f("",!0),t.text?(a(),c("p",{key:1,innerHTML:t.text,class:"text"},null,8,To)):f("",!0),t.tagline?(a(),c("p",{key:2,innerHTML:t.tagline,class:"tagline"},null,8,Io)):f("",!0)],!0),l(t.$slots,"home-hero-info-after",{},void 0,!0),t.actions?(a(),c("div",wo,[(a(!0),c(M,null,E(t.actions,n=>(a(),c("div",{key:n.link,class:"action"},[m($o,{tag:"a",size:"medium",theme:n.theme,text:n.text,href:n.link,target:n.target,rel:n.rel},null,8,["theme","text","href","target","rel"])]))),128))])):f("",!0),l(t.$slots,"home-hero-actions-after",{},void 0,!0)]),t.image||r(e)?(a(),c("div",No,[v("div",Mo,[Ao,l(t.$slots,"home-hero-image",{},()=>[t.image?(a(),k(Q,{key:0,class:"image-src",image:t.image},null,8,["image"])):f("",!0)],!0)])])):f("",!0)])],2))}}),Co=b(Bo,[["__scopeId","data-v-e302b8ce"]]),Ho=_({__name:"VPHomeHero",setup(o){const{frontmatter:e}=P();return(t,s)=>r(e).hero?(a(),k(Co,{key:0,class:"VPHomeHero",name:r(e).hero.name,text:r(e).hero.text,tagline:r(e).hero.tagline,image:r(e).hero.image,actions:r(e).hero.actions},{"home-hero-info-before":d(()=>[l(t.$slots,"home-hero-info-before")]),"home-hero-info":d(()=>[l(t.$slots,"home-hero-info")]),"home-hero-info-after":d(()=>[l(t.$slots,"home-hero-info-after")]),"home-hero-actions-after":d(()=>[l(t.$slots,"home-hero-actions-after")]),"home-hero-image":d(()=>[l(t.$slots,"home-hero-image")]),_:3},8,["name","text","tagline","image","actions"])):f("",!0)}}),Eo=o=>(C("data-v-f77e80b4"),o=o(),H(),o),Fo={class:"box"},Do={key:0,class:"icon"},Oo=["innerHTML"],Go=["innerHTML"],Uo=["innerHTML"],jo={key:4,class:"link-text"},zo={class:"link-text-value"},qo=Eo(()=>v("span",{class:"vpi-arrow-right link-text-icon"},null,-1)),Ko=_({__name:"VPFeature",props:{icon:{},title:{},details:{},link:{},linkText:{},rel:{},target:{}},setup(o){return(e,t)=>(a(),k(D,{class:"VPFeature",href:e.link,rel:e.rel,target:e.target,"no-icon":!0,tag:e.link?"a":"div"},{default:d(()=>[v("article",Fo,[typeof e.icon=="object"&&e.icon.wrap?(a(),c("div",Do,[m(Q,{image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])])):typeof e.icon=="object"?(a(),k(Q,{key:1,image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])):e.icon?(a(),c("div",{key:2,class:"icon",innerHTML:e.icon},null,8,Oo)):f("",!0),v("h2",{class:"title",innerHTML:e.title},null,8,Go),e.details?(a(),c("p",{key:3,class:"details",innerHTML:e.details},null,8,Uo)):f("",!0),e.linkText?(a(),c("div",jo,[v("p",zo,[O(I(e.linkText)+" ",1),qo])])):f("",!0)])]),_:1},8,["href","rel","target","tag"]))}}),Wo=b(Ko,[["__scopeId","data-v-f77e80b4"]]),Ro={key:0,class:"VPFeatures"},Jo={class:"container"},Xo={class:"items"},Yo=_({__name:"VPFeatures",props:{features:{}},setup(o){const e=o,t=y(()=>{const s=e.features.length;if(s){if(s===2)return"grid-2";if(s===3)return"grid-3";if(s%3===0)return"grid-6";if(s>3)return"grid-4"}else return});return(s,n)=>s.features?(a(),c("div",Ro,[v("div",Jo,[v("div",Xo,[(a(!0),c(M,null,E(s.features,i=>(a(),c("div",{key:i.title,class:N(["item",[t.value]])},[m(Wo,{icon:i.icon,title:i.title,details:i.details,link:i.link,"link-text":i.linkText,rel:i.rel,target:i.target},null,8,["icon","title","details","link","link-text","rel","target"])],2))),128))])])])):f("",!0)}}),Qo=b(Yo,[["__scopeId","data-v-8e833103"]]),Zo=_({__name:"VPHomeFeatures",setup(o){const{frontmatter:e}=P();return(t,s)=>r(e).features?(a(),k(Qo,{key:0,class:"VPHomeFeatures",features:r(e).features},null,8,["features"])):f("",!0)}}),xo=_({__name:"VPHomeContent",setup(o){const{width:e}=Ke({initialWidth:0,includeScrollbar:!1});return(t,s)=>(a(),c("div",{class:"vp-doc container",style:Le(r(e)?{"--vp-offset":`calc(50% - ${r(e)/2}px)`}:{})},[l(t.$slots,"default",{},void 0,!0)],4))}}),en=b(xo,[["__scopeId","data-v-90605523"]]),tn={class:"VPHome"},on=_({__name:"VPHome",setup(o){const{frontmatter:e}=P();return(t,s)=>{const n=R("Content");return a(),c("div",tn,[l(t.$slots,"home-hero-before",{},void 0,!0),m(Ho,null,{"home-hero-info-before":d(()=>[l(t.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":d(()=>[l(t.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":d(()=>[l(t.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":d(()=>[l(t.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":d(()=>[l(t.$slots,"home-hero-image",{},void 0,!0)]),_:3}),l(t.$slots,"home-hero-after",{},void 0,!0),l(t.$slots,"home-features-before",{},void 0,!0),m(Zo),l(t.$slots,"home-features-after",{},void 0,!0),r(e).markdownStyles!==!1?(a(),k(en,{key:0},{default:d(()=>[m(n)]),_:1})):(a(),k(n,{key:1}))])}}}),nn=b(on,[["__scopeId","data-v-55977d12"]]),sn={},an={class:"VPPage"};function rn(o,e){const t=R("Content");return a(),c("div",an,[l(o.$slots,"page-top"),m(t),l(o.$slots,"page-bottom")])}const ln=b(sn,[["render",rn]]),cn=_({__name:"VPContent",setup(o){const{page:e,frontmatter:t}=P(),{hasSidebar:s}=U();return(n,i)=>(a(),c("div",{class:N(["VPContent",{"has-sidebar":r(s),"is-home":r(t).layout==="home"}]),id:"VPContent"},[r(e).isNotFound?l(n.$slots,"not-found",{key:0},()=>[m(_t)],!0):r(t).layout==="page"?(a(),k(ln,{key:1},{"page-top":d(()=>[l(n.$slots,"page-top",{},void 0,!0)]),"page-bottom":d(()=>[l(n.$slots,"page-bottom",{},void 0,!0)]),_:3})):r(t).layout==="home"?(a(),k(nn,{key:2},{"home-hero-before":d(()=>[l(n.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":d(()=>[l(n.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":d(()=>[l(n.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":d(()=>[l(n.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":d(()=>[l(n.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":d(()=>[l(n.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":d(()=>[l(n.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":d(()=>[l(n.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":d(()=>[l(n.$slots,"home-features-after",{},void 0,!0)]),_:3})):r(t).layout&&r(t).layout!=="doc"?(a(),k(F(r(t).layout),{key:3})):(a(),k(mo,{key:4},{"doc-top":d(()=>[l(n.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":d(()=>[l(n.$slots,"doc-bottom",{},void 0,!0)]),"doc-footer-before":d(()=>[l(n.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":d(()=>[l(n.$slots,"doc-before",{},void 0,!0)]),"doc-after":d(()=>[l(n.$slots,"doc-after",{},void 0,!0)]),"aside-top":d(()=>[l(n.$slots,"aside-top",{},void 0,!0)]),"aside-outline-before":d(()=>[l(n.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":d(()=>[l(n.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":d(()=>[l(n.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":d(()=>[l(n.$slots,"aside-ads-after",{},void 0,!0)]),"aside-bottom":d(()=>[l(n.$slots,"aside-bottom",{},void 0,!0)]),_:3}))],2))}}),un=b(cn,[["__scopeId","data-v-fc04087f"]]),dn={class:"container"},vn=["innerHTML"],pn=["innerHTML"],hn=_({__name:"VPFooter",setup(o){const{theme:e,frontmatter:t}=P(),{hasSidebar:s}=U();return(n,i)=>r(e).footer&&r(t).footer!==!1?(a(),c("footer",{key:0,class:N(["VPFooter",{"has-sidebar":r(s)}])},[v("div",dn,[r(e).footer.message?(a(),c("p",{key:0,class:"message",innerHTML:r(e).footer.message},null,8,vn)):f("",!0),r(e).footer.copyright?(a(),c("p",{key:1,class:"copyright",innerHTML:r(e).footer.copyright},null,8,pn)):f("",!0)])],2)):f("",!0)}}),fn=b(hn,[["__scopeId","data-v-d69bcf5d"]]);function _n(){const{theme:o,frontmatter:e}=P(),t=Pe([]),s=y(()=>t.value.length>0);return x(()=>{t.value=me(e.value.outline??o.value.outline)}),{headers:t,hasLocalNav:s}}const mn=o=>(C("data-v-9dd5e197"),o=o(),H(),o),kn={class:"menu-text"},$n=mn(()=>v("span",{class:"vpi-chevron-right icon"},null,-1)),bn={class:"header"},gn={class:"outline"},yn=_({__name:"VPLocalNavOutlineDropdown",props:{headers:{},navHeight:{}},setup(o){const e=o,{theme:t}=P(),s=w(!1),n=w(0),i=w(),u=w();function h($){var V;(V=i.value)!=null&&V.contains($.target)||(s.value=!1)}G(s,$=>{if($){document.addEventListener("click",h);return}document.removeEventListener("click",h)}),le("Escape",()=>{s.value=!1}),x(()=>{s.value=!1});function p(){s.value=!s.value,n.value=window.innerHeight+Math.min(window.scrollY-e.navHeight,0)}function g($){$.target.classList.contains("outline-link")&&(u.value&&(u.value.style.transition="none"),We(()=>{s.value=!1}))}function L(){s.value=!1,window.scrollTo({top:0,left:0,behavior:"smooth"})}return($,V)=>(a(),c("div",{class:"VPLocalNavOutlineDropdown",style:Le({"--vp-vh":n.value+"px"}),ref_key:"main",ref:i},[$.headers.length>0?(a(),c("button",{key:0,onClick:p,class:N({open:s.value})},[v("span",kn,I(r(Ne)(r(t))),1),$n],2)):(a(),c("button",{key:1,onClick:L},I(r(t).returnToTopLabel||"Return to top"),1)),m(ve,{name:"flyout"},{default:d(()=>[s.value?(a(),c("div",{key:0,ref_key:"items",ref:u,class:"items",onClick:g},[v("div",bn,[v("a",{class:"top-link",href:"#",onClick:L},I(r(t).returnToTopLabel||"Return to top"),1)]),v("div",gn,[m(Me,{headers:$.headers},null,8,["headers"])])],512)):f("",!0)]),_:1})],4))}}),Pn=b(yn,[["__scopeId","data-v-9dd5e197"]]),Vn=o=>(C("data-v-9c649187"),o=o(),H(),o),Ln={class:"container"},Sn=["aria-expanded"],Tn=Vn(()=>v("span",{class:"vpi-align-left menu-icon"},null,-1)),In={class:"menu-text"},wn=_({__name:"VPLocalNav",props:{open:{type:Boolean}},emits:["open-menu"],setup(o){const{theme:e,frontmatter:t}=P(),{hasSidebar:s}=U(),{headers:n}=_n(),{y:i}=Se(),u=w(0);W(()=>{u.value=parseInt(getComputedStyle(document.documentElement).getPropertyValue("--vp-nav-height"))}),x(()=>{n.value=me(t.value.outline??e.value.outline)});const h=y(()=>n.value.length===0),p=y(()=>h.value&&!s.value),g=y(()=>({VPLocalNav:!0,"has-sidebar":s.value,empty:h.value,fixed:p.value}));return(L,$)=>r(t).layout!=="home"&&(!p.value||r(i)>=u.value)?(a(),c("div",{key:0,class:N(g.value)},[v("div",Ln,[r(s)?(a(),c("button",{key:0,class:"menu","aria-expanded":L.open,"aria-controls":"VPSidebarNav",onClick:$[0]||($[0]=V=>L.$emit("open-menu"))},[Tn,v("span",In,I(r(e).sidebarMenuLabel||"Menu"),1)],8,Sn)):f("",!0),m(Pn,{headers:r(n),navHeight:u.value},null,8,["headers","navHeight"])])],2)):f("",!0)}}),Nn=b(wn,[["__scopeId","data-v-9c649187"]]);function Mn(){const o=w(!1);function e(){o.value=!0,window.addEventListener("resize",n)}function t(){o.value=!1,window.removeEventListener("resize",n)}function s(){o.value?t():e()}function n(){window.outerWidth>=768&&t()}const i=ee();return G(()=>i.path,t),{isScreenOpen:o,openScreen:e,closeScreen:t,toggleScreen:s}}const An={},Bn={class:"VPSwitch",type:"button",role:"switch"},Cn={class:"check"},Hn={key:0,class:"icon"};function En(o,e){return a(),c("button",Bn,[v("span",Cn,[o.$slots.default?(a(),c("span",Hn,[l(o.$slots,"default",{},void 0,!0)])):f("",!0)])])}const Fn=b(An,[["render",En],["__scopeId","data-v-846fe538"]]),Be=o=>(C("data-v-3125216b"),o=o(),H(),o),Dn=Be(()=>v("span",{class:"vpi-sun sun"},null,-1)),On=Be(()=>v("span",{class:"vpi-moon moon"},null,-1)),Gn=_({__name:"VPSwitchAppearance",setup(o){const{isDark:e,theme:t}=P(),s=te("toggle-appearance",()=>{e.value=!e.value}),n=w("");return fe(()=>{n.value=e.value?t.value.lightModeSwitchTitle||"Switch to light theme":t.value.darkModeSwitchTitle||"Switch to dark theme"}),(i,u)=>(a(),k(Fn,{title:n.value,class:"VPSwitchAppearance","aria-checked":r(e),onClick:r(s)},{default:d(()=>[Dn,On]),_:1},8,["title","aria-checked","onClick"]))}}),ke=b(Gn,[["__scopeId","data-v-3125216b"]]),Un={key:0,class:"VPNavBarAppearance"},jn=_({__name:"VPNavBarAppearance",setup(o){const{site:e}=P();return(t,s)=>r(e).appearance&&r(e).appearance!=="force-dark"&&r(e).appearance!=="force-auto"?(a(),c("div",Un,[m(ke)])):f("",!0)}}),zn=b(jn,[["__scopeId","data-v-864d2abc"]]),$e=w();let Ce=!1,re=0;function qn(o){const e=w(!1);if(oe){!Ce&&Kn(),re++;const t=G($e,s=>{var n,i,u;s===o.el.value||(n=o.el.value)!=null&&n.contains(s)?(e.value=!0,(i=o.onFocus)==null||i.call(o)):(e.value=!1,(u=o.onBlur)==null||u.call(o))});he(()=>{t(),re--,re||Wn()})}return Re(e)}function Kn(){document.addEventListener("focusin",He),Ce=!0,$e.value=document.activeElement}function Wn(){document.removeEventListener("focusin",He)}function He(){$e.value=document.activeElement}const Rn={class:"VPMenuLink"},Jn=_({__name:"VPMenuLink",props:{item:{}},setup(o){const{page:e}=P();return(t,s)=>(a(),c("div",Rn,[m(D,{class:N({active:r(K)(r(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel},{default:d(()=>[O(I(t.item.text),1)]),_:1},8,["class","href","target","rel"])]))}}),ne=b(Jn,[["__scopeId","data-v-25a54821"]]),Xn={class:"VPMenuGroup"},Yn={key:0,class:"title"},Qn=_({__name:"VPMenuGroup",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),c("div",Xn,[e.text?(a(),c("p",Yn,I(e.text),1)):f("",!0),(a(!0),c(M,null,E(e.items,s=>(a(),c(M,null,["link"in s?(a(),k(ne,{key:0,item:s},null,8,["item"])):f("",!0)],64))),256))]))}}),Zn=b(Qn,[["__scopeId","data-v-4dd03e28"]]),xn={class:"VPMenu"},es={key:0,class:"items"},ts=_({__name:"VPMenu",props:{items:{}},setup(o){return(e,t)=>(a(),c("div",xn,[e.items?(a(),c("div",es,[(a(!0),c(M,null,E(e.items,s=>(a(),c(M,{key:JSON.stringify(s)},["link"in s?(a(),k(ne,{key:0,item:s},null,8,["item"])):"component"in s?(a(),k(F(s.component),q({key:1,ref_for:!0},s.props),null,16)):(a(),k(Zn,{key:2,text:s.text,items:s.items},null,8,["text","items"]))],64))),128))])):f("",!0),l(e.$slots,"default",{},void 0,!0)]))}}),os=b(ts,[["__scopeId","data-v-809b8af7"]]),ns=o=>(C("data-v-00660109"),o=o(),H(),o),ss=["aria-expanded","aria-label"],as={key:0,class:"text"},rs=["innerHTML"],is=ns(()=>v("span",{class:"vpi-chevron-down text-icon"},null,-1)),ls={key:1,class:"vpi-more-horizontal icon"},cs={class:"menu"},us=_({__name:"VPFlyout",props:{icon:{},button:{},label:{},items:{}},setup(o){const e=w(!1),t=w();qn({el:t,onBlur:s});function s(){e.value=!1}return(n,i)=>(a(),c("div",{class:"VPFlyout",ref_key:"el",ref:t,onMouseenter:i[1]||(i[1]=u=>e.value=!0),onMouseleave:i[2]||(i[2]=u=>e.value=!1)},[v("button",{type:"button",class:"button","aria-haspopup":"true","aria-expanded":e.value,"aria-label":n.label,onClick:i[0]||(i[0]=u=>e.value=!e.value)},[n.button||n.icon?(a(),c("span",as,[n.icon?(a(),c("span",{key:0,class:N([n.icon,"option-icon"])},null,2)):f("",!0),n.button?(a(),c("span",{key:1,innerHTML:n.button},null,8,rs)):f("",!0),is])):(a(),c("span",ls))],8,ss),v("div",cs,[m(os,{items:n.items},{default:d(()=>[l(n.$slots,"default",{},void 0,!0)]),_:3},8,["items"])])],544))}}),be=b(us,[["__scopeId","data-v-00660109"]]),ds=["href","aria-label","innerHTML"],vs=_({__name:"VPSocialLink",props:{icon:{},link:{},ariaLabel:{}},setup(o){const e=o,t=y(()=>typeof e.icon=="object"?e.icon.svg:``);return(s,n)=>(a(),c("a",{class:"VPSocialLink no-icon",href:s.link,"aria-label":s.ariaLabel??(typeof s.icon=="string"?s.icon:""),target:"_blank",rel:"noopener",innerHTML:t.value},null,8,ds))}}),ps=b(vs,[["__scopeId","data-v-15a5c40e"]]),hs={class:"VPSocialLinks"},fs=_({__name:"VPSocialLinks",props:{links:{}},setup(o){return(e,t)=>(a(),c("div",hs,[(a(!0),c(M,null,E(e.links,({link:s,icon:n,ariaLabel:i})=>(a(),k(ps,{key:s,icon:n,link:s,ariaLabel:i},null,8,["icon","link","ariaLabel"]))),128))]))}}),ge=b(fs,[["__scopeId","data-v-100434c4"]]),_s={key:0,class:"group translations"},ms={class:"trans-title"},ks={key:1,class:"group"},$s={class:"item appearance"},bs={class:"label"},gs={class:"appearance-action"},ys={key:2,class:"group"},Ps={class:"item social-links"},Vs=_({__name:"VPNavBarExtra",setup(o){const{site:e,theme:t}=P(),{localeLinks:s,currentLang:n}=X({correspondingLink:!0}),i=y(()=>s.value.length&&n.value.label||e.value.appearance||t.value.socialLinks);return(u,h)=>i.value?(a(),k(be,{key:0,class:"VPNavBarExtra",label:"extra navigation"},{default:d(()=>[r(s).length&&r(n).label?(a(),c("div",_s,[v("p",ms,I(r(n).label),1),(a(!0),c(M,null,E(r(s),p=>(a(),k(ne,{key:p.link,item:p},null,8,["item"]))),128))])):f("",!0),r(e).appearance&&r(e).appearance!=="force-dark"&&r(e).appearance!=="force-auto"?(a(),c("div",ks,[v("div",$s,[v("p",bs,I(r(t).darkModeSwitchLabel||"Appearance"),1),v("div",gs,[m(ke)])])])):f("",!0),r(t).socialLinks?(a(),c("div",ys,[v("div",Ps,[m(ge,{class:"social-links-list",links:r(t).socialLinks},null,8,["links"])])])):f("",!0)]),_:1})):f("",!0)}}),Ls=b(Vs,[["__scopeId","data-v-60cefd62"]]),Ss=o=>(C("data-v-e047a1f2"),o=o(),H(),o),Ts=["aria-expanded"],Is=Ss(()=>v("span",{class:"container"},[v("span",{class:"top"}),v("span",{class:"middle"}),v("span",{class:"bottom"})],-1)),ws=[Is],Ns=_({__name:"VPNavBarHamburger",props:{active:{type:Boolean}},emits:["click"],setup(o){return(e,t)=>(a(),c("button",{type:"button",class:N(["VPNavBarHamburger",{active:e.active}]),"aria-label":"mobile navigation","aria-expanded":e.active,"aria-controls":"VPNavScreen",onClick:t[0]||(t[0]=s=>e.$emit("click"))},ws,10,Ts))}}),Ms=b(Ns,[["__scopeId","data-v-e047a1f2"]]),As=["innerHTML"],Bs=_({__name:"VPNavBarMenuLink",props:{item:{}},setup(o){const{page:e}=P();return(t,s)=>(a(),k(D,{class:N({VPNavBarMenuLink:!0,active:r(K)(r(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,noIcon:t.item.noIcon,target:t.item.target,rel:t.item.rel,tabindex:"0"},{default:d(()=>[v("span",{innerHTML:t.item.text},null,8,As)]),_:1},8,["class","href","noIcon","target","rel"]))}}),Cs=b(Bs,[["__scopeId","data-v-9a0da802"]]),Hs=_({__name:"VPNavBarMenuGroup",props:{item:{}},setup(o){const e=o,{page:t}=P(),s=i=>"component"in i?!1:"link"in i?K(t.value.relativePath,i.link,!!e.item.activeMatch):i.items.some(s),n=y(()=>s(e.item));return(i,u)=>(a(),k(be,{class:N({VPNavBarMenuGroup:!0,active:r(K)(r(t).relativePath,i.item.activeMatch,!!i.item.activeMatch)||n.value}),button:i.item.text,items:i.item.items},null,8,["class","button","items"]))}}),Es=o=>(C("data-v-bf53b681"),o=o(),H(),o),Fs={key:0,"aria-labelledby":"main-nav-aria-label",class:"VPNavBarMenu"},Ds=Es(()=>v("span",{id:"main-nav-aria-label",class:"visually-hidden"}," Main Navigation ",-1)),Os=_({__name:"VPNavBarMenu",setup(o){const{theme:e}=P();return(t,s)=>r(e).nav?(a(),c("nav",Fs,[Ds,(a(!0),c(M,null,E(r(e).nav,n=>(a(),c(M,{key:JSON.stringify(n)},["link"in n?(a(),k(Cs,{key:0,item:n},null,8,["item"])):"component"in n?(a(),k(F(n.component),q({key:1,ref_for:!0},n.props),null,16)):(a(),k(Hs,{key:2,item:n},null,8,["item"]))],64))),128))])):f("",!0)}}),Gs=b(Os,[["__scopeId","data-v-bf53b681"]]);function Us(o){const{localeIndex:e,theme:t}=P();function s(n){var A,B,S;const i=n.split("."),u=(A=t.value.search)==null?void 0:A.options,h=u&&typeof u=="object",p=h&&((S=(B=u.locales)==null?void 0:B[e.value])==null?void 0:S.translations)||null,g=h&&u.translations||null;let L=p,$=g,V=o;const T=i.pop();for(const j of i){let z=null;const J=V==null?void 0:V[j];J&&(z=V=J);const se=$==null?void 0:$[j];se&&(z=$=se);const ae=L==null?void 0:L[j];ae&&(z=L=ae),J||(V=z),se||($=z),ae||(L=z)}return(L==null?void 0:L[T])??($==null?void 0:$[T])??(V==null?void 0:V[T])??""}return s}const js=["aria-label"],zs={class:"DocSearch-Button-Container"},qs=v("span",{class:"vp-icon DocSearch-Search-Icon"},null,-1),Ks={class:"DocSearch-Button-Placeholder"},Ws=v("span",{class:"DocSearch-Button-Keys"},[v("kbd",{class:"DocSearch-Button-Key"}),v("kbd",{class:"DocSearch-Button-Key"},"K")],-1),ye=_({__name:"VPNavBarSearchButton",setup(o){const t=Us({button:{buttonText:"Search",buttonAriaLabel:"Search"}});return(s,n)=>(a(),c("button",{type:"button",class:"DocSearch DocSearch-Button","aria-label":r(t)("button.buttonAriaLabel")},[v("span",zs,[qs,v("span",Ks,I(r(t)("button.buttonText")),1)]),Ws],8,js))}}),Rs={class:"VPNavBarSearch"},Js={id:"local-search"},Xs={key:1,id:"docsearch"},Ys=_({__name:"VPNavBarSearch",setup(o){const e=Je(()=>Xe(()=>import("./VPLocalSearchBox.Lyrn-94G.js"),__vite__mapDeps([0,1]))),t=()=>null,{theme:s}=P(),n=w(!1),i=w(!1);W(()=>{});function u(){n.value||(n.value=!0,setTimeout(h,16))}function h(){const $=new Event("keydown");$.key="k",$.metaKey=!0,window.dispatchEvent($),setTimeout(()=>{document.querySelector(".DocSearch-Modal")||h()},16)}function p($){const V=$.target,T=V.tagName;return V.isContentEditable||T==="INPUT"||T==="SELECT"||T==="TEXTAREA"}const g=w(!1);le("k",$=>{($.ctrlKey||$.metaKey)&&($.preventDefault(),g.value=!0)}),le("/",$=>{p($)||($.preventDefault(),g.value=!0)});const L="local";return($,V)=>{var T;return a(),c("div",Rs,[r(L)==="local"?(a(),c(M,{key:0},[g.value?(a(),k(r(e),{key:0,onClose:V[0]||(V[0]=A=>g.value=!1)})):f("",!0),v("div",Js,[m(ye,{onClick:V[1]||(V[1]=A=>g.value=!0)})])],64)):r(L)==="algolia"?(a(),c(M,{key:1},[n.value?(a(),k(r(t),{key:0,algolia:((T=r(s).search)==null?void 0:T.options)??r(s).algolia,onVnodeBeforeMount:V[2]||(V[2]=A=>i.value=!0)},null,8,["algolia"])):f("",!0),i.value?f("",!0):(a(),c("div",Xs,[m(ye,{onClick:u})]))],64)):f("",!0)])}}}),Qs=_({__name:"VPNavBarSocialLinks",setup(o){const{theme:e}=P();return(t,s)=>r(e).socialLinks?(a(),k(ge,{key:0,class:"VPNavBarSocialLinks",links:r(e).socialLinks},null,8,["links"])):f("",!0)}}),Zs=b(Qs,[["__scopeId","data-v-2c606308"]]),xs=["href","rel","target"],ea={key:1},ta={key:2},oa=_({__name:"VPNavBarTitle",setup(o){const{site:e,theme:t}=P(),{hasSidebar:s}=U(),{currentLang:n}=X(),i=y(()=>{var p;return typeof t.value.logoLink=="string"?t.value.logoLink:(p=t.value.logoLink)==null?void 0:p.link}),u=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.rel}),h=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.target});return(p,g)=>(a(),c("div",{class:N(["VPNavBarTitle",{"has-sidebar":r(s)}])},[v("a",{class:"title",href:i.value??r(_e)(r(n).link),rel:u.value,target:h.value},[l(p.$slots,"nav-bar-title-before",{},void 0,!0),r(t).logo?(a(),k(Q,{key:0,class:"logo",image:r(t).logo},null,8,["image"])):f("",!0),r(t).siteTitle?(a(),c("span",ea,I(r(t).siteTitle),1)):r(t).siteTitle===void 0?(a(),c("span",ta,I(r(e).title),1)):f("",!0),l(p.$slots,"nav-bar-title-after",{},void 0,!0)],8,xs)],2))}}),na=b(oa,[["__scopeId","data-v-606a7e0f"]]),sa={class:"items"},aa={class:"title"},ra=_({__name:"VPNavBarTranslations",setup(o){const{theme:e}=P(),{localeLinks:t,currentLang:s}=X({correspondingLink:!0});return(n,i)=>r(t).length&&r(s).label?(a(),k(be,{key:0,class:"VPNavBarTranslations",icon:"vpi-languages",label:r(e).langMenuLabel||"Change language"},{default:d(()=>[v("div",sa,[v("p",aa,I(r(s).label),1),(a(!0),c(M,null,E(r(t),u=>(a(),k(ne,{key:u.link,item:u},null,8,["item"]))),128))])]),_:1},8,["label"])):f("",!0)}}),ia=b(ra,[["__scopeId","data-v-912817b1"]]),la=o=>(C("data-v-da0688be"),o=o(),H(),o),ca={class:"wrapper"},ua={class:"container"},da={class:"title"},va={class:"content"},pa={class:"content-body"},ha=la(()=>v("div",{class:"divider"},[v("div",{class:"divider-line"})],-1)),fa=_({__name:"VPNavBar",props:{isScreenOpen:{type:Boolean}},emits:["toggle-screen"],setup(o){const e=o,{y:t}=Se(),{hasSidebar:s}=U(),{frontmatter:n}=P(),i=w({});return fe(()=>{i.value={"has-sidebar":s.value,home:n.value.layout==="home",top:t.value===0,"screen-open":e.isScreenOpen}}),(u,h)=>(a(),c("div",{class:N(["VPNavBar",i.value])},[v("div",ca,[v("div",ua,[v("div",da,[m(na,null,{"nav-bar-title-before":d(()=>[l(u.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":d(()=>[l(u.$slots,"nav-bar-title-after",{},void 0,!0)]),_:3})]),v("div",va,[v("div",pa,[l(u.$slots,"nav-bar-content-before",{},void 0,!0),m(Ys,{class:"search"}),m(Gs,{class:"menu"}),m(ia,{class:"translations"}),m(zn,{class:"appearance"}),m(Zs,{class:"social-links"}),m(Ls,{class:"extra"}),l(u.$slots,"nav-bar-content-after",{},void 0,!0),m(Ms,{class:"hamburger",active:u.isScreenOpen,onClick:h[0]||(h[0]=p=>u.$emit("toggle-screen"))},null,8,["active"])])])])]),ha],2))}}),_a=b(fa,[["__scopeId","data-v-da0688be"]]),ma={key:0,class:"VPNavScreenAppearance"},ka={class:"text"},$a=_({__name:"VPNavScreenAppearance",setup(o){const{site:e,theme:t}=P();return(s,n)=>r(e).appearance&&r(e).appearance!=="force-dark"&&r(e).appearance!=="force-auto"?(a(),c("div",ma,[v("p",ka,I(r(t).darkModeSwitchLabel||"Appearance"),1),m(ke)])):f("",!0)}}),ba=b($a,[["__scopeId","data-v-dfcc1536"]]),ga=_({__name:"VPNavScreenMenuLink",props:{item:{}},setup(o){const e=te("close-screen");return(t,s)=>(a(),k(D,{class:"VPNavScreenMenuLink",href:t.item.link,target:t.item.target,rel:t.item.rel,onClick:r(e),innerHTML:t.item.text},null,8,["href","target","rel","onClick","innerHTML"]))}}),ya=b(ga,[["__scopeId","data-v-8cd41455"]]),Pa=_({__name:"VPNavScreenMenuGroupLink",props:{item:{}},setup(o){const e=te("close-screen");return(t,s)=>(a(),k(D,{class:"VPNavScreenMenuGroupLink",href:t.item.link,target:t.item.target,rel:t.item.rel,onClick:r(e)},{default:d(()=>[O(I(t.item.text),1)]),_:1},8,["href","target","rel","onClick"]))}}),Ee=b(Pa,[["__scopeId","data-v-b8c7c580"]]),Va={class:"VPNavScreenMenuGroupSection"},La={key:0,class:"title"},Sa=_({__name:"VPNavScreenMenuGroupSection",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),c("div",Va,[e.text?(a(),c("p",La,I(e.text),1)):f("",!0),(a(!0),c(M,null,E(e.items,s=>(a(),k(Ee,{key:s.text,item:s},null,8,["item"]))),128))]))}}),Ta=b(Sa,[["__scopeId","data-v-a3e7a51c"]]),Ia=o=>(C("data-v-90f695a2"),o=o(),H(),o),wa=["aria-controls","aria-expanded"],Na=["innerHTML"],Ma=Ia(()=>v("span",{class:"vpi-plus button-icon"},null,-1)),Aa=["id"],Ba={key:0,class:"item"},Ca={key:1,class:"item"},Ha={key:2,class:"group"},Ea=_({__name:"VPNavScreenMenuGroup",props:{text:{},items:{}},setup(o){const e=o,t=w(!1),s=y(()=>`NavScreenGroup-${e.text.replace(" ","-").toLowerCase()}`);function n(){t.value=!t.value}return(i,u)=>(a(),c("div",{class:N(["VPNavScreenMenuGroup",{open:t.value}])},[v("button",{class:"button","aria-controls":s.value,"aria-expanded":t.value,onClick:n},[v("span",{class:"button-text",innerHTML:i.text},null,8,Na),Ma],8,wa),v("div",{id:s.value,class:"items"},[(a(!0),c(M,null,E(i.items,h=>(a(),c(M,{key:JSON.stringify(h)},["link"in h?(a(),c("div",Ba,[m(Ee,{item:h},null,8,["item"])])):"component"in h?(a(),c("div",Ca,[(a(),k(F(h.component),q({ref_for:!0},h.props,{"screen-menu":""}),null,16))])):(a(),c("div",Ha,[m(Ta,{text:h.text,items:h.items},null,8,["text","items"])]))],64))),128))],8,Aa)],2))}}),Fa=b(Ea,[["__scopeId","data-v-90f695a2"]]),Da={key:0,class:"VPNavScreenMenu"},Oa=_({__name:"VPNavScreenMenu",setup(o){const{theme:e}=P();return(t,s)=>r(e).nav?(a(),c("nav",Da,[(a(!0),c(M,null,E(r(e).nav,n=>(a(),c(M,{key:JSON.stringify(n)},["link"in n?(a(),k(ya,{key:0,item:n},null,8,["item"])):"component"in n?(a(),k(F(n.component),q({key:1,ref_for:!0},n.props,{"screen-menu":""}),null,16)):(a(),k(Fa,{key:2,text:n.text||"",items:n.items},null,8,["text","items"]))],64))),128))])):f("",!0)}}),Ga=_({__name:"VPNavScreenSocialLinks",setup(o){const{theme:e}=P();return(t,s)=>r(e).socialLinks?(a(),k(ge,{key:0,class:"VPNavScreenSocialLinks",links:r(e).socialLinks},null,8,["links"])):f("",!0)}}),Fe=o=>(C("data-v-95c61444"),o=o(),H(),o),Ua=Fe(()=>v("span",{class:"vpi-languages icon lang"},null,-1)),ja=Fe(()=>v("span",{class:"vpi-chevron-down icon chevron"},null,-1)),za={class:"list"},qa=_({__name:"VPNavScreenTranslations",setup(o){const{localeLinks:e,currentLang:t}=X({correspondingLink:!0}),s=w(!1);function n(){s.value=!s.value}return(i,u)=>r(e).length&&r(t).label?(a(),c("div",{key:0,class:N(["VPNavScreenTranslations",{open:s.value}])},[v("button",{class:"title",onClick:n},[Ua,O(" "+I(r(t).label)+" ",1),ja]),v("ul",za,[(a(!0),c(M,null,E(r(e),h=>(a(),c("li",{key:h.link,class:"item"},[m(D,{class:"link",href:h.link},{default:d(()=>[O(I(h.text),1)]),_:2},1032,["href"])]))),128))])],2)):f("",!0)}}),Ka=b(qa,[["__scopeId","data-v-95c61444"]]),Wa={class:"container"},Ra=_({__name:"VPNavScreen",props:{open:{type:Boolean}},setup(o){const e=w(null),t=Te(oe?document.body:null);return(s,n)=>(a(),k(ve,{name:"fade",onEnter:n[0]||(n[0]=i=>t.value=!0),onAfterLeave:n[1]||(n[1]=i=>t.value=!1)},{default:d(()=>[s.open?(a(),c("div",{key:0,class:"VPNavScreen",ref_key:"screen",ref:e,id:"VPNavScreen"},[v("div",Wa,[l(s.$slots,"nav-screen-content-before",{},void 0,!0),m(Oa,{class:"menu"}),m(Ka,{class:"translations"}),m(ba,{class:"appearance"}),m(Ga,{class:"social-links"}),l(s.$slots,"nav-screen-content-after",{},void 0,!0)])],512)):f("",!0)]),_:3}))}}),Ja=b(Ra,[["__scopeId","data-v-c14c1e21"]]),Xa={key:0,class:"VPNav"},Ya=_({__name:"VPNav",setup(o){const{isScreenOpen:e,closeScreen:t,toggleScreen:s}=Mn(),{frontmatter:n}=P(),i=y(()=>n.value.navbar!==!1);return Ie("close-screen",t),Z(()=>{oe&&document.documentElement.classList.toggle("hide-nav",!i.value)}),(u,h)=>i.value?(a(),c("header",Xa,[m(_a,{"is-screen-open":r(e),onToggleScreen:r(s)},{"nav-bar-title-before":d(()=>[l(u.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":d(()=>[l(u.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":d(()=>[l(u.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":d(()=>[l(u.$slots,"nav-bar-content-after",{},void 0,!0)]),_:3},8,["is-screen-open","onToggleScreen"]),m(Ja,{open:r(e)},{"nav-screen-content-before":d(()=>[l(u.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":d(()=>[l(u.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3},8,["open"])])):f("",!0)}}),Qa=b(Ya,[["__scopeId","data-v-e823d444"]]),De=o=>(C("data-v-a9cdba99"),o=o(),H(),o),Za=["role","tabindex"],xa=De(()=>v("div",{class:"indicator"},null,-1)),er=De(()=>v("span",{class:"vpi-chevron-right caret-icon"},null,-1)),tr=[er],or={key:1,class:"items"},nr=_({__name:"VPSidebarItem",props:{item:{},depth:{}},setup(o){const e=o,{collapsed:t,collapsible:s,isLink:n,isActiveLink:i,hasActiveLink:u,hasChildren:h,toggle:p}=bt(y(()=>e.item)),g=y(()=>h.value?"section":"div"),L=y(()=>n.value?"a":"div"),$=y(()=>h.value?e.depth+2===7?"p":`h${e.depth+2}`:"p"),V=y(()=>n.value?void 0:"button"),T=y(()=>[[`level-${e.depth}`],{collapsible:s.value},{collapsed:t.value},{"is-link":n.value},{"is-active":i.value},{"has-active":u.value}]);function A(S){"key"in S&&S.key!=="Enter"||!e.item.link&&p()}function B(){e.item.link&&p()}return(S,j)=>{const z=R("VPSidebarItem",!0);return a(),k(F(g.value),{class:N(["VPSidebarItem",T.value])},{default:d(()=>[S.item.text?(a(),c("div",q({key:0,class:"item",role:V.value},Qe(S.item.items?{click:A,keydown:A}:{},!0),{tabindex:S.item.items&&0}),[xa,S.item.link?(a(),k(D,{key:0,tag:L.value,class:"link",href:S.item.link,rel:S.item.rel,target:S.item.target},{default:d(()=>[(a(),k(F($.value),{class:"text",innerHTML:S.item.text},null,8,["innerHTML"]))]),_:1},8,["tag","href","rel","target"])):(a(),k(F($.value),{key:1,class:"text",innerHTML:S.item.text},null,8,["innerHTML"])),S.item.collapsed!=null&&S.item.items&&S.item.items.length?(a(),c("div",{key:2,class:"caret",role:"button","aria-label":"toggle section",onClick:B,onKeydown:Ye(B,["enter"]),tabindex:"0"},tr,32)):f("",!0)],16,Za)):f("",!0),S.item.items&&S.item.items.length?(a(),c("div",or,[S.depth<5?(a(!0),c(M,{key:0},E(S.item.items,J=>(a(),k(z,{key:J.text,item:J,depth:S.depth+1},null,8,["item","depth"]))),128)):f("",!0)])):f("",!0)]),_:1},8,["class"])}}}),sr=b(nr,[["__scopeId","data-v-a9cdba99"]]),ar=_({__name:"VPSidebarGroup",props:{items:{}},setup(o){const e=w(!0);let t=null;return W(()=>{t=setTimeout(()=>{t=null,e.value=!1},300)}),Ze(()=>{t!=null&&(clearTimeout(t),t=null)}),(s,n)=>(a(!0),c(M,null,E(s.items,i=>(a(),c("div",{key:i.text,class:N(["group",{"no-transition":e.value}])},[m(sr,{item:i,depth:0},null,8,["item"])],2))),128))}}),rr=b(ar,[["__scopeId","data-v-72c67ed4"]]),Oe=o=>(C("data-v-59ceefa4"),o=o(),H(),o),ir=Oe(()=>v("div",{class:"curtain"},null,-1)),lr={class:"nav",id:"VPSidebarNav","aria-labelledby":"sidebar-aria-label",tabindex:"-1"},cr=Oe(()=>v("span",{class:"visually-hidden",id:"sidebar-aria-label"}," Sidebar Navigation ",-1)),ur=_({__name:"VPSidebar",props:{open:{type:Boolean}},setup(o){const{sidebarGroups:e,hasSidebar:t}=U(),s=o,n=w(null),i=Te(oe?document.body:null);G([s,n],()=>{var h;s.open?(i.value=!0,(h=n.value)==null||h.focus()):i.value=!1},{immediate:!0,flush:"post"});const u=w(0);return G(e,()=>{u.value+=1},{deep:!0}),(h,p)=>r(t)?(a(),c("aside",{key:0,class:N(["VPSidebar",{open:h.open}]),ref_key:"navEl",ref:n,onClick:p[0]||(p[0]=xe(()=>{},["stop"]))},[ir,v("nav",lr,[cr,l(h.$slots,"sidebar-nav-before",{},void 0,!0),(a(),k(rr,{items:r(e),key:u.value},null,8,["items"])),l(h.$slots,"sidebar-nav-after",{},void 0,!0)])],2)):f("",!0)}}),dr=b(ur,[["__scopeId","data-v-59ceefa4"]]),vr=_({__name:"VPSkipLink",setup(o){const e=ee(),t=w();G(()=>e.path,()=>t.value.focus());function s({target:n}){const i=document.getElementById(decodeURIComponent(n.hash).slice(1));if(i){const u=()=>{i.removeAttribute("tabindex"),i.removeEventListener("blur",u)};i.setAttribute("tabindex","-1"),i.addEventListener("blur",u),i.focus(),window.scrollTo(0,0)}}return(n,i)=>(a(),c(M,null,[v("span",{ref_key:"backToTop",ref:t,tabindex:"-1"},null,512),v("a",{href:"#VPContent",class:"VPSkipLink visually-hidden",onClick:s}," Skip to content ")],64))}}),pr=b(vr,[["__scopeId","data-v-e813112c"]]),hr=_({__name:"Layout",setup(o){const{isOpen:e,open:t,close:s}=U(),n=ee();G(()=>n.path,s),$t(e,s);const{frontmatter:i}=P(),u=et(),h=y(()=>!!u["home-hero-image"]);return Ie("hero-image-slot-exists",h),(p,g)=>{const L=R("Content");return r(i).layout!==!1?(a(),c("div",{key:0,class:N(["Layout",r(i).pageClass])},[l(p.$slots,"layout-top",{},void 0,!0),m(pr),m(st,{class:"backdrop",show:r(e),onClick:r(s)},null,8,["show","onClick"]),m(Qa,null,{"nav-bar-title-before":d(()=>[l(p.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":d(()=>[l(p.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":d(()=>[l(p.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":d(()=>[l(p.$slots,"nav-bar-content-after",{},void 0,!0)]),"nav-screen-content-before":d(()=>[l(p.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":d(()=>[l(p.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3}),m(Nn,{open:r(e),onOpenMenu:r(t)},null,8,["open","onOpenMenu"]),m(dr,{open:r(e)},{"sidebar-nav-before":d(()=>[l(p.$slots,"sidebar-nav-before",{},void 0,!0)]),"sidebar-nav-after":d(()=>[l(p.$slots,"sidebar-nav-after",{},void 0,!0)]),_:3},8,["open"]),m(un,null,{"page-top":d(()=>[l(p.$slots,"page-top",{},void 0,!0)]),"page-bottom":d(()=>[l(p.$slots,"page-bottom",{},void 0,!0)]),"not-found":d(()=>[l(p.$slots,"not-found",{},void 0,!0)]),"home-hero-before":d(()=>[l(p.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":d(()=>[l(p.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":d(()=>[l(p.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":d(()=>[l(p.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":d(()=>[l(p.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":d(()=>[l(p.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":d(()=>[l(p.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":d(()=>[l(p.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":d(()=>[l(p.$slots,"home-features-after",{},void 0,!0)]),"doc-footer-before":d(()=>[l(p.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":d(()=>[l(p.$slots,"doc-before",{},void 0,!0)]),"doc-after":d(()=>[l(p.$slots,"doc-after",{},void 0,!0)]),"doc-top":d(()=>[l(p.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":d(()=>[l(p.$slots,"doc-bottom",{},void 0,!0)]),"aside-top":d(()=>[l(p.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":d(()=>[l(p.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":d(()=>[l(p.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":d(()=>[l(p.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":d(()=>[l(p.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":d(()=>[l(p.$slots,"aside-ads-after",{},void 0,!0)]),_:3}),m(fn),l(p.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),k(L,{key:1}))}}}),fr=b(hr,[["__scopeId","data-v-3b4648ff"]]),mr={Layout:fr,enhanceApp:({app:o})=>{o.component("Badge",tt)}};export{Us as c,mr as t,P as u};
+const __vite__mapDeps=(i,m=__vite__mapDeps,d=(m.f||(m.f=["assets/chunks/VPLocalSearchBox.DhHzxM_l.js","assets/chunks/framework.DpC1ZpOZ.js"])))=>i.map(i=>d[i]);
+import{d as _,o as a,c,r as l,n as N,a as O,t as I,b as k,w as d,e as f,T as ve,_ as b,u as Ge,i as Ue,f as je,g as pe,h as y,j as v,k as r,p as C,l as H,m as K,q as ie,s as w,v as G,x as Z,y as W,z as he,A as fe,B as ze,C as qe,D as R,F as M,E,G as Pe,H as x,I as m,J as F,K as Ve,L as ee,M as q,N as te,O as Ke,P as Le,Q as le,R as We,S as Se,U as oe,V as Re,W as Je,X as Xe,Y as Te,Z as Ie,$ as Ye,a0 as Qe,a1 as Ze,a2 as xe,a3 as et}from"./framework.DpC1ZpOZ.js";const tt=_({__name:"VPBadge",props:{text:{},type:{default:"tip"}},setup(o){return(e,t)=>(a(),c("span",{class:N(["VPBadge",e.type])},[l(e.$slots,"default",{},()=>[O(I(e.text),1)])],2))}}),ot={key:0,class:"VPBackdrop"},nt=_({__name:"VPBackdrop",props:{show:{type:Boolean}},setup(o){return(e,t)=>(a(),k(ve,{name:"fade"},{default:d(()=>[e.show?(a(),c("div",ot)):f("",!0)]),_:1}))}}),st=b(nt,[["__scopeId","data-v-daa1937f"]]),P=Ge;function at(o,e){let t,s=!1;return()=>{t&&clearTimeout(t),s?t=setTimeout(o,e):(o(),(s=!0)&&setTimeout(()=>s=!1,e))}}function ce(o){return/^\//.test(o)?o:`/${o}`}function _e(o){const{pathname:e,search:t,hash:s,protocol:n}=new URL(o,"http://a.com");if(Ue(o)||o.startsWith("#")||!n.startsWith("http")||!je(e))return o;const{site:i}=P(),u=e.endsWith("/")||e.endsWith(".html")?o:o.replace(/(?:(^\.+)\/)?.*$/,`$1${e.replace(/(\.md)?$/,i.value.cleanUrls?"":".html")}${t}${s}`);return pe(u)}function X({correspondingLink:o=!1}={}){const{site:e,localeIndex:t,page:s,theme:n,hash:i}=P(),u=y(()=>{var p,g;return{label:(p=e.value.locales[t.value])==null?void 0:p.label,link:((g=e.value.locales[t.value])==null?void 0:g.link)||(t.value==="root"?"/":`/${t.value}/`)}});return{localeLinks:y(()=>Object.entries(e.value.locales).flatMap(([p,g])=>u.value.label===g.label?[]:{text:g.label,link:rt(g.link||(p==="root"?"/":`/${p}/`),n.value.i18nRouting!==!1&&o,s.value.relativePath.slice(u.value.link.length-1),!e.value.cleanUrls)+i.value})),currentLang:u}}function rt(o,e,t,s){return e?o.replace(/\/$/,"")+ce(t.replace(/(^|\/)index\.md$/,"$1").replace(/\.md$/,s?".html":"")):o}const it=o=>(C("data-v-2aa14331"),o=o(),H(),o),lt={class:"NotFound"},ct={class:"code"},ut={class:"title"},dt=it(()=>v("div",{class:"divider"},null,-1)),vt={class:"quote"},pt={class:"action"},ht=["href","aria-label"],ft=_({__name:"NotFound",setup(o){const{theme:e}=P(),{currentLang:t}=X();return(s,n)=>{var i,u,h,p,g;return a(),c("div",lt,[v("p",ct,I(((i=r(e).notFound)==null?void 0:i.code)??"404"),1),v("h1",ut,I(((u=r(e).notFound)==null?void 0:u.title)??"PAGE NOT FOUND"),1),dt,v("blockquote",vt,I(((h=r(e).notFound)==null?void 0:h.quote)??"But if you don't change your direction, and if you keep looking, you may end up where you are heading."),1),v("div",pt,[v("a",{class:"link",href:r(pe)(r(t).link),"aria-label":((p=r(e).notFound)==null?void 0:p.linkLabel)??"go to home"},I(((g=r(e).notFound)==null?void 0:g.linkText)??"Take me home"),9,ht)])])}}}),_t=b(ft,[["__scopeId","data-v-2aa14331"]]);function we(o,e){if(Array.isArray(o))return Y(o);if(o==null)return[];e=ce(e);const t=Object.keys(o).sort((n,i)=>i.split("/").length-n.split("/").length).find(n=>e.startsWith(ce(n))),s=t?o[t]:[];return Array.isArray(s)?Y(s):Y(s.items,s.base)}function mt(o){const e=[];let t=0;for(const s in o){const n=o[s];if(n.items){t=e.push(n);continue}e[t]||e.push({items:[]}),e[t].items.push(n)}return e}function kt(o){const e=[];function t(s){for(const n of s)n.text&&n.link&&e.push({text:n.text,link:n.link,docFooterText:n.docFooterText}),n.items&&t(n.items)}return t(o),e}function ue(o,e){return Array.isArray(e)?e.some(t=>ue(o,t)):K(o,e.link)?!0:e.items?ue(o,e.items):!1}function Y(o,e){return[...o].map(t=>{const s={...t},n=s.base||e;return n&&s.link&&(s.link=n+s.link),s.items&&(s.items=Y(s.items,n)),s})}function U(){const{frontmatter:o,page:e,theme:t}=P(),s=ie("(min-width: 960px)"),n=w(!1),i=y(()=>{const B=t.value.sidebar,S=e.value.relativePath;return B?we(B,S):[]}),u=w(i.value);G(i,(B,S)=>{JSON.stringify(B)!==JSON.stringify(S)&&(u.value=i.value)});const h=y(()=>o.value.sidebar!==!1&&u.value.length>0&&o.value.layout!=="home"),p=y(()=>g?o.value.aside==null?t.value.aside==="left":o.value.aside==="left":!1),g=y(()=>o.value.layout==="home"?!1:o.value.aside!=null?!!o.value.aside:t.value.aside!==!1),L=y(()=>h.value&&s.value),$=y(()=>h.value?mt(u.value):[]);function V(){n.value=!0}function T(){n.value=!1}function A(){n.value?T():V()}return{isOpen:n,sidebar:u,sidebarGroups:$,hasSidebar:h,hasAside:g,leftAside:p,isSidebarEnabled:L,open:V,close:T,toggle:A}}function $t(o,e){let t;Z(()=>{t=o.value?document.activeElement:void 0}),W(()=>{window.addEventListener("keyup",s)}),he(()=>{window.removeEventListener("keyup",s)});function s(n){n.key==="Escape"&&o.value&&(e(),t==null||t.focus())}}function bt(o){const{page:e,hash:t}=P(),s=w(!1),n=y(()=>o.value.collapsed!=null),i=y(()=>!!o.value.link),u=w(!1),h=()=>{u.value=K(e.value.relativePath,o.value.link)};G([e,o,t],h),W(h);const p=y(()=>u.value?!0:o.value.items?ue(e.value.relativePath,o.value.items):!1),g=y(()=>!!(o.value.items&&o.value.items.length));Z(()=>{s.value=!!(n.value&&o.value.collapsed)}),fe(()=>{(u.value||p.value)&&(s.value=!1)});function L(){n.value&&(s.value=!s.value)}return{collapsed:s,collapsible:n,isLink:i,isActiveLink:u,hasActiveLink:p,hasChildren:g,toggle:L}}function gt(){const{hasSidebar:o}=U(),e=ie("(min-width: 960px)"),t=ie("(min-width: 1280px)");return{isAsideEnabled:y(()=>!t.value&&!e.value?!1:o.value?t.value:e.value)}}const de=[];function Ne(o){return typeof o.outline=="object"&&!Array.isArray(o.outline)&&o.outline.label||o.outlineTitle||"On this page"}function me(o){const e=[...document.querySelectorAll(".VPDoc :where(h1,h2,h3,h4,h5,h6)")].filter(t=>t.id&&t.hasChildNodes()).map(t=>{const s=Number(t.tagName[1]);return{element:t,title:yt(t),link:"#"+t.id,level:s}});return Pt(e,o)}function yt(o){let e="";for(const t of o.childNodes)if(t.nodeType===1){if(t.classList.contains("VPBadge")||t.classList.contains("header-anchor")||t.classList.contains("ignore-header"))continue;e+=t.textContent}else t.nodeType===3&&(e+=t.textContent);return e.trim()}function Pt(o,e){if(e===!1)return[];const t=(typeof e=="object"&&!Array.isArray(e)?e.level:e)||2,[s,n]=typeof t=="number"?[t,t]:t==="deep"?[2,6]:t;o=o.filter(u=>u.level>=s&&u.level<=n),de.length=0;for(const{element:u,link:h}of o)de.push({element:u,link:h});const i=[];e:for(let u=0;u=0;p--){const g=o[p];if(g.level{requestAnimationFrame(i),window.addEventListener("scroll",s)}),ze(()=>{u(location.hash)}),he(()=>{window.removeEventListener("scroll",s)});function i(){if(!t.value)return;const h=window.scrollY,p=window.innerHeight,g=document.body.offsetHeight,L=Math.abs(h+p-g)<1,$=de.map(({element:T,link:A})=>({link:A,top:Lt(T)})).filter(({top:T})=>!Number.isNaN(T)).sort((T,A)=>T.top-A.top);if(!$.length){u(null);return}if(h<1){u(null);return}if(L){u($[$.length-1].link);return}let V=null;for(const{link:T,top:A}of $){if(A>h+qe()+4)break;V=T}u(V)}function u(h){n&&n.classList.remove("active"),h==null?n=null:n=o.value.querySelector(`a[href="${decodeURIComponent(h)}"]`);const p=n;p?(p.classList.add("active"),e.value.style.top=p.offsetTop+39+"px",e.value.style.opacity="1"):(e.value.style.top="33px",e.value.style.opacity="0")}}function Lt(o){let e=0;for(;o!==document.body;){if(o===null)return NaN;e+=o.offsetTop,o=o.offsetParent}return e}const St=["href","title"],Tt=_({__name:"VPDocOutlineItem",props:{headers:{},root:{type:Boolean}},setup(o){function e({target:t}){const s=t.href.split("#")[1],n=document.getElementById(decodeURIComponent(s));n==null||n.focus({preventScroll:!0})}return(t,s)=>{const n=R("VPDocOutlineItem",!0);return a(),c("ul",{class:N(["VPDocOutlineItem",t.root?"root":"nested"])},[(a(!0),c(M,null,E(t.headers,({children:i,link:u,title:h})=>(a(),c("li",null,[v("a",{class:"outline-link",href:u,onClick:e,title:h},I(h),9,St),i!=null&&i.length?(a(),k(n,{key:0,headers:i},null,8,["headers"])):f("",!0)]))),256))],2)}}}),Me=b(Tt,[["__scopeId","data-v-b9c884bb"]]),It={class:"content"},wt={"aria-level":"2",class:"outline-title",id:"doc-outline-aria-label",role:"heading"},Nt=_({__name:"VPDocAsideOutline",setup(o){const{frontmatter:e,theme:t}=P(),s=Pe([]);x(()=>{s.value=me(e.value.outline??t.value.outline)});const n=w(),i=w();return Vt(n,i),(u,h)=>(a(),c("nav",{"aria-labelledby":"doc-outline-aria-label",class:N(["VPDocAsideOutline",{"has-outline":s.value.length>0}]),ref_key:"container",ref:n},[v("div",It,[v("div",{class:"outline-marker",ref_key:"marker",ref:i},null,512),v("div",wt,I(r(Ne)(r(t))),1),m(Me,{headers:s.value,root:!0},null,8,["headers"])])],2))}}),Mt=b(Nt,[["__scopeId","data-v-d34649dc"]]),At={class:"VPDocAsideCarbonAds"},Bt=_({__name:"VPDocAsideCarbonAds",props:{carbonAds:{}},setup(o){const e=()=>null;return(t,s)=>(a(),c("div",At,[m(r(e),{"carbon-ads":t.carbonAds},null,8,["carbon-ads"])]))}}),Ct=o=>(C("data-v-8951c20f"),o=o(),H(),o),Ht={class:"VPDocAside"},Et=Ct(()=>v("div",{class:"spacer"},null,-1)),Ft=_({__name:"VPDocAside",setup(o){const{theme:e}=P();return(t,s)=>(a(),c("div",Ht,[l(t.$slots,"aside-top",{},void 0,!0),l(t.$slots,"aside-outline-before",{},void 0,!0),m(Mt),l(t.$slots,"aside-outline-after",{},void 0,!0),Et,l(t.$slots,"aside-ads-before",{},void 0,!0),r(e).carbonAds?(a(),k(Bt,{key:0,"carbon-ads":r(e).carbonAds},null,8,["carbon-ads"])):f("",!0),l(t.$slots,"aside-ads-after",{},void 0,!0),l(t.$slots,"aside-bottom",{},void 0,!0)]))}}),Dt=b(Ft,[["__scopeId","data-v-8951c20f"]]);function Ot(){const{theme:o,page:e}=P();return y(()=>{const{text:t="Edit this page",pattern:s=""}=o.value.editLink||{};let n;return typeof s=="function"?n=s(e.value):n=s.replace(/:path/g,e.value.filePath),{url:n,text:t}})}function Gt(){const{page:o,theme:e,frontmatter:t}=P();return y(()=>{var g,L,$,V,T,A,B,S;const s=we(e.value.sidebar,o.value.relativePath),n=kt(s),i=Ut(n,j=>j.link.replace(/[?#].*$/,"")),u=i.findIndex(j=>K(o.value.relativePath,j.link)),h=((g=e.value.docFooter)==null?void 0:g.prev)===!1&&!t.value.prev||t.value.prev===!1,p=((L=e.value.docFooter)==null?void 0:L.next)===!1&&!t.value.next||t.value.next===!1;return{prev:h?void 0:{text:(typeof t.value.prev=="string"?t.value.prev:typeof t.value.prev=="object"?t.value.prev.text:void 0)??(($=i[u-1])==null?void 0:$.docFooterText)??((V=i[u-1])==null?void 0:V.text),link:(typeof t.value.prev=="object"?t.value.prev.link:void 0)??((T=i[u-1])==null?void 0:T.link)},next:p?void 0:{text:(typeof t.value.next=="string"?t.value.next:typeof t.value.next=="object"?t.value.next.text:void 0)??((A=i[u+1])==null?void 0:A.docFooterText)??((B=i[u+1])==null?void 0:B.text),link:(typeof t.value.next=="object"?t.value.next.link:void 0)??((S=i[u+1])==null?void 0:S.link)}}})}function Ut(o,e){const t=new Set;return o.filter(s=>{const n=e(s);return t.has(n)?!1:t.add(n)})}const D=_({__name:"VPLink",props:{tag:{},href:{},noIcon:{type:Boolean},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.tag??(e.href?"a":"span")),s=y(()=>e.href&&Ve.test(e.href)||e.target==="_blank");return(n,i)=>(a(),k(F(t.value),{class:N(["VPLink",{link:n.href,"vp-external-link-icon":s.value,"no-icon":n.noIcon}]),href:n.href?r(_e)(n.href):void 0,target:n.target??(s.value?"_blank":void 0),rel:n.rel??(s.value?"noreferrer":void 0)},{default:d(()=>[l(n.$slots,"default")]),_:3},8,["class","href","target","rel"]))}}),jt={class:"VPLastUpdated"},zt=["datetime"],qt=_({__name:"VPDocFooterLastUpdated",setup(o){const{theme:e,page:t,lang:s}=P(),n=y(()=>new Date(t.value.lastUpdated)),i=y(()=>n.value.toISOString()),u=w("");return W(()=>{Z(()=>{var h,p,g;u.value=new Intl.DateTimeFormat((p=(h=e.value.lastUpdated)==null?void 0:h.formatOptions)!=null&&p.forceLocale?s.value:void 0,((g=e.value.lastUpdated)==null?void 0:g.formatOptions)??{dateStyle:"short",timeStyle:"short"}).format(n.value)})}),(h,p)=>{var g;return a(),c("p",jt,[O(I(((g=r(e).lastUpdated)==null?void 0:g.text)||r(e).lastUpdatedText||"Last updated")+": ",1),v("time",{datetime:i.value},I(u.value),9,zt)])}}}),Kt=b(qt,[["__scopeId","data-v-19bf19fb"]]),Ae=o=>(C("data-v-28deee4a"),o=o(),H(),o),Wt={key:0,class:"VPDocFooter"},Rt={key:0,class:"edit-info"},Jt={key:0,class:"edit-link"},Xt=Ae(()=>v("span",{class:"vpi-square-pen edit-link-icon"},null,-1)),Yt={key:1,class:"last-updated"},Qt={key:1,class:"prev-next","aria-labelledby":"doc-footer-aria-label"},Zt=Ae(()=>v("span",{class:"visually-hidden",id:"doc-footer-aria-label"},"Pager",-1)),xt={class:"pager"},eo=["innerHTML"],to=["innerHTML"],oo={class:"pager"},no=["innerHTML"],so=["innerHTML"],ao=_({__name:"VPDocFooter",setup(o){const{theme:e,page:t,frontmatter:s}=P(),n=Ot(),i=Gt(),u=y(()=>e.value.editLink&&s.value.editLink!==!1),h=y(()=>t.value.lastUpdated),p=y(()=>u.value||h.value||i.value.prev||i.value.next);return(g,L)=>{var $,V,T,A;return p.value?(a(),c("footer",Wt,[l(g.$slots,"doc-footer-before",{},void 0,!0),u.value||h.value?(a(),c("div",Rt,[u.value?(a(),c("div",Jt,[m(D,{class:"edit-link-button",href:r(n).url,"no-icon":!0},{default:d(()=>[Xt,O(" "+I(r(n).text),1)]),_:1},8,["href"])])):f("",!0),h.value?(a(),c("div",Yt,[m(Kt)])):f("",!0)])):f("",!0),($=r(i).prev)!=null&&$.link||(V=r(i).next)!=null&&V.link?(a(),c("nav",Qt,[Zt,v("div",xt,[(T=r(i).prev)!=null&&T.link?(a(),k(D,{key:0,class:"pager-link prev",href:r(i).prev.link},{default:d(()=>{var B;return[v("span",{class:"desc",innerHTML:((B=r(e).docFooter)==null?void 0:B.prev)||"Previous page"},null,8,eo),v("span",{class:"title",innerHTML:r(i).prev.text},null,8,to)]}),_:1},8,["href"])):f("",!0)]),v("div",oo,[(A=r(i).next)!=null&&A.link?(a(),k(D,{key:0,class:"pager-link next",href:r(i).next.link},{default:d(()=>{var B;return[v("span",{class:"desc",innerHTML:((B=r(e).docFooter)==null?void 0:B.next)||"Next page"},null,8,no),v("span",{class:"title",innerHTML:r(i).next.text},null,8,so)]}),_:1},8,["href"])):f("",!0)])])):f("",!0)])):f("",!0)}}}),ro=b(ao,[["__scopeId","data-v-28deee4a"]]),io=o=>(C("data-v-01c90815"),o=o(),H(),o),lo={class:"container"},co=io(()=>v("div",{class:"aside-curtain"},null,-1)),uo={class:"aside-container"},vo={class:"aside-content"},po={class:"content"},ho={class:"content-container"},fo={class:"main"},_o=_({__name:"VPDoc",setup(o){const{theme:e}=P(),t=ee(),{hasSidebar:s,hasAside:n,leftAside:i}=U(),u=y(()=>t.path.replace(/[./]+/g,"_").replace(/_html$/,""));return(h,p)=>{const g=R("Content");return a(),c("div",{class:N(["VPDoc",{"has-sidebar":r(s),"has-aside":r(n)}])},[l(h.$slots,"doc-top",{},void 0,!0),v("div",lo,[r(n)?(a(),c("div",{key:0,class:N(["aside",{"left-aside":r(i)}])},[co,v("div",uo,[v("div",vo,[m(Dt,null,{"aside-top":d(()=>[l(h.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":d(()=>[l(h.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":d(()=>[l(h.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":d(()=>[l(h.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":d(()=>[l(h.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":d(()=>[l(h.$slots,"aside-ads-after",{},void 0,!0)]),_:3})])])],2)):f("",!0),v("div",po,[v("div",ho,[l(h.$slots,"doc-before",{},void 0,!0),v("main",fo,[m(g,{class:N(["vp-doc",[u.value,r(e).externalLinkIcon&&"external-link-icon-enabled"]])},null,8,["class"])]),m(ro,null,{"doc-footer-before":d(()=>[l(h.$slots,"doc-footer-before",{},void 0,!0)]),_:3}),l(h.$slots,"doc-after",{},void 0,!0)])])]),l(h.$slots,"doc-bottom",{},void 0,!0)],2)}}}),mo=b(_o,[["__scopeId","data-v-01c90815"]]),ko=_({__name:"VPButton",props:{tag:{},size:{default:"medium"},theme:{default:"brand"},text:{},href:{},target:{},rel:{}},setup(o){const e=o,t=y(()=>e.href&&Ve.test(e.href)),s=y(()=>e.tag||e.href?"a":"button");return(n,i)=>(a(),k(F(s.value),{class:N(["VPButton",[n.size,n.theme]]),href:n.href?r(_e)(n.href):void 0,target:e.target??(t.value?"_blank":void 0),rel:e.rel??(t.value?"noreferrer":void 0)},{default:d(()=>[O(I(n.text),1)]),_:1},8,["class","href","target","rel"]))}}),$o=b(ko,[["__scopeId","data-v-f549f0f3"]]),bo=["src","alt"],go=_({inheritAttrs:!1,__name:"VPImage",props:{image:{},alt:{}},setup(o){return(e,t)=>{const s=R("VPImage",!0);return e.image?(a(),c(M,{key:0},[typeof e.image=="string"||"src"in e.image?(a(),c("img",q({key:0,class:"VPImage"},typeof e.image=="string"?e.$attrs:{...e.image,...e.$attrs},{src:r(pe)(typeof e.image=="string"?e.image:e.image.src),alt:e.alt??(typeof e.image=="string"?"":e.image.alt||"")}),null,16,bo)):(a(),c(M,{key:1},[m(s,q({class:"dark",image:e.image.dark,alt:e.image.alt},e.$attrs),null,16,["image","alt"]),m(s,q({class:"light",image:e.image.light,alt:e.image.alt},e.$attrs),null,16,["image","alt"])],64))],64)):f("",!0)}}}),Q=b(go,[["__scopeId","data-v-cc63e071"]]),yo=o=>(C("data-v-e302b8ce"),o=o(),H(),o),Po={class:"container"},Vo={class:"main"},Lo={key:0,class:"name"},So=["innerHTML"],To=["innerHTML"],Io=["innerHTML"],wo={key:0,class:"actions"},No={key:0,class:"image"},Mo={class:"image-container"},Ao=yo(()=>v("div",{class:"image-bg"},null,-1)),Bo=_({__name:"VPHero",props:{name:{},text:{},tagline:{},image:{},actions:{}},setup(o){const e=te("hero-image-slot-exists");return(t,s)=>(a(),c("div",{class:N(["VPHero",{"has-image":t.image||r(e)}])},[v("div",Po,[v("div",Vo,[l(t.$slots,"home-hero-info-before",{},void 0,!0),l(t.$slots,"home-hero-info",{},()=>[t.name?(a(),c("h1",Lo,[v("span",{innerHTML:t.name,class:"clip"},null,8,So)])):f("",!0),t.text?(a(),c("p",{key:1,innerHTML:t.text,class:"text"},null,8,To)):f("",!0),t.tagline?(a(),c("p",{key:2,innerHTML:t.tagline,class:"tagline"},null,8,Io)):f("",!0)],!0),l(t.$slots,"home-hero-info-after",{},void 0,!0),t.actions?(a(),c("div",wo,[(a(!0),c(M,null,E(t.actions,n=>(a(),c("div",{key:n.link,class:"action"},[m($o,{tag:"a",size:"medium",theme:n.theme,text:n.text,href:n.link,target:n.target,rel:n.rel},null,8,["theme","text","href","target","rel"])]))),128))])):f("",!0),l(t.$slots,"home-hero-actions-after",{},void 0,!0)]),t.image||r(e)?(a(),c("div",No,[v("div",Mo,[Ao,l(t.$slots,"home-hero-image",{},()=>[t.image?(a(),k(Q,{key:0,class:"image-src",image:t.image},null,8,["image"])):f("",!0)],!0)])])):f("",!0)])],2))}}),Co=b(Bo,[["__scopeId","data-v-e302b8ce"]]),Ho=_({__name:"VPHomeHero",setup(o){const{frontmatter:e}=P();return(t,s)=>r(e).hero?(a(),k(Co,{key:0,class:"VPHomeHero",name:r(e).hero.name,text:r(e).hero.text,tagline:r(e).hero.tagline,image:r(e).hero.image,actions:r(e).hero.actions},{"home-hero-info-before":d(()=>[l(t.$slots,"home-hero-info-before")]),"home-hero-info":d(()=>[l(t.$slots,"home-hero-info")]),"home-hero-info-after":d(()=>[l(t.$slots,"home-hero-info-after")]),"home-hero-actions-after":d(()=>[l(t.$slots,"home-hero-actions-after")]),"home-hero-image":d(()=>[l(t.$slots,"home-hero-image")]),_:3},8,["name","text","tagline","image","actions"])):f("",!0)}}),Eo=o=>(C("data-v-f77e80b4"),o=o(),H(),o),Fo={class:"box"},Do={key:0,class:"icon"},Oo=["innerHTML"],Go=["innerHTML"],Uo=["innerHTML"],jo={key:4,class:"link-text"},zo={class:"link-text-value"},qo=Eo(()=>v("span",{class:"vpi-arrow-right link-text-icon"},null,-1)),Ko=_({__name:"VPFeature",props:{icon:{},title:{},details:{},link:{},linkText:{},rel:{},target:{}},setup(o){return(e,t)=>(a(),k(D,{class:"VPFeature",href:e.link,rel:e.rel,target:e.target,"no-icon":!0,tag:e.link?"a":"div"},{default:d(()=>[v("article",Fo,[typeof e.icon=="object"&&e.icon.wrap?(a(),c("div",Do,[m(Q,{image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])])):typeof e.icon=="object"?(a(),k(Q,{key:1,image:e.icon,alt:e.icon.alt,height:e.icon.height||48,width:e.icon.width||48},null,8,["image","alt","height","width"])):e.icon?(a(),c("div",{key:2,class:"icon",innerHTML:e.icon},null,8,Oo)):f("",!0),v("h2",{class:"title",innerHTML:e.title},null,8,Go),e.details?(a(),c("p",{key:3,class:"details",innerHTML:e.details},null,8,Uo)):f("",!0),e.linkText?(a(),c("div",jo,[v("p",zo,[O(I(e.linkText)+" ",1),qo])])):f("",!0)])]),_:1},8,["href","rel","target","tag"]))}}),Wo=b(Ko,[["__scopeId","data-v-f77e80b4"]]),Ro={key:0,class:"VPFeatures"},Jo={class:"container"},Xo={class:"items"},Yo=_({__name:"VPFeatures",props:{features:{}},setup(o){const e=o,t=y(()=>{const s=e.features.length;if(s){if(s===2)return"grid-2";if(s===3)return"grid-3";if(s%3===0)return"grid-6";if(s>3)return"grid-4"}else return});return(s,n)=>s.features?(a(),c("div",Ro,[v("div",Jo,[v("div",Xo,[(a(!0),c(M,null,E(s.features,i=>(a(),c("div",{key:i.title,class:N(["item",[t.value]])},[m(Wo,{icon:i.icon,title:i.title,details:i.details,link:i.link,"link-text":i.linkText,rel:i.rel,target:i.target},null,8,["icon","title","details","link","link-text","rel","target"])],2))),128))])])])):f("",!0)}}),Qo=b(Yo,[["__scopeId","data-v-8e833103"]]),Zo=_({__name:"VPHomeFeatures",setup(o){const{frontmatter:e}=P();return(t,s)=>r(e).features?(a(),k(Qo,{key:0,class:"VPHomeFeatures",features:r(e).features},null,8,["features"])):f("",!0)}}),xo=_({__name:"VPHomeContent",setup(o){const{width:e}=Ke({initialWidth:0,includeScrollbar:!1});return(t,s)=>(a(),c("div",{class:"vp-doc container",style:Le(r(e)?{"--vp-offset":`calc(50% - ${r(e)/2}px)`}:{})},[l(t.$slots,"default",{},void 0,!0)],4))}}),en=b(xo,[["__scopeId","data-v-90605523"]]),tn={class:"VPHome"},on=_({__name:"VPHome",setup(o){const{frontmatter:e}=P();return(t,s)=>{const n=R("Content");return a(),c("div",tn,[l(t.$slots,"home-hero-before",{},void 0,!0),m(Ho,null,{"home-hero-info-before":d(()=>[l(t.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":d(()=>[l(t.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":d(()=>[l(t.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":d(()=>[l(t.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":d(()=>[l(t.$slots,"home-hero-image",{},void 0,!0)]),_:3}),l(t.$slots,"home-hero-after",{},void 0,!0),l(t.$slots,"home-features-before",{},void 0,!0),m(Zo),l(t.$slots,"home-features-after",{},void 0,!0),r(e).markdownStyles!==!1?(a(),k(en,{key:0},{default:d(()=>[m(n)]),_:1})):(a(),k(n,{key:1}))])}}}),nn=b(on,[["__scopeId","data-v-55977d12"]]),sn={},an={class:"VPPage"};function rn(o,e){const t=R("Content");return a(),c("div",an,[l(o.$slots,"page-top"),m(t),l(o.$slots,"page-bottom")])}const ln=b(sn,[["render",rn]]),cn=_({__name:"VPContent",setup(o){const{page:e,frontmatter:t}=P(),{hasSidebar:s}=U();return(n,i)=>(a(),c("div",{class:N(["VPContent",{"has-sidebar":r(s),"is-home":r(t).layout==="home"}]),id:"VPContent"},[r(e).isNotFound?l(n.$slots,"not-found",{key:0},()=>[m(_t)],!0):r(t).layout==="page"?(a(),k(ln,{key:1},{"page-top":d(()=>[l(n.$slots,"page-top",{},void 0,!0)]),"page-bottom":d(()=>[l(n.$slots,"page-bottom",{},void 0,!0)]),_:3})):r(t).layout==="home"?(a(),k(nn,{key:2},{"home-hero-before":d(()=>[l(n.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":d(()=>[l(n.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":d(()=>[l(n.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":d(()=>[l(n.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":d(()=>[l(n.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":d(()=>[l(n.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":d(()=>[l(n.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":d(()=>[l(n.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":d(()=>[l(n.$slots,"home-features-after",{},void 0,!0)]),_:3})):r(t).layout&&r(t).layout!=="doc"?(a(),k(F(r(t).layout),{key:3})):(a(),k(mo,{key:4},{"doc-top":d(()=>[l(n.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":d(()=>[l(n.$slots,"doc-bottom",{},void 0,!0)]),"doc-footer-before":d(()=>[l(n.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":d(()=>[l(n.$slots,"doc-before",{},void 0,!0)]),"doc-after":d(()=>[l(n.$slots,"doc-after",{},void 0,!0)]),"aside-top":d(()=>[l(n.$slots,"aside-top",{},void 0,!0)]),"aside-outline-before":d(()=>[l(n.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":d(()=>[l(n.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":d(()=>[l(n.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":d(()=>[l(n.$slots,"aside-ads-after",{},void 0,!0)]),"aside-bottom":d(()=>[l(n.$slots,"aside-bottom",{},void 0,!0)]),_:3}))],2))}}),un=b(cn,[["__scopeId","data-v-fc04087f"]]),dn={class:"container"},vn=["innerHTML"],pn=["innerHTML"],hn=_({__name:"VPFooter",setup(o){const{theme:e,frontmatter:t}=P(),{hasSidebar:s}=U();return(n,i)=>r(e).footer&&r(t).footer!==!1?(a(),c("footer",{key:0,class:N(["VPFooter",{"has-sidebar":r(s)}])},[v("div",dn,[r(e).footer.message?(a(),c("p",{key:0,class:"message",innerHTML:r(e).footer.message},null,8,vn)):f("",!0),r(e).footer.copyright?(a(),c("p",{key:1,class:"copyright",innerHTML:r(e).footer.copyright},null,8,pn)):f("",!0)])],2)):f("",!0)}}),fn=b(hn,[["__scopeId","data-v-d69bcf5d"]]);function _n(){const{theme:o,frontmatter:e}=P(),t=Pe([]),s=y(()=>t.value.length>0);return x(()=>{t.value=me(e.value.outline??o.value.outline)}),{headers:t,hasLocalNav:s}}const mn=o=>(C("data-v-9dd5e197"),o=o(),H(),o),kn={class:"menu-text"},$n=mn(()=>v("span",{class:"vpi-chevron-right icon"},null,-1)),bn={class:"header"},gn={class:"outline"},yn=_({__name:"VPLocalNavOutlineDropdown",props:{headers:{},navHeight:{}},setup(o){const e=o,{theme:t}=P(),s=w(!1),n=w(0),i=w(),u=w();function h($){var V;(V=i.value)!=null&&V.contains($.target)||(s.value=!1)}G(s,$=>{if($){document.addEventListener("click",h);return}document.removeEventListener("click",h)}),le("Escape",()=>{s.value=!1}),x(()=>{s.value=!1});function p(){s.value=!s.value,n.value=window.innerHeight+Math.min(window.scrollY-e.navHeight,0)}function g($){$.target.classList.contains("outline-link")&&(u.value&&(u.value.style.transition="none"),We(()=>{s.value=!1}))}function L(){s.value=!1,window.scrollTo({top:0,left:0,behavior:"smooth"})}return($,V)=>(a(),c("div",{class:"VPLocalNavOutlineDropdown",style:Le({"--vp-vh":n.value+"px"}),ref_key:"main",ref:i},[$.headers.length>0?(a(),c("button",{key:0,onClick:p,class:N({open:s.value})},[v("span",kn,I(r(Ne)(r(t))),1),$n],2)):(a(),c("button",{key:1,onClick:L},I(r(t).returnToTopLabel||"Return to top"),1)),m(ve,{name:"flyout"},{default:d(()=>[s.value?(a(),c("div",{key:0,ref_key:"items",ref:u,class:"items",onClick:g},[v("div",bn,[v("a",{class:"top-link",href:"#",onClick:L},I(r(t).returnToTopLabel||"Return to top"),1)]),v("div",gn,[m(Me,{headers:$.headers},null,8,["headers"])])],512)):f("",!0)]),_:1})],4))}}),Pn=b(yn,[["__scopeId","data-v-9dd5e197"]]),Vn=o=>(C("data-v-9c649187"),o=o(),H(),o),Ln={class:"container"},Sn=["aria-expanded"],Tn=Vn(()=>v("span",{class:"vpi-align-left menu-icon"},null,-1)),In={class:"menu-text"},wn=_({__name:"VPLocalNav",props:{open:{type:Boolean}},emits:["open-menu"],setup(o){const{theme:e,frontmatter:t}=P(),{hasSidebar:s}=U(),{headers:n}=_n(),{y:i}=Se(),u=w(0);W(()=>{u.value=parseInt(getComputedStyle(document.documentElement).getPropertyValue("--vp-nav-height"))}),x(()=>{n.value=me(t.value.outline??e.value.outline)});const h=y(()=>n.value.length===0),p=y(()=>h.value&&!s.value),g=y(()=>({VPLocalNav:!0,"has-sidebar":s.value,empty:h.value,fixed:p.value}));return(L,$)=>r(t).layout!=="home"&&(!p.value||r(i)>=u.value)?(a(),c("div",{key:0,class:N(g.value)},[v("div",Ln,[r(s)?(a(),c("button",{key:0,class:"menu","aria-expanded":L.open,"aria-controls":"VPSidebarNav",onClick:$[0]||($[0]=V=>L.$emit("open-menu"))},[Tn,v("span",In,I(r(e).sidebarMenuLabel||"Menu"),1)],8,Sn)):f("",!0),m(Pn,{headers:r(n),navHeight:u.value},null,8,["headers","navHeight"])])],2)):f("",!0)}}),Nn=b(wn,[["__scopeId","data-v-9c649187"]]);function Mn(){const o=w(!1);function e(){o.value=!0,window.addEventListener("resize",n)}function t(){o.value=!1,window.removeEventListener("resize",n)}function s(){o.value?t():e()}function n(){window.outerWidth>=768&&t()}const i=ee();return G(()=>i.path,t),{isScreenOpen:o,openScreen:e,closeScreen:t,toggleScreen:s}}const An={},Bn={class:"VPSwitch",type:"button",role:"switch"},Cn={class:"check"},Hn={key:0,class:"icon"};function En(o,e){return a(),c("button",Bn,[v("span",Cn,[o.$slots.default?(a(),c("span",Hn,[l(o.$slots,"default",{},void 0,!0)])):f("",!0)])])}const Fn=b(An,[["render",En],["__scopeId","data-v-846fe538"]]),Be=o=>(C("data-v-3125216b"),o=o(),H(),o),Dn=Be(()=>v("span",{class:"vpi-sun sun"},null,-1)),On=Be(()=>v("span",{class:"vpi-moon moon"},null,-1)),Gn=_({__name:"VPSwitchAppearance",setup(o){const{isDark:e,theme:t}=P(),s=te("toggle-appearance",()=>{e.value=!e.value}),n=w("");return fe(()=>{n.value=e.value?t.value.lightModeSwitchTitle||"Switch to light theme":t.value.darkModeSwitchTitle||"Switch to dark theme"}),(i,u)=>(a(),k(Fn,{title:n.value,class:"VPSwitchAppearance","aria-checked":r(e),onClick:r(s)},{default:d(()=>[Dn,On]),_:1},8,["title","aria-checked","onClick"]))}}),ke=b(Gn,[["__scopeId","data-v-3125216b"]]),Un={key:0,class:"VPNavBarAppearance"},jn=_({__name:"VPNavBarAppearance",setup(o){const{site:e}=P();return(t,s)=>r(e).appearance&&r(e).appearance!=="force-dark"&&r(e).appearance!=="force-auto"?(a(),c("div",Un,[m(ke)])):f("",!0)}}),zn=b(jn,[["__scopeId","data-v-864d2abc"]]),$e=w();let Ce=!1,re=0;function qn(o){const e=w(!1);if(oe){!Ce&&Kn(),re++;const t=G($e,s=>{var n,i,u;s===o.el.value||(n=o.el.value)!=null&&n.contains(s)?(e.value=!0,(i=o.onFocus)==null||i.call(o)):(e.value=!1,(u=o.onBlur)==null||u.call(o))});he(()=>{t(),re--,re||Wn()})}return Re(e)}function Kn(){document.addEventListener("focusin",He),Ce=!0,$e.value=document.activeElement}function Wn(){document.removeEventListener("focusin",He)}function He(){$e.value=document.activeElement}const Rn={class:"VPMenuLink"},Jn=_({__name:"VPMenuLink",props:{item:{}},setup(o){const{page:e}=P();return(t,s)=>(a(),c("div",Rn,[m(D,{class:N({active:r(K)(r(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,target:t.item.target,rel:t.item.rel},{default:d(()=>[O(I(t.item.text),1)]),_:1},8,["class","href","target","rel"])]))}}),ne=b(Jn,[["__scopeId","data-v-25a54821"]]),Xn={class:"VPMenuGroup"},Yn={key:0,class:"title"},Qn=_({__name:"VPMenuGroup",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),c("div",Xn,[e.text?(a(),c("p",Yn,I(e.text),1)):f("",!0),(a(!0),c(M,null,E(e.items,s=>(a(),c(M,null,["link"in s?(a(),k(ne,{key:0,item:s},null,8,["item"])):f("",!0)],64))),256))]))}}),Zn=b(Qn,[["__scopeId","data-v-4dd03e28"]]),xn={class:"VPMenu"},es={key:0,class:"items"},ts=_({__name:"VPMenu",props:{items:{}},setup(o){return(e,t)=>(a(),c("div",xn,[e.items?(a(),c("div",es,[(a(!0),c(M,null,E(e.items,s=>(a(),c(M,{key:JSON.stringify(s)},["link"in s?(a(),k(ne,{key:0,item:s},null,8,["item"])):"component"in s?(a(),k(F(s.component),q({key:1,ref_for:!0},s.props),null,16)):(a(),k(Zn,{key:2,text:s.text,items:s.items},null,8,["text","items"]))],64))),128))])):f("",!0),l(e.$slots,"default",{},void 0,!0)]))}}),os=b(ts,[["__scopeId","data-v-809b8af7"]]),ns=o=>(C("data-v-00660109"),o=o(),H(),o),ss=["aria-expanded","aria-label"],as={key:0,class:"text"},rs=["innerHTML"],is=ns(()=>v("span",{class:"vpi-chevron-down text-icon"},null,-1)),ls={key:1,class:"vpi-more-horizontal icon"},cs={class:"menu"},us=_({__name:"VPFlyout",props:{icon:{},button:{},label:{},items:{}},setup(o){const e=w(!1),t=w();qn({el:t,onBlur:s});function s(){e.value=!1}return(n,i)=>(a(),c("div",{class:"VPFlyout",ref_key:"el",ref:t,onMouseenter:i[1]||(i[1]=u=>e.value=!0),onMouseleave:i[2]||(i[2]=u=>e.value=!1)},[v("button",{type:"button",class:"button","aria-haspopup":"true","aria-expanded":e.value,"aria-label":n.label,onClick:i[0]||(i[0]=u=>e.value=!e.value)},[n.button||n.icon?(a(),c("span",as,[n.icon?(a(),c("span",{key:0,class:N([n.icon,"option-icon"])},null,2)):f("",!0),n.button?(a(),c("span",{key:1,innerHTML:n.button},null,8,rs)):f("",!0),is])):(a(),c("span",ls))],8,ss),v("div",cs,[m(os,{items:n.items},{default:d(()=>[l(n.$slots,"default",{},void 0,!0)]),_:3},8,["items"])])],544))}}),be=b(us,[["__scopeId","data-v-00660109"]]),ds=["href","aria-label","innerHTML"],vs=_({__name:"VPSocialLink",props:{icon:{},link:{},ariaLabel:{}},setup(o){const e=o,t=y(()=>typeof e.icon=="object"?e.icon.svg:``);return(s,n)=>(a(),c("a",{class:"VPSocialLink no-icon",href:s.link,"aria-label":s.ariaLabel??(typeof s.icon=="string"?s.icon:""),target:"_blank",rel:"noopener",innerHTML:t.value},null,8,ds))}}),ps=b(vs,[["__scopeId","data-v-15a5c40e"]]),hs={class:"VPSocialLinks"},fs=_({__name:"VPSocialLinks",props:{links:{}},setup(o){return(e,t)=>(a(),c("div",hs,[(a(!0),c(M,null,E(e.links,({link:s,icon:n,ariaLabel:i})=>(a(),k(ps,{key:s,icon:n,link:s,ariaLabel:i},null,8,["icon","link","ariaLabel"]))),128))]))}}),ge=b(fs,[["__scopeId","data-v-100434c4"]]),_s={key:0,class:"group translations"},ms={class:"trans-title"},ks={key:1,class:"group"},$s={class:"item appearance"},bs={class:"label"},gs={class:"appearance-action"},ys={key:2,class:"group"},Ps={class:"item social-links"},Vs=_({__name:"VPNavBarExtra",setup(o){const{site:e,theme:t}=P(),{localeLinks:s,currentLang:n}=X({correspondingLink:!0}),i=y(()=>s.value.length&&n.value.label||e.value.appearance||t.value.socialLinks);return(u,h)=>i.value?(a(),k(be,{key:0,class:"VPNavBarExtra",label:"extra navigation"},{default:d(()=>[r(s).length&&r(n).label?(a(),c("div",_s,[v("p",ms,I(r(n).label),1),(a(!0),c(M,null,E(r(s),p=>(a(),k(ne,{key:p.link,item:p},null,8,["item"]))),128))])):f("",!0),r(e).appearance&&r(e).appearance!=="force-dark"&&r(e).appearance!=="force-auto"?(a(),c("div",ks,[v("div",$s,[v("p",bs,I(r(t).darkModeSwitchLabel||"Appearance"),1),v("div",gs,[m(ke)])])])):f("",!0),r(t).socialLinks?(a(),c("div",ys,[v("div",Ps,[m(ge,{class:"social-links-list",links:r(t).socialLinks},null,8,["links"])])])):f("",!0)]),_:1})):f("",!0)}}),Ls=b(Vs,[["__scopeId","data-v-60cefd62"]]),Ss=o=>(C("data-v-e047a1f2"),o=o(),H(),o),Ts=["aria-expanded"],Is=Ss(()=>v("span",{class:"container"},[v("span",{class:"top"}),v("span",{class:"middle"}),v("span",{class:"bottom"})],-1)),ws=[Is],Ns=_({__name:"VPNavBarHamburger",props:{active:{type:Boolean}},emits:["click"],setup(o){return(e,t)=>(a(),c("button",{type:"button",class:N(["VPNavBarHamburger",{active:e.active}]),"aria-label":"mobile navigation","aria-expanded":e.active,"aria-controls":"VPNavScreen",onClick:t[0]||(t[0]=s=>e.$emit("click"))},ws,10,Ts))}}),Ms=b(Ns,[["__scopeId","data-v-e047a1f2"]]),As=["innerHTML"],Bs=_({__name:"VPNavBarMenuLink",props:{item:{}},setup(o){const{page:e}=P();return(t,s)=>(a(),k(D,{class:N({VPNavBarMenuLink:!0,active:r(K)(r(e).relativePath,t.item.activeMatch||t.item.link,!!t.item.activeMatch)}),href:t.item.link,noIcon:t.item.noIcon,target:t.item.target,rel:t.item.rel,tabindex:"0"},{default:d(()=>[v("span",{innerHTML:t.item.text},null,8,As)]),_:1},8,["class","href","noIcon","target","rel"]))}}),Cs=b(Bs,[["__scopeId","data-v-9a0da802"]]),Hs=_({__name:"VPNavBarMenuGroup",props:{item:{}},setup(o){const e=o,{page:t}=P(),s=i=>"component"in i?!1:"link"in i?K(t.value.relativePath,i.link,!!e.item.activeMatch):i.items.some(s),n=y(()=>s(e.item));return(i,u)=>(a(),k(be,{class:N({VPNavBarMenuGroup:!0,active:r(K)(r(t).relativePath,i.item.activeMatch,!!i.item.activeMatch)||n.value}),button:i.item.text,items:i.item.items},null,8,["class","button","items"]))}}),Es=o=>(C("data-v-bf53b681"),o=o(),H(),o),Fs={key:0,"aria-labelledby":"main-nav-aria-label",class:"VPNavBarMenu"},Ds=Es(()=>v("span",{id:"main-nav-aria-label",class:"visually-hidden"}," Main Navigation ",-1)),Os=_({__name:"VPNavBarMenu",setup(o){const{theme:e}=P();return(t,s)=>r(e).nav?(a(),c("nav",Fs,[Ds,(a(!0),c(M,null,E(r(e).nav,n=>(a(),c(M,{key:JSON.stringify(n)},["link"in n?(a(),k(Cs,{key:0,item:n},null,8,["item"])):"component"in n?(a(),k(F(n.component),q({key:1,ref_for:!0},n.props),null,16)):(a(),k(Hs,{key:2,item:n},null,8,["item"]))],64))),128))])):f("",!0)}}),Gs=b(Os,[["__scopeId","data-v-bf53b681"]]);function Us(o){const{localeIndex:e,theme:t}=P();function s(n){var A,B,S;const i=n.split("."),u=(A=t.value.search)==null?void 0:A.options,h=u&&typeof u=="object",p=h&&((S=(B=u.locales)==null?void 0:B[e.value])==null?void 0:S.translations)||null,g=h&&u.translations||null;let L=p,$=g,V=o;const T=i.pop();for(const j of i){let z=null;const J=V==null?void 0:V[j];J&&(z=V=J);const se=$==null?void 0:$[j];se&&(z=$=se);const ae=L==null?void 0:L[j];ae&&(z=L=ae),J||(V=z),se||($=z),ae||(L=z)}return(L==null?void 0:L[T])??($==null?void 0:$[T])??(V==null?void 0:V[T])??""}return s}const js=["aria-label"],zs={class:"DocSearch-Button-Container"},qs=v("span",{class:"vp-icon DocSearch-Search-Icon"},null,-1),Ks={class:"DocSearch-Button-Placeholder"},Ws=v("span",{class:"DocSearch-Button-Keys"},[v("kbd",{class:"DocSearch-Button-Key"}),v("kbd",{class:"DocSearch-Button-Key"},"K")],-1),ye=_({__name:"VPNavBarSearchButton",setup(o){const t=Us({button:{buttonText:"Search",buttonAriaLabel:"Search"}});return(s,n)=>(a(),c("button",{type:"button",class:"DocSearch DocSearch-Button","aria-label":r(t)("button.buttonAriaLabel")},[v("span",zs,[qs,v("span",Ks,I(r(t)("button.buttonText")),1)]),Ws],8,js))}}),Rs={class:"VPNavBarSearch"},Js={id:"local-search"},Xs={key:1,id:"docsearch"},Ys=_({__name:"VPNavBarSearch",setup(o){const e=Je(()=>Xe(()=>import("./VPLocalSearchBox.DhHzxM_l.js"),__vite__mapDeps([0,1]))),t=()=>null,{theme:s}=P(),n=w(!1),i=w(!1);W(()=>{});function u(){n.value||(n.value=!0,setTimeout(h,16))}function h(){const $=new Event("keydown");$.key="k",$.metaKey=!0,window.dispatchEvent($),setTimeout(()=>{document.querySelector(".DocSearch-Modal")||h()},16)}function p($){const V=$.target,T=V.tagName;return V.isContentEditable||T==="INPUT"||T==="SELECT"||T==="TEXTAREA"}const g=w(!1);le("k",$=>{($.ctrlKey||$.metaKey)&&($.preventDefault(),g.value=!0)}),le("/",$=>{p($)||($.preventDefault(),g.value=!0)});const L="local";return($,V)=>{var T;return a(),c("div",Rs,[r(L)==="local"?(a(),c(M,{key:0},[g.value?(a(),k(r(e),{key:0,onClose:V[0]||(V[0]=A=>g.value=!1)})):f("",!0),v("div",Js,[m(ye,{onClick:V[1]||(V[1]=A=>g.value=!0)})])],64)):r(L)==="algolia"?(a(),c(M,{key:1},[n.value?(a(),k(r(t),{key:0,algolia:((T=r(s).search)==null?void 0:T.options)??r(s).algolia,onVnodeBeforeMount:V[2]||(V[2]=A=>i.value=!0)},null,8,["algolia"])):f("",!0),i.value?f("",!0):(a(),c("div",Xs,[m(ye,{onClick:u})]))],64)):f("",!0)])}}}),Qs=_({__name:"VPNavBarSocialLinks",setup(o){const{theme:e}=P();return(t,s)=>r(e).socialLinks?(a(),k(ge,{key:0,class:"VPNavBarSocialLinks",links:r(e).socialLinks},null,8,["links"])):f("",!0)}}),Zs=b(Qs,[["__scopeId","data-v-2c606308"]]),xs=["href","rel","target"],ea={key:1},ta={key:2},oa=_({__name:"VPNavBarTitle",setup(o){const{site:e,theme:t}=P(),{hasSidebar:s}=U(),{currentLang:n}=X(),i=y(()=>{var p;return typeof t.value.logoLink=="string"?t.value.logoLink:(p=t.value.logoLink)==null?void 0:p.link}),u=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.rel}),h=y(()=>{var p;return typeof t.value.logoLink=="string"||(p=t.value.logoLink)==null?void 0:p.target});return(p,g)=>(a(),c("div",{class:N(["VPNavBarTitle",{"has-sidebar":r(s)}])},[v("a",{class:"title",href:i.value??r(_e)(r(n).link),rel:u.value,target:h.value},[l(p.$slots,"nav-bar-title-before",{},void 0,!0),r(t).logo?(a(),k(Q,{key:0,class:"logo",image:r(t).logo},null,8,["image"])):f("",!0),r(t).siteTitle?(a(),c("span",ea,I(r(t).siteTitle),1)):r(t).siteTitle===void 0?(a(),c("span",ta,I(r(e).title),1)):f("",!0),l(p.$slots,"nav-bar-title-after",{},void 0,!0)],8,xs)],2))}}),na=b(oa,[["__scopeId","data-v-606a7e0f"]]),sa={class:"items"},aa={class:"title"},ra=_({__name:"VPNavBarTranslations",setup(o){const{theme:e}=P(),{localeLinks:t,currentLang:s}=X({correspondingLink:!0});return(n,i)=>r(t).length&&r(s).label?(a(),k(be,{key:0,class:"VPNavBarTranslations",icon:"vpi-languages",label:r(e).langMenuLabel||"Change language"},{default:d(()=>[v("div",sa,[v("p",aa,I(r(s).label),1),(a(!0),c(M,null,E(r(t),u=>(a(),k(ne,{key:u.link,item:u},null,8,["item"]))),128))])]),_:1},8,["label"])):f("",!0)}}),ia=b(ra,[["__scopeId","data-v-912817b1"]]),la=o=>(C("data-v-da0688be"),o=o(),H(),o),ca={class:"wrapper"},ua={class:"container"},da={class:"title"},va={class:"content"},pa={class:"content-body"},ha=la(()=>v("div",{class:"divider"},[v("div",{class:"divider-line"})],-1)),fa=_({__name:"VPNavBar",props:{isScreenOpen:{type:Boolean}},emits:["toggle-screen"],setup(o){const e=o,{y:t}=Se(),{hasSidebar:s}=U(),{frontmatter:n}=P(),i=w({});return fe(()=>{i.value={"has-sidebar":s.value,home:n.value.layout==="home",top:t.value===0,"screen-open":e.isScreenOpen}}),(u,h)=>(a(),c("div",{class:N(["VPNavBar",i.value])},[v("div",ca,[v("div",ua,[v("div",da,[m(na,null,{"nav-bar-title-before":d(()=>[l(u.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":d(()=>[l(u.$slots,"nav-bar-title-after",{},void 0,!0)]),_:3})]),v("div",va,[v("div",pa,[l(u.$slots,"nav-bar-content-before",{},void 0,!0),m(Ys,{class:"search"}),m(Gs,{class:"menu"}),m(ia,{class:"translations"}),m(zn,{class:"appearance"}),m(Zs,{class:"social-links"}),m(Ls,{class:"extra"}),l(u.$slots,"nav-bar-content-after",{},void 0,!0),m(Ms,{class:"hamburger",active:u.isScreenOpen,onClick:h[0]||(h[0]=p=>u.$emit("toggle-screen"))},null,8,["active"])])])])]),ha],2))}}),_a=b(fa,[["__scopeId","data-v-da0688be"]]),ma={key:0,class:"VPNavScreenAppearance"},ka={class:"text"},$a=_({__name:"VPNavScreenAppearance",setup(o){const{site:e,theme:t}=P();return(s,n)=>r(e).appearance&&r(e).appearance!=="force-dark"&&r(e).appearance!=="force-auto"?(a(),c("div",ma,[v("p",ka,I(r(t).darkModeSwitchLabel||"Appearance"),1),m(ke)])):f("",!0)}}),ba=b($a,[["__scopeId","data-v-dfcc1536"]]),ga=_({__name:"VPNavScreenMenuLink",props:{item:{}},setup(o){const e=te("close-screen");return(t,s)=>(a(),k(D,{class:"VPNavScreenMenuLink",href:t.item.link,target:t.item.target,rel:t.item.rel,onClick:r(e),innerHTML:t.item.text},null,8,["href","target","rel","onClick","innerHTML"]))}}),ya=b(ga,[["__scopeId","data-v-8cd41455"]]),Pa=_({__name:"VPNavScreenMenuGroupLink",props:{item:{}},setup(o){const e=te("close-screen");return(t,s)=>(a(),k(D,{class:"VPNavScreenMenuGroupLink",href:t.item.link,target:t.item.target,rel:t.item.rel,onClick:r(e)},{default:d(()=>[O(I(t.item.text),1)]),_:1},8,["href","target","rel","onClick"]))}}),Ee=b(Pa,[["__scopeId","data-v-b8c7c580"]]),Va={class:"VPNavScreenMenuGroupSection"},La={key:0,class:"title"},Sa=_({__name:"VPNavScreenMenuGroupSection",props:{text:{},items:{}},setup(o){return(e,t)=>(a(),c("div",Va,[e.text?(a(),c("p",La,I(e.text),1)):f("",!0),(a(!0),c(M,null,E(e.items,s=>(a(),k(Ee,{key:s.text,item:s},null,8,["item"]))),128))]))}}),Ta=b(Sa,[["__scopeId","data-v-a3e7a51c"]]),Ia=o=>(C("data-v-90f695a2"),o=o(),H(),o),wa=["aria-controls","aria-expanded"],Na=["innerHTML"],Ma=Ia(()=>v("span",{class:"vpi-plus button-icon"},null,-1)),Aa=["id"],Ba={key:0,class:"item"},Ca={key:1,class:"item"},Ha={key:2,class:"group"},Ea=_({__name:"VPNavScreenMenuGroup",props:{text:{},items:{}},setup(o){const e=o,t=w(!1),s=y(()=>`NavScreenGroup-${e.text.replace(" ","-").toLowerCase()}`);function n(){t.value=!t.value}return(i,u)=>(a(),c("div",{class:N(["VPNavScreenMenuGroup",{open:t.value}])},[v("button",{class:"button","aria-controls":s.value,"aria-expanded":t.value,onClick:n},[v("span",{class:"button-text",innerHTML:i.text},null,8,Na),Ma],8,wa),v("div",{id:s.value,class:"items"},[(a(!0),c(M,null,E(i.items,h=>(a(),c(M,{key:JSON.stringify(h)},["link"in h?(a(),c("div",Ba,[m(Ee,{item:h},null,8,["item"])])):"component"in h?(a(),c("div",Ca,[(a(),k(F(h.component),q({ref_for:!0},h.props,{"screen-menu":""}),null,16))])):(a(),c("div",Ha,[m(Ta,{text:h.text,items:h.items},null,8,["text","items"])]))],64))),128))],8,Aa)],2))}}),Fa=b(Ea,[["__scopeId","data-v-90f695a2"]]),Da={key:0,class:"VPNavScreenMenu"},Oa=_({__name:"VPNavScreenMenu",setup(o){const{theme:e}=P();return(t,s)=>r(e).nav?(a(),c("nav",Da,[(a(!0),c(M,null,E(r(e).nav,n=>(a(),c(M,{key:JSON.stringify(n)},["link"in n?(a(),k(ya,{key:0,item:n},null,8,["item"])):"component"in n?(a(),k(F(n.component),q({key:1,ref_for:!0},n.props,{"screen-menu":""}),null,16)):(a(),k(Fa,{key:2,text:n.text||"",items:n.items},null,8,["text","items"]))],64))),128))])):f("",!0)}}),Ga=_({__name:"VPNavScreenSocialLinks",setup(o){const{theme:e}=P();return(t,s)=>r(e).socialLinks?(a(),k(ge,{key:0,class:"VPNavScreenSocialLinks",links:r(e).socialLinks},null,8,["links"])):f("",!0)}}),Fe=o=>(C("data-v-95c61444"),o=o(),H(),o),Ua=Fe(()=>v("span",{class:"vpi-languages icon lang"},null,-1)),ja=Fe(()=>v("span",{class:"vpi-chevron-down icon chevron"},null,-1)),za={class:"list"},qa=_({__name:"VPNavScreenTranslations",setup(o){const{localeLinks:e,currentLang:t}=X({correspondingLink:!0}),s=w(!1);function n(){s.value=!s.value}return(i,u)=>r(e).length&&r(t).label?(a(),c("div",{key:0,class:N(["VPNavScreenTranslations",{open:s.value}])},[v("button",{class:"title",onClick:n},[Ua,O(" "+I(r(t).label)+" ",1),ja]),v("ul",za,[(a(!0),c(M,null,E(r(e),h=>(a(),c("li",{key:h.link,class:"item"},[m(D,{class:"link",href:h.link},{default:d(()=>[O(I(h.text),1)]),_:2},1032,["href"])]))),128))])],2)):f("",!0)}}),Ka=b(qa,[["__scopeId","data-v-95c61444"]]),Wa={class:"container"},Ra=_({__name:"VPNavScreen",props:{open:{type:Boolean}},setup(o){const e=w(null),t=Te(oe?document.body:null);return(s,n)=>(a(),k(ve,{name:"fade",onEnter:n[0]||(n[0]=i=>t.value=!0),onAfterLeave:n[1]||(n[1]=i=>t.value=!1)},{default:d(()=>[s.open?(a(),c("div",{key:0,class:"VPNavScreen",ref_key:"screen",ref:e,id:"VPNavScreen"},[v("div",Wa,[l(s.$slots,"nav-screen-content-before",{},void 0,!0),m(Oa,{class:"menu"}),m(Ka,{class:"translations"}),m(ba,{class:"appearance"}),m(Ga,{class:"social-links"}),l(s.$slots,"nav-screen-content-after",{},void 0,!0)])],512)):f("",!0)]),_:3}))}}),Ja=b(Ra,[["__scopeId","data-v-c14c1e21"]]),Xa={key:0,class:"VPNav"},Ya=_({__name:"VPNav",setup(o){const{isScreenOpen:e,closeScreen:t,toggleScreen:s}=Mn(),{frontmatter:n}=P(),i=y(()=>n.value.navbar!==!1);return Ie("close-screen",t),Z(()=>{oe&&document.documentElement.classList.toggle("hide-nav",!i.value)}),(u,h)=>i.value?(a(),c("header",Xa,[m(_a,{"is-screen-open":r(e),onToggleScreen:r(s)},{"nav-bar-title-before":d(()=>[l(u.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":d(()=>[l(u.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":d(()=>[l(u.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":d(()=>[l(u.$slots,"nav-bar-content-after",{},void 0,!0)]),_:3},8,["is-screen-open","onToggleScreen"]),m(Ja,{open:r(e)},{"nav-screen-content-before":d(()=>[l(u.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":d(()=>[l(u.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3},8,["open"])])):f("",!0)}}),Qa=b(Ya,[["__scopeId","data-v-e823d444"]]),De=o=>(C("data-v-a9cdba99"),o=o(),H(),o),Za=["role","tabindex"],xa=De(()=>v("div",{class:"indicator"},null,-1)),er=De(()=>v("span",{class:"vpi-chevron-right caret-icon"},null,-1)),tr=[er],or={key:1,class:"items"},nr=_({__name:"VPSidebarItem",props:{item:{},depth:{}},setup(o){const e=o,{collapsed:t,collapsible:s,isLink:n,isActiveLink:i,hasActiveLink:u,hasChildren:h,toggle:p}=bt(y(()=>e.item)),g=y(()=>h.value?"section":"div"),L=y(()=>n.value?"a":"div"),$=y(()=>h.value?e.depth+2===7?"p":`h${e.depth+2}`:"p"),V=y(()=>n.value?void 0:"button"),T=y(()=>[[`level-${e.depth}`],{collapsible:s.value},{collapsed:t.value},{"is-link":n.value},{"is-active":i.value},{"has-active":u.value}]);function A(S){"key"in S&&S.key!=="Enter"||!e.item.link&&p()}function B(){e.item.link&&p()}return(S,j)=>{const z=R("VPSidebarItem",!0);return a(),k(F(g.value),{class:N(["VPSidebarItem",T.value])},{default:d(()=>[S.item.text?(a(),c("div",q({key:0,class:"item",role:V.value},Qe(S.item.items?{click:A,keydown:A}:{},!0),{tabindex:S.item.items&&0}),[xa,S.item.link?(a(),k(D,{key:0,tag:L.value,class:"link",href:S.item.link,rel:S.item.rel,target:S.item.target},{default:d(()=>[(a(),k(F($.value),{class:"text",innerHTML:S.item.text},null,8,["innerHTML"]))]),_:1},8,["tag","href","rel","target"])):(a(),k(F($.value),{key:1,class:"text",innerHTML:S.item.text},null,8,["innerHTML"])),S.item.collapsed!=null&&S.item.items&&S.item.items.length?(a(),c("div",{key:2,class:"caret",role:"button","aria-label":"toggle section",onClick:B,onKeydown:Ye(B,["enter"]),tabindex:"0"},tr,32)):f("",!0)],16,Za)):f("",!0),S.item.items&&S.item.items.length?(a(),c("div",or,[S.depth<5?(a(!0),c(M,{key:0},E(S.item.items,J=>(a(),k(z,{key:J.text,item:J,depth:S.depth+1},null,8,["item","depth"]))),128)):f("",!0)])):f("",!0)]),_:1},8,["class"])}}}),sr=b(nr,[["__scopeId","data-v-a9cdba99"]]),ar=_({__name:"VPSidebarGroup",props:{items:{}},setup(o){const e=w(!0);let t=null;return W(()=>{t=setTimeout(()=>{t=null,e.value=!1},300)}),Ze(()=>{t!=null&&(clearTimeout(t),t=null)}),(s,n)=>(a(!0),c(M,null,E(s.items,i=>(a(),c("div",{key:i.text,class:N(["group",{"no-transition":e.value}])},[m(sr,{item:i,depth:0},null,8,["item"])],2))),128))}}),rr=b(ar,[["__scopeId","data-v-72c67ed4"]]),Oe=o=>(C("data-v-59ceefa4"),o=o(),H(),o),ir=Oe(()=>v("div",{class:"curtain"},null,-1)),lr={class:"nav",id:"VPSidebarNav","aria-labelledby":"sidebar-aria-label",tabindex:"-1"},cr=Oe(()=>v("span",{class:"visually-hidden",id:"sidebar-aria-label"}," Sidebar Navigation ",-1)),ur=_({__name:"VPSidebar",props:{open:{type:Boolean}},setup(o){const{sidebarGroups:e,hasSidebar:t}=U(),s=o,n=w(null),i=Te(oe?document.body:null);G([s,n],()=>{var h;s.open?(i.value=!0,(h=n.value)==null||h.focus()):i.value=!1},{immediate:!0,flush:"post"});const u=w(0);return G(e,()=>{u.value+=1},{deep:!0}),(h,p)=>r(t)?(a(),c("aside",{key:0,class:N(["VPSidebar",{open:h.open}]),ref_key:"navEl",ref:n,onClick:p[0]||(p[0]=xe(()=>{},["stop"]))},[ir,v("nav",lr,[cr,l(h.$slots,"sidebar-nav-before",{},void 0,!0),(a(),k(rr,{items:r(e),key:u.value},null,8,["items"])),l(h.$slots,"sidebar-nav-after",{},void 0,!0)])],2)):f("",!0)}}),dr=b(ur,[["__scopeId","data-v-59ceefa4"]]),vr=_({__name:"VPSkipLink",setup(o){const e=ee(),t=w();G(()=>e.path,()=>t.value.focus());function s({target:n}){const i=document.getElementById(decodeURIComponent(n.hash).slice(1));if(i){const u=()=>{i.removeAttribute("tabindex"),i.removeEventListener("blur",u)};i.setAttribute("tabindex","-1"),i.addEventListener("blur",u),i.focus(),window.scrollTo(0,0)}}return(n,i)=>(a(),c(M,null,[v("span",{ref_key:"backToTop",ref:t,tabindex:"-1"},null,512),v("a",{href:"#VPContent",class:"VPSkipLink visually-hidden",onClick:s}," Skip to content ")],64))}}),pr=b(vr,[["__scopeId","data-v-e813112c"]]),hr=_({__name:"Layout",setup(o){const{isOpen:e,open:t,close:s}=U(),n=ee();G(()=>n.path,s),$t(e,s);const{frontmatter:i}=P(),u=et(),h=y(()=>!!u["home-hero-image"]);return Ie("hero-image-slot-exists",h),(p,g)=>{const L=R("Content");return r(i).layout!==!1?(a(),c("div",{key:0,class:N(["Layout",r(i).pageClass])},[l(p.$slots,"layout-top",{},void 0,!0),m(pr),m(st,{class:"backdrop",show:r(e),onClick:r(s)},null,8,["show","onClick"]),m(Qa,null,{"nav-bar-title-before":d(()=>[l(p.$slots,"nav-bar-title-before",{},void 0,!0)]),"nav-bar-title-after":d(()=>[l(p.$slots,"nav-bar-title-after",{},void 0,!0)]),"nav-bar-content-before":d(()=>[l(p.$slots,"nav-bar-content-before",{},void 0,!0)]),"nav-bar-content-after":d(()=>[l(p.$slots,"nav-bar-content-after",{},void 0,!0)]),"nav-screen-content-before":d(()=>[l(p.$slots,"nav-screen-content-before",{},void 0,!0)]),"nav-screen-content-after":d(()=>[l(p.$slots,"nav-screen-content-after",{},void 0,!0)]),_:3}),m(Nn,{open:r(e),onOpenMenu:r(t)},null,8,["open","onOpenMenu"]),m(dr,{open:r(e)},{"sidebar-nav-before":d(()=>[l(p.$slots,"sidebar-nav-before",{},void 0,!0)]),"sidebar-nav-after":d(()=>[l(p.$slots,"sidebar-nav-after",{},void 0,!0)]),_:3},8,["open"]),m(un,null,{"page-top":d(()=>[l(p.$slots,"page-top",{},void 0,!0)]),"page-bottom":d(()=>[l(p.$slots,"page-bottom",{},void 0,!0)]),"not-found":d(()=>[l(p.$slots,"not-found",{},void 0,!0)]),"home-hero-before":d(()=>[l(p.$slots,"home-hero-before",{},void 0,!0)]),"home-hero-info-before":d(()=>[l(p.$slots,"home-hero-info-before",{},void 0,!0)]),"home-hero-info":d(()=>[l(p.$slots,"home-hero-info",{},void 0,!0)]),"home-hero-info-after":d(()=>[l(p.$slots,"home-hero-info-after",{},void 0,!0)]),"home-hero-actions-after":d(()=>[l(p.$slots,"home-hero-actions-after",{},void 0,!0)]),"home-hero-image":d(()=>[l(p.$slots,"home-hero-image",{},void 0,!0)]),"home-hero-after":d(()=>[l(p.$slots,"home-hero-after",{},void 0,!0)]),"home-features-before":d(()=>[l(p.$slots,"home-features-before",{},void 0,!0)]),"home-features-after":d(()=>[l(p.$slots,"home-features-after",{},void 0,!0)]),"doc-footer-before":d(()=>[l(p.$slots,"doc-footer-before",{},void 0,!0)]),"doc-before":d(()=>[l(p.$slots,"doc-before",{},void 0,!0)]),"doc-after":d(()=>[l(p.$slots,"doc-after",{},void 0,!0)]),"doc-top":d(()=>[l(p.$slots,"doc-top",{},void 0,!0)]),"doc-bottom":d(()=>[l(p.$slots,"doc-bottom",{},void 0,!0)]),"aside-top":d(()=>[l(p.$slots,"aside-top",{},void 0,!0)]),"aside-bottom":d(()=>[l(p.$slots,"aside-bottom",{},void 0,!0)]),"aside-outline-before":d(()=>[l(p.$slots,"aside-outline-before",{},void 0,!0)]),"aside-outline-after":d(()=>[l(p.$slots,"aside-outline-after",{},void 0,!0)]),"aside-ads-before":d(()=>[l(p.$slots,"aside-ads-before",{},void 0,!0)]),"aside-ads-after":d(()=>[l(p.$slots,"aside-ads-after",{},void 0,!0)]),_:3}),m(fn),l(p.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),k(L,{key:1}))}}}),fr=b(hr,[["__scopeId","data-v-3b4648ff"]]),mr={Layout:fr,enhanceApp:({app:o})=>{o.component("Badge",tt)}};export{Us as c,mr as t,P as u};
diff --git a/assets/en_api_mp_math_line.md.Bd5Z3iC3.js b/assets/en_api_mp_math_line.md.DFwE8llX.js
similarity index 96%
rename from assets/en_api_mp_math_line.md.Bd5Z3iC3.js
rename to assets/en_api_mp_math_line.md.DFwE8llX.js
index 30b81c6..07428d2 100644
--- a/assets/en_api_mp_math_line.md.Bd5Z3iC3.js
+++ b/assets/en_api_mp_math_line.md.DFwE8llX.js
@@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

Description: 工厂函数 由两点构造直线。

Arguments:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

Arguments:

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

Arguments:

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
diff --git a/assets/en_api_mp_math_line.md.Bd5Z3iC3.lean.js b/assets/en_api_mp_math_line.md.DFwE8llX.lean.js
similarity index 100%
rename from assets/en_api_mp_math_line.md.Bd5Z3iC3.lean.js
rename to assets/en_api_mp_math_line.md.DFwE8llX.lean.js
diff --git a/assets/en_api_mp_math_plane.md.D91Vt6aU.js b/assets/en_api_mp_math_plane.md.CBNCeDF4.js
similarity index 97%
rename from assets/en_api_mp_math_plane.md.D91Vt6aU.js
rename to assets/en_api_mp_math_plane.md.CBNCeDF4.js
index f8a4dc1..4260098 100644
--- a/assets/en_api_mp_math_plane.md.D91Vt6aU.js
+++ b/assets/en_api_mp_math_plane.md.CBNCeDF4.js
@@ -13,7 +13,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False

method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​

Description: 计算平面与平面之间的夹角。

`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t('',1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),D={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},L={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},R=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[R],z=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),G=t(`

Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​

Description: 计算平面与平面之间的夹角。

`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t('',1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),D={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},L={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},R=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[R],z=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),G=t(`

Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     elif isinstance(other, Plane3):
@@ -25,7 +25,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3 ​

Description: 计算两平面的交线。

`,16),I={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t('',1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`

Arguments:

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_intersection_line3(self, other: Plane3) -> Line3 ​

Description: 计算两平面的交线。

`,16),I={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t('',1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`

Arguments:

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -68,11 +68,11 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         v2 = l2.get_point(1) - l1.point
     return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method __and__(self, other: Line3) -> Point3 | None ​

Source code or View on GitHub
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None ​

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method __and__(self, other: Plane3) -> Line3 | None ​

Source code or View on GitHub
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None ​

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method __and__(self, other) ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
+    ...

method self & other ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -84,4 +84,4 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     else:
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

Description: 判断两个平面是否等价。

Arguments:

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method __rand__(self, other: Line3) -> Point3 ​

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,81);function Hs(Ds,Ls,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",D,[(i(),a("svg",L,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),z]),e(" 为直线的方向向量")])]),G,s("div",I,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default}; + return self.cal_intersection_point3(other)`,81);function Hs(Ds,Ls,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",D,[(i(),a("svg",L,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),z]),e(" 为直线的方向向量")])]),G,s("div",I,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default}; diff --git a/assets/en_api_mp_math_plane.md.D91Vt6aU.lean.js b/assets/en_api_mp_math_plane.md.CBNCeDF4.lean.js similarity index 98% rename from assets/en_api_mp_math_plane.md.D91Vt6aU.lean.js rename to assets/en_api_mp_math_plane.md.CBNCeDF4.lean.js index 6f7c97d..c605671 100644 --- a/assets/en_api_mp_math_plane.md.D91Vt6aU.lean.js +++ b/assets/en_api_mp_math_plane.md.CBNCeDF4.lean.js @@ -1 +1 @@ -import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t("",1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),D={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},L={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},R=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[R],z=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),G=t("",16),I={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t("",1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ds,Ls,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",D,[(i(),a("svg",L,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),z]),e(" 为直线的方向向量")])]),G,s("div",I,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default}; +import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t("",1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),D={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},L={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},R=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[R],z=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),G=t("",16),I={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t("",1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ds,Ls,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",D,[(i(),a("svg",L,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),z]),e(" 为直线的方向向量")])]),G,s("div",I,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default}; diff --git a/assets/ja_api_mp_math_line.md.BbbGydDH.js b/assets/ja_api_mp_math_line.md.CMckwGpV.js similarity index 96% rename from assets/ja_api_mp_math_line.md.BbbGydDH.js rename to assets/ja_api_mp_math_line.md.CMckwGpV.js index 984e8d0..1ffcad7 100644 --- a/assets/ja_api_mp_math_line.md.BbbGydDH.js +++ b/assets/ja_api_mp_math_line.md.CMckwGpV.js @@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

説明: 工厂函数 由两点构造直线。

引数:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

引数:

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

引数:

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
diff --git a/assets/ja_api_mp_math_line.md.BbbGydDH.lean.js b/assets/ja_api_mp_math_line.md.CMckwGpV.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_line.md.BbbGydDH.lean.js
rename to assets/ja_api_mp_math_line.md.CMckwGpV.lean.js
diff --git a/assets/ja_api_mp_math_plane.md.BvT51o_C.js b/assets/ja_api_mp_math_plane.md.D549kBN0.js
similarity index 97%
rename from assets/ja_api_mp_math_plane.md.BvT51o_C.js
rename to assets/ja_api_mp_math_plane.md.D549kBN0.js
index 17c8542..246a27f 100644
--- a/assets/ja_api_mp_math_plane.md.BvT51o_C.js
+++ b/assets/ja_api_mp_math_plane.md.D549kBN0.js
@@ -1,4 +1,4 @@
-import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=t(`
モジュール mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),n={name:"ja/api/mp_math/plane.md"},h=t(`
モジュール mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,7 +13,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t('',1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t(`
引数:
戻り値: AnyAngle: 夹角
例外:
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t('',1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t(`
引数:
戻り値: AnyAngle: 夹角
例外:
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     elif isinstance(other, Plane3):
@@ -25,7 +25,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t('',1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
引数:
  • other (Plane3): 另一个平面
戻り値: Line3: 交线
例外:
ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ls=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t('',1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
引数:
  • other (Plane3): 另一个平面
戻り値: Line3: 交线
例外:
ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -68,11 +68,11 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         v2 = l2.get_point(1) - l1.point
     return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード または GitHubで表示
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method self & other: Line3 => Point3 | None ​
ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self & other: Plane3 => Line3 | None ​
ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
戻り値: Line3 | Point3 | None: 交集
例外:
ソースコード または GitHubで表示
python
def __and__(self, other):
+    ...
method self & other ​
説明: 取两平面的交集（人话：交线）
引数:
戻り値: Line3 | Point3 | None: 交集
例外:
ソースコード または GitHubで表示
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -84,4 +84,4 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     else:
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default};
+    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default};
diff --git a/assets/ja_api_mp_math_plane.md.BvT51o_C.lean.js b/assets/ja_api_mp_math_plane.md.D549kBN0.lean.js
similarity index 95%
rename from assets/ja_api_mp_math_plane.md.BvT51o_C.lean.js
rename to assets/ja_api_mp_math_plane.md.D549kBN0.lean.js
index 0d3a76f..d8b76f9 100644
--- a/assets/ja_api_mp_math_plane.md.BvT51o_C.lean.js
+++ b/assets/ja_api_mp_math_plane.md.D549kBN0.lean.js
@@ -1 +1 @@
-import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t("",1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t("",16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t("",1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default};
+import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),n={name:"ja/api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t("",1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},N=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),z=[N],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t("",16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ls=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t("",1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,z)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default};
diff --git a/assets/style.Bh0M9mVm.css b/assets/style.Bh0M9mVm.css
deleted file mode 100644
index 2527c8f..0000000
--- a/assets/style.Bh0M9mVm.css
+++ /dev/null
@@ -1 +0,0 @@
-:root{--vp-c-white: #ffffff;--vp-c-black: #000000;--vp-c-neutral: var(--vp-c-black);--vp-c-neutral-inverse: var(--vp-c-white)}.dark{--vp-c-neutral: var(--vp-c-white);--vp-c-neutral-inverse: var(--vp-c-black)}:root{--vp-c-gray-1: #dddde3;--vp-c-gray-2: #e4e4e9;--vp-c-gray-3: #ebebef;--vp-c-gray-soft: rgba(142, 150, 170, .14);--vp-c-indigo-1: #3451b2;--vp-c-indigo-2: #3a5ccc;--vp-c-indigo-3: #5672cd;--vp-c-indigo-soft: rgba(100, 108, 255, .14);--vp-c-purple-1: #6f42c1;--vp-c-purple-2: #7e4cc9;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .14);--vp-c-green-1: #18794e;--vp-c-green-2: #299764;--vp-c-green-3: #30a46c;--vp-c-green-soft: rgba(16, 185, 129, .14);--vp-c-yellow-1: #915930;--vp-c-yellow-2: #946300;--vp-c-yellow-3: #9f6a00;--vp-c-yellow-soft: rgba(234, 179, 8, .14);--vp-c-red-1: #b8272c;--vp-c-red-2: #d5393e;--vp-c-red-3: #e0575b;--vp-c-red-soft: rgba(244, 63, 94, .14);--vp-c-sponsor: #db2777}.dark{--vp-c-gray-1: #515c67;--vp-c-gray-2: #414853;--vp-c-gray-3: #32363f;--vp-c-gray-soft: rgba(101, 117, 133, .16);--vp-c-indigo-1: #a8b1ff;--vp-c-indigo-2: #5c73e7;--vp-c-indigo-3: #3e63dd;--vp-c-indigo-soft: rgba(100, 108, 255, .16);--vp-c-purple-1: #c8abfa;--vp-c-purple-2: #a879e6;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .16);--vp-c-green-1: #3dd68c;--vp-c-green-2: #30a46c;--vp-c-green-3: #298459;--vp-c-green-soft: rgba(16, 185, 129, .16);--vp-c-yellow-1: #f9b44e;--vp-c-yellow-2: #da8b17;--vp-c-yellow-3: #a46a0a;--vp-c-yellow-soft: rgba(234, 179, 8, .16);--vp-c-red-1: #f66f81;--vp-c-red-2: #f14158;--vp-c-red-3: #b62a3c;--vp-c-red-soft: rgba(244, 63, 94, .16)}:root{--vp-c-bg: #ffffff;--vp-c-bg-alt: #f6f6f7;--vp-c-bg-elv: #ffffff;--vp-c-bg-soft: #f6f6f7}.dark{--vp-c-bg: #1b1b1f;--vp-c-bg-alt: #161618;--vp-c-bg-elv: #202127;--vp-c-bg-soft: #202127}:root{--vp-c-border: #c2c2c4;--vp-c-divider: #e2e2e3;--vp-c-gutter: #e2e2e3}.dark{--vp-c-border: #3c3f44;--vp-c-divider: #2e2e32;--vp-c-gutter: #000000}:root{--vp-c-text-1: rgba(60, 60, 67);--vp-c-text-2: rgba(60, 60, 67, .78);--vp-c-text-3: rgba(60, 60, 67, .56)}.dark{--vp-c-text-1: rgba(255, 255, 245, .86);--vp-c-text-2: rgba(235, 235, 245, .6);--vp-c-text-3: rgba(235, 235, 245, .38)}:root{--vp-c-default-1: var(--vp-c-gray-1);--vp-c-default-2: var(--vp-c-gray-2);--vp-c-default-3: var(--vp-c-gray-3);--vp-c-default-soft: var(--vp-c-gray-soft);--vp-c-brand-1: var(--vp-c-indigo-1);--vp-c-brand-2: var(--vp-c-indigo-2);--vp-c-brand-3: var(--vp-c-indigo-3);--vp-c-brand-soft: var(--vp-c-indigo-soft);--vp-c-brand: var(--vp-c-brand-1);--vp-c-tip-1: var(--vp-c-brand-1);--vp-c-tip-2: var(--vp-c-brand-2);--vp-c-tip-3: var(--vp-c-brand-3);--vp-c-tip-soft: var(--vp-c-brand-soft);--vp-c-note-1: var(--vp-c-brand-1);--vp-c-note-2: var(--vp-c-brand-2);--vp-c-note-3: var(--vp-c-brand-3);--vp-c-note-soft: var(--vp-c-brand-soft);--vp-c-success-1: var(--vp-c-green-1);--vp-c-success-2: var(--vp-c-green-2);--vp-c-success-3: var(--vp-c-green-3);--vp-c-success-soft: var(--vp-c-green-soft);--vp-c-important-1: var(--vp-c-purple-1);--vp-c-important-2: var(--vp-c-purple-2);--vp-c-important-3: var(--vp-c-purple-3);--vp-c-important-soft: var(--vp-c-purple-soft);--vp-c-warning-1: var(--vp-c-yellow-1);--vp-c-warning-2: var(--vp-c-yellow-2);--vp-c-warning-3: var(--vp-c-yellow-3);--vp-c-warning-soft: var(--vp-c-yellow-soft);--vp-c-danger-1: var(--vp-c-red-1);--vp-c-danger-2: var(--vp-c-red-2);--vp-c-danger-3: var(--vp-c-red-3);--vp-c-danger-soft: var(--vp-c-red-soft);--vp-c-caution-1: var(--vp-c-red-1);--vp-c-caution-2: var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, "Menlo", "Monaco", "Consolas", "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root:where(:lang(zh)){--vp-font-family-base: "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: var(--vp-c-text-1);--vp-custom-block-warning-bg: var(--vp-c-warning-soft);--vp-custom-block-warning-code-bg: var(--vp-c-warning-soft);--vp-custom-block-danger-border: transparent;--vp-custom-block-danger-text: var(--vp-c-text-1);--vp-custom-block-danger-bg: var(--vp-c-danger-soft);--vp-custom-block-danger-code-bg: var(--vp-c-danger-soft);--vp-custom-block-caution-border: transparent;--vp-custom-block-caution-text: var(--vp-c-text-1);--vp-custom-block-caution-bg: var(--vp-c-caution-soft);--vp-custom-block-caution-code-bg: var(--vp-c-caution-soft);--vp-custom-block-details-border: var(--vp-custom-block-info-border);--vp-custom-block-details-text: var(--vp-custom-block-info-text);--vp-custom-block-details-bg: var(--vp-custom-block-info-bg);--vp-custom-block-details-code-bg: var(--vp-custom-block-info-code-bg)}:root{--vp-input-border-color: var(--vp-c-border);--vp-input-bg-color: var(--vp-c-bg-alt);--vp-input-switch-bg-color: var(--vp-c-default-soft)}:root{--vp-nav-height: 64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: var(--vp-c-bg);--vp-local-search-result-bg: var(--vp-c-bg);--vp-local-search-result-border: var(--vp-c-divider);--vp-local-search-result-selected-bg: var(--vp-c-bg);--vp-local-search-result-selected-border: var(--vp-c-brand-1);--vp-local-search-highlight-bg: var(--vp-c-brand-1);--vp-local-search-highlight-text: var(--vp-c-neutral-inverse)}@media (prefers-reduced-motion: reduce){*,:before,:after{animation-delay:-1ms!important;animation-duration:1ms!important;animation-iteration-count:1!important;background-attachment:initial!important;scroll-behavior:auto!important;transition-duration:0s!important;transition-delay:0s!important}}*,:before,:after{box-sizing:border-box}html{line-height:1.4;font-size:16px;-webkit-text-size-adjust:100%}html.dark{color-scheme:dark}body{margin:0;width:100%;min-width:320px;min-height:100vh;line-height:24px;font-family:var(--vp-font-family-base);font-size:16px;font-weight:400;color:var(--vp-c-text-1);background-color:var(--vp-c-bg);font-synthesis:style;text-rendering:optimizeLegibility;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}main{display:block}h1,h2,h3,h4,h5,h6{margin:0;line-height:24px;font-size:16px;font-weight:400}p{margin:0}strong,b{font-weight:600}a,area,button,[role=button],input,label,select,summary,textarea{touch-action:manipulation}a{color:inherit;text-decoration:inherit}ol,ul{list-style:none;margin:0;padding:0}blockquote{margin:0}pre,code,kbd,samp{font-family:var(--vp-font-family-mono)}img,svg,video,canvas,audio,iframe,embed,object{display:block}figure{margin:0}img,video{max-width:100%;height:auto}button,input,optgroup,select,textarea{border:0;padding:0;line-height:inherit;color:inherit}button{padding:0;font-family:inherit;background-color:transparent;background-image:none}button:enabled,[role=button]:enabled{cursor:pointer}button:focus,button:focus-visible{outline:1px dotted;outline:4px auto -webkit-focus-ring-color}button:focus:not(:focus-visible){outline:none!important}input:focus,textarea:focus,select:focus{outline:none}table{border-collapse:collapse}input{background-color:transparent}input:-ms-input-placeholder,textarea:-ms-input-placeholder{color:var(--vp-c-text-3)}input::-ms-input-placeholder,textarea::-ms-input-placeholder{color:var(--vp-c-text-3)}input::placeholder,textarea::placeholder{color:var(--vp-c-text-3)}input::-webkit-outer-spin-button,input::-webkit-inner-spin-button{-webkit-appearance:none;margin:0}input[type=number]{-moz-appearance:textfield}textarea{resize:vertical}select{-webkit-appearance:none}fieldset{margin:0;padding:0}h1,h2,h3,h4,h5,h6,li,p{overflow-wrap:break-word}vite-error-overlay{z-index:9999}mjx-container{overflow-x:auto}mjx-container>svg{display:inline-block;margin:auto}[class^=vpi-],[class*=" vpi-"],.vp-icon{width:1em;height:1em}[class^=vpi-].bg,[class*=" vpi-"].bg,.vp-icon.bg{background-size:100% 100%;background-color:transparent}[class^=vpi-]:not(.bg),[class*=" vpi-"]:not(.bg),.vp-icon:not(.bg){-webkit-mask:var(--icon) no-repeat;mask:var(--icon) no-repeat;-webkit-mask-size:100% 100%;mask-size:100% 100%;background-color:currentColor;color:inherit}.vpi-align-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M21 6H3M15 12H3M17 18H3'/%3E%3C/svg%3E")}.vpi-arrow-right,.vpi-arrow-down,.vpi-arrow-left,.vpi-arrow-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5l7 7-7 7'/%3E%3C/svg%3E")}.vpi-chevron-right,.vpi-chevron-down,.vpi-chevron-left,.vpi-chevron-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 18 6-6-6-6'/%3E%3C/svg%3E")}.vpi-chevron-down,.vpi-arrow-down{transform:rotate(90deg)}.vpi-chevron-left,.vpi-arrow-left{transform:rotate(180deg)}.vpi-chevron-up,.vpi-arrow-up{transform:rotate(-90deg)}.vpi-square-pen{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3H5a2 2 0 0 0-2 2v14a2 2 0 0 0 2 2h14a2 2 0 0 0 2-2v-7'/%3E%3Cpath d='M18.375 2.625a2.121 2.121 0 1 1 3 3L12 15l-4 1 1-4Z'/%3E%3C/svg%3E")}.vpi-plus{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5v14'/%3E%3C/svg%3E")}.vpi-sun{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='4'/%3E%3Cpath d='M12 2v2M12 20v2M4.93 4.93l1.41 1.41M17.66 17.66l1.41 1.41M2 12h2M20 12h2M6.34 17.66l-1.41 1.41M19.07 4.93l-1.41 1.41'/%3E%3C/svg%3E")}.vpi-moon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3a6 6 0 0 0 9 9 9 9 0 1 1-9-9Z'/%3E%3C/svg%3E")}.vpi-more-horizontal{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='1'/%3E%3Ccircle cx='19' cy='12' r='1'/%3E%3Ccircle cx='5' cy='12' r='1'/%3E%3C/svg%3E")}.vpi-languages{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6'/%3E%3C/svg%3E")}.vpi-heart{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M19 14c1.49-1.46 3-3.21 3-5.5A5.5 5.5 0 0 0 16.5 3c-1.76 0-3 .5-4.5 2-1.5-1.5-2.74-2-4.5-2A5.5 5.5 0 0 0 2 8.5c0 2.3 1.5 4.05 3 5.5l7 7Z'/%3E%3C/svg%3E")}.vpi-search{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='11' cy='11' r='8'/%3E%3Cpath d='m21 21-4.3-4.3'/%3E%3C/svg%3E")}.vpi-layout-list{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='7' height='7' x='3' y='3' rx='1'/%3E%3Crect width='7' height='7' x='3' y='14' rx='1'/%3E%3Cpath d='M14 4h7M14 9h7M14 15h7M14 20h7'/%3E%3C/svg%3E")}.vpi-delete{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M20 5H9l-7 7 7 7h11a2 2 0 0 0 2-2V7a2 2 0 0 0-2-2ZM18 9l-6 6M12 9l6 6'/%3E%3C/svg%3E")}.vpi-corner-down-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 10-5 5 5 5'/%3E%3Cpath d='M20 4v7a4 4 0 0 1-4 4H4'/%3E%3C/svg%3E")}:root{--vp-icon-copy: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3C/svg%3E");--vp-icon-copied: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3Cpath d='m9 14 2 2 4-4'/%3E%3C/svg%3E")}.vpi-social-discord{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.317 4.37a19.791 19.791 0 0 0-4.885-1.515.074.074 0 0 0-.079.037c-.21.375-.444.864-.608 1.25a18.27 18.27 0 0 0-5.487 0 12.64 12.64 0 0 0-.617-1.25.077.077 0 0 0-.079-.037A19.736 19.736 0 0 0 3.677 4.37a.07.07 0 0 0-.032.027C.533 9.046-.32 13.58.099 18.057a.082.082 0 0 0 .031.057 19.9 19.9 0 0 0 5.993 3.03.078.078 0 0 0 .084-.028c.462-.63.874-1.295 1.226-1.994a.076.076 0 0 0-.041-.106 13.107 13.107 0 0 1-1.872-.892.077.077 0 0 1-.008-.128 10.2 10.2 0 0 0 .372-.292.074.074 0 0 1 .077-.01c3.928 1.793 8.18 1.793 12.062 0a.074.074 0 0 1 .078.01c.12.098.246.198.373.292a.077.077 0 0 1-.006.127 12.299 12.299 0 0 1-1.873.892.077.077 0 0 0-.041.107c.36.698.772 1.362 1.225 1.993a.076.076 0 0 0 .084.028 19.839 19.839 0 0 0 6.002-3.03.077.077 0 0 0 .032-.054c.5-5.177-.838-9.674-3.549-13.66a.061.061 0 0 0-.031-.03zM8.02 15.33c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.956-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.956 2.418-2.157 2.418zm7.975 0c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.955-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.946 2.418-2.157 2.418Z'/%3E%3C/svg%3E")}.vpi-social-facebook{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M9.101 23.691v-7.98H6.627v-3.667h2.474v-1.58c0-4.085 1.848-5.978 5.858-5.978.401 0 .955.042 1.468.103a8.68 8.68 0 0 1 1.141.195v3.325a8.623 8.623 0 0 0-.653-.036 26.805 26.805 0 0 0-.733-.009c-.707 0-1.259.096-1.675.309a1.686 1.686 0 0 0-.679.622c-.258.42-.374.995-.374 1.752v1.297h3.919l-.386 2.103-.287 1.564h-3.246v8.245C19.396 23.238 24 18.179 24 12.044c0-6.627-5.373-12-12-12s-12 5.373-12 12c0 5.628 3.874 10.35 9.101 11.647Z'/%3E%3C/svg%3E")}.vpi-social-github{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12'/%3E%3C/svg%3E")}.vpi-social-instagram{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M7.03.084c-1.277.06-2.149.264-2.91.563a5.874 5.874 0 0 0-2.124 1.388 5.878 5.878 0 0 0-1.38 2.127C.321 4.926.12 5.8.064 7.076.008 8.354-.005 8.764.001 12.023c.007 3.259.021 3.667.083 4.947.061 1.277.264 2.149.563 2.911.308.789.72 1.457 1.388 2.123a5.872 5.872 0 0 0 2.129 1.38c.763.295 1.636.496 2.913.552 1.278.056 1.689.069 4.947.063 3.257-.007 3.668-.021 4.947-.082 1.28-.06 2.147-.265 2.91-.563a5.881 5.881 0 0 0 2.123-1.388 5.881 5.881 0 0 0 1.38-2.129c.295-.763.496-1.636.551-2.912.056-1.28.07-1.69.063-4.948-.006-3.258-.02-3.667-.081-4.947-.06-1.28-.264-2.148-.564-2.911a5.892 5.892 0 0 0-1.387-2.123 5.857 5.857 0 0 0-2.128-1.38C19.074.322 18.202.12 16.924.066 15.647.009 15.236-.006 11.977 0 8.718.008 8.31.021 7.03.084m.14 21.693c-1.17-.05-1.805-.245-2.228-.408a3.736 3.736 0 0 1-1.382-.895 3.695 3.695 0 0 1-.9-1.378c-.165-.423-.363-1.058-.417-2.228-.06-1.264-.072-1.644-.08-4.848-.006-3.204.006-3.583.061-4.848.05-1.169.246-1.805.408-2.228.216-.561.477-.96.895-1.382a3.705 3.705 0 0 1 1.379-.9c.423-.165 1.057-.361 2.227-.417 1.265-.06 1.644-.072 4.848-.08 3.203-.006 3.583.006 4.85.062 1.168.05 1.804.244 2.227.408.56.216.96.475 1.382.895.421.42.681.817.9 1.378.165.422.362 1.056.417 2.227.06 1.265.074 1.645.08 4.848.005 3.203-.006 3.583-.061 4.848-.051 1.17-.245 1.805-.408 2.23-.216.56-.477.96-.896 1.38a3.705 3.705 0 0 1-1.378.9c-.422.165-1.058.362-2.226.418-1.266.06-1.645.072-4.85.079-3.204.007-3.582-.006-4.848-.06m9.783-16.192a1.44 1.44 0 1 0 1.437-1.442 1.44 1.44 0 0 0-1.437 1.442M5.839 12.012a6.161 6.161 0 1 0 12.323-.024 6.162 6.162 0 0 0-12.323.024M8 12.008A4 4 0 1 1 12.008 16 4 4 0 0 1 8 12.008'/%3E%3C/svg%3E")}.vpi-social-linkedin{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.447 20.452h-3.554v-5.569c0-1.328-.027-3.037-1.852-3.037-1.853 0-2.136 1.445-2.136 2.939v5.667H9.351V9h3.414v1.561h.046c.477-.9 1.637-1.85 3.37-1.85 3.601 0 4.267 2.37 4.267 5.455v6.286zM5.337 7.433a2.062 2.062 0 0 1-2.063-2.065 2.064 2.064 0 1 1 2.063 2.065zm1.782 13.019H3.555V9h3.564v11.452zM22.225 0H1.771C.792 0 0 .774 0 1.729v20.542C0 23.227.792 24 1.771 24h20.451C23.2 24 24 23.227 24 22.271V1.729C24 .774 23.2 0 22.222 0h.003z'/%3E%3C/svg%3E")}.vpi-social-mastodon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.268 5.313c-.35-2.578-2.617-4.61-5.304-5.004C17.51.242 15.792 0 11.813 0h-.03c-3.98 0-4.835.242-5.288.309C3.882.692 1.496 2.518.917 5.127.64 6.412.61 7.837.661 9.143c.074 1.874.088 3.745.26 5.611.118 1.24.325 2.47.62 3.68.55 2.237 2.777 4.098 4.96 4.857 2.336.792 4.849.923 7.256.38.265-.061.527-.132.786-.213.585-.184 1.27-.39 1.774-.753a.057.057 0 0 0 .023-.043v-1.809a.052.052 0 0 0-.02-.041.053.053 0 0 0-.046-.01 20.282 20.282 0 0 1-4.709.545c-2.73 0-3.463-1.284-3.674-1.818a5.593 5.593 0 0 1-.319-1.433.053.053 0 0 1 .066-.054c1.517.363 3.072.546 4.632.546.376 0 .75 0 1.125-.01 1.57-.044 3.224-.124 4.768-.422.038-.008.077-.015.11-.024 2.435-.464 4.753-1.92 4.989-5.604.008-.145.03-1.52.03-1.67.002-.512.167-3.63-.024-5.545zm-3.748 9.195h-2.561V8.29c0-1.309-.55-1.976-1.67-1.976-1.23 0-1.846.79-1.846 2.35v3.403h-2.546V8.663c0-1.56-.617-2.35-1.848-2.35-1.112 0-1.668.668-1.67 1.977v6.218H4.822V8.102c0-1.31.337-2.35 1.011-3.12.696-.77 1.608-1.164 2.74-1.164 1.311 0 2.302.5 2.962 1.498l.638 1.06.638-1.06c.66-.999 1.65-1.498 2.96-1.498 1.13 0 2.043.395 2.74 1.164.675.77 1.012 1.81 1.012 3.12z'/%3E%3C/svg%3E")}.vpi-social-npm{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M1.763 0C.786 0 0 .786 0 1.763v20.474C0 23.214.786 24 1.763 24h20.474c.977 0 1.763-.786 1.763-1.763V1.763C24 .786 23.214 0 22.237 0zM5.13 5.323l13.837.019-.009 13.836h-3.464l.01-10.382h-3.456L12.04 19.17H5.113z'/%3E%3C/svg%3E")}.vpi-social-slack{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M5.042 15.165a2.528 2.528 0 0 1-2.52 2.523A2.528 2.528 0 0 1 0 15.165a2.527 2.527 0 0 1 2.522-2.52h2.52v2.52zm1.271 0a2.527 2.527 0 0 1 2.521-2.52 2.527 2.527 0 0 1 2.521 2.52v6.313A2.528 2.528 0 0 1 8.834 24a2.528 2.528 0 0 1-2.521-2.522v-6.313zM8.834 5.042a2.528 2.528 0 0 1-2.521-2.52A2.528 2.528 0 0 1 8.834 0a2.528 2.528 0 0 1 2.521 2.522v2.52H8.834zm0 1.271a2.528 2.528 0 0 1 2.521 2.521 2.528 2.528 0 0 1-2.521 2.521H2.522A2.528 2.528 0 0 1 0 8.834a2.528 2.528 0 0 1 2.522-2.521h6.312zm10.122 2.521a2.528 2.528 0 0 1 2.522-2.521A2.528 2.528 0 0 1 24 8.834a2.528 2.528 0 0 1-2.522 2.521h-2.522V8.834zm-1.268 0a2.528 2.528 0 0 1-2.523 2.521 2.527 2.527 0 0 1-2.52-2.521V2.522A2.527 2.527 0 0 1 15.165 0a2.528 2.528 0 0 1 2.523 2.522v6.312zm-2.523 10.122a2.528 2.528 0 0 1 2.523 2.522A2.528 2.528 0 0 1 15.165 24a2.527 2.527 0 0 1-2.52-2.522v-2.522h2.52zm0-1.268a2.527 2.527 0 0 1-2.52-2.523 2.526 2.526 0 0 1 2.52-2.52h6.313A2.527 2.527 0 0 1 24 15.165a2.528 2.528 0 0 1-2.522 2.523h-6.313z'/%3E%3C/svg%3E")}.vpi-social-twitter,.vpi-social-x{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M18.901 1.153h3.68l-8.04 9.19L24 22.846h-7.406l-5.8-7.584-6.638 7.584H.474l8.6-9.83L0 1.154h7.594l5.243 6.932ZM17.61 20.644h2.039L6.486 3.24H4.298Z'/%3E%3C/svg%3E")}.vpi-social-youtube{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.498 6.186a3.016 3.016 0 0 0-2.122-2.136C19.505 3.545 12 3.545 12 3.545s-7.505 0-9.377.505A3.017 3.017 0 0 0 .502 6.186C0 8.07 0 12 0 12s0 3.93.502 5.814a3.016 3.016 0 0 0 2.122 2.136c1.871.505 9.376.505 9.376.505s7.505 0 9.377-.505a3.015 3.015 0 0 0 2.122-2.136C24 15.93 24 12 24 12s0-3.93-.502-5.814zM9.545 15.568V8.432L15.818 12l-6.273 3.568z'/%3E%3C/svg%3E")}.visually-hidden{position:absolute;width:1px;height:1px;white-space:nowrap;clip:rect(0 0 0 0);clip-path:inset(50%);overflow:hidden}.custom-block{border:1px solid transparent;border-radius:8px;padding:16px 16px 8px;line-height:24px;font-size:var(--vp-custom-block-font-size);color:var(--vp-c-text-2)}.custom-block.info{border-color:var(--vp-custom-block-info-border);color:var(--vp-custom-block-info-text);background-color:var(--vp-custom-block-info-bg)}.custom-block.info a,.custom-block.info code{color:var(--vp-c-brand-1)}.custom-block.info a:hover,.custom-block.info a:hover>code{color:var(--vp-c-brand-2)}.custom-block.info code{background-color:var(--vp-custom-block-info-code-bg)}.custom-block.note{border-color:var(--vp-custom-block-note-border);color:var(--vp-custom-block-note-text);background-color:var(--vp-custom-block-note-bg)}.custom-block.note a,.custom-block.note code{color:var(--vp-c-brand-1)}.custom-block.note a:hover,.custom-block.note a:hover>code{color:var(--vp-c-brand-2)}.custom-block.note code{background-color:var(--vp-custom-block-note-code-bg)}.custom-block.tip{border-color:var(--vp-custom-block-tip-border);color:var(--vp-custom-block-tip-text);background-color:var(--vp-custom-block-tip-bg)}.custom-block.tip a,.custom-block.tip code{color:var(--vp-c-tip-1)}.custom-block.tip a:hover,.custom-block.tip a:hover>code{color:var(--vp-c-tip-2)}.custom-block.tip code{background-color:var(--vp-custom-block-tip-code-bg)}.custom-block.important{border-color:var(--vp-custom-block-important-border);color:var(--vp-custom-block-important-text);background-color:var(--vp-custom-block-important-bg)}.custom-block.important a,.custom-block.important code{color:var(--vp-c-important-1)}.custom-block.important a:hover,.custom-block.important a:hover>code{color:var(--vp-c-important-2)}.custom-block.important code{background-color:var(--vp-custom-block-important-code-bg)}.custom-block.warning{border-color:var(--vp-custom-block-warning-border);color:var(--vp-custom-block-warning-text);background-color:var(--vp-custom-block-warning-bg)}.custom-block.warning a,.custom-block.warning code{color:var(--vp-c-warning-1)}.custom-block.warning a:hover,.custom-block.warning a:hover>code{color:var(--vp-c-warning-2)}.custom-block.warning code{background-color:var(--vp-custom-block-warning-code-bg)}.custom-block.danger{border-color:var(--vp-custom-block-danger-border);color:var(--vp-custom-block-danger-text);background-color:var(--vp-custom-block-danger-bg)}.custom-block.danger a,.custom-block.danger code{color:var(--vp-c-danger-1)}.custom-block.danger a:hover,.custom-block.danger a:hover>code{color:var(--vp-c-danger-2)}.custom-block.danger code{background-color:var(--vp-custom-block-danger-code-bg)}.custom-block.caution{border-color:var(--vp-custom-block-caution-border);color:var(--vp-custom-block-caution-text);background-color:var(--vp-custom-block-caution-bg)}.custom-block.caution a,.custom-block.caution code{color:var(--vp-c-caution-1)}.custom-block.caution a:hover,.custom-block.caution a:hover>code{color:var(--vp-c-caution-2)}.custom-block.caution code{background-color:var(--vp-custom-block-caution-code-bg)}.custom-block.details{border-color:var(--vp-custom-block-details-border);color:var(--vp-custom-block-details-text);background-color:var(--vp-custom-block-details-bg)}.custom-block.details a{color:var(--vp-c-brand-1)}.custom-block.details a:hover,.custom-block.details a:hover>code{color:var(--vp-c-brand-2)}.custom-block.details code{background-color:var(--vp-custom-block-details-code-bg)}.custom-block-title{font-weight:600}.custom-block p+p{margin:8px 0}.custom-block.details summary{margin:0 0 8px;font-weight:700;cursor:pointer;-webkit-user-select:none;user-select:none}.custom-block.details summary+p{margin:8px 0}.custom-block a{color:inherit;font-weight:600;text-decoration:underline;text-underline-offset:2px;transition:opacity .25s}.custom-block a:hover{opacity:.75}.custom-block code{font-size:var(--vp-custom-block-code-font-size)}.custom-block.custom-block th,.custom-block.custom-block blockquote>p{font-size:var(--vp-custom-block-font-size);color:inherit}.dark .vp-code span{color:var(--shiki-dark, inherit)}html:not(.dark) .vp-code span{color:var(--shiki-light, inherit)}.vp-code-group{margin-top:16px}.vp-code-group .tabs{position:relative;display:flex;margin-right:-24px;margin-left:-24px;padding:0 12px;background-color:var(--vp-code-tab-bg);overflow-x:auto;overflow-y:hidden;box-shadow:inset 0 -1px var(--vp-code-tab-divider)}@media (min-width: 640px){.vp-code-group .tabs{margin-right:0;margin-left:0;border-radius:8px 8px 0 0}}.vp-code-group .tabs input{position:fixed;opacity:0;pointer-events:none}.vp-code-group .tabs label{position:relative;display:inline-block;border-bottom:1px solid transparent;padding:0 12px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-code-tab-text-color);white-space:nowrap;cursor:pointer;transition:color .25s}.vp-code-group .tabs label:after{position:absolute;right:8px;bottom:-1px;left:8px;z-index:1;height:2px;border-radius:2px;content:"";background-color:transparent;transition:background-color .25s}.vp-code-group label:hover{color:var(--vp-code-tab-hover-text-color)}.vp-code-group input:checked+label{color:var(--vp-code-tab-active-text-color)}.vp-code-group input:checked+label:after{background-color:var(--vp-code-tab-active-bar-color)}.vp-code-group div[class*=language-],.vp-block{display:none;margin-top:0!important;border-top-left-radius:0!important;border-top-right-radius:0!important}.vp-code-group div[class*=language-].active,.vp-block.active{display:block}.vp-block{padding:20px 24px}.vp-doc h1,.vp-doc h2,.vp-doc h3,.vp-doc h4,.vp-doc h5,.vp-doc h6{position:relative;font-weight:600;outline:none}.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:28px}.vp-doc h2{margin:48px 0 16px;border-top:1px solid var(--vp-c-divider);padding-top:24px;letter-spacing:-.02em;line-height:32px;font-size:24px}.vp-doc h3{margin:32px 0 0;letter-spacing:-.01em;line-height:28px;font-size:20px}.vp-doc h4{margin:24px 0 0;letter-spacing:-.01em;line-height:24px;font-size:18px}.vp-doc .header-anchor{position:absolute;top:0;left:0;margin-left:-.87em;font-weight:500;-webkit-user-select:none;user-select:none;opacity:0;text-decoration:none;transition:color .25s,opacity .25s}.vp-doc .header-anchor:before{content:var(--vp-header-anchor-symbol)}.vp-doc h1:hover .header-anchor,.vp-doc h1 .header-anchor:focus,.vp-doc h2:hover .header-anchor,.vp-doc h2 .header-anchor:focus,.vp-doc h3:hover .header-anchor,.vp-doc h3 .header-anchor:focus,.vp-doc h4:hover .header-anchor,.vp-doc h4 .header-anchor:focus,.vp-doc h5:hover .header-anchor,.vp-doc h5 .header-anchor:focus,.vp-doc h6:hover .header-anchor,.vp-doc h6 .header-anchor:focus{opacity:1}@media (min-width: 768px){.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:32px}}.vp-doc h2 .header-anchor{top:24px}.vp-doc p,.vp-doc summary{margin:16px 0}.vp-doc p{line-height:28px}.vp-doc blockquote{margin:16px 0;border-left:2px solid var(--vp-c-divider);padding-left:16px;transition:border-color .5s;color:var(--vp-c-text-2)}.vp-doc blockquote>p{margin:0;font-size:16px;transition:color .5s}.vp-doc a{font-weight:500;color:var(--vp-c-brand-1);text-decoration:underline;text-underline-offset:2px;transition:color .25s,opacity .25s}.vp-doc a:hover{color:var(--vp-c-brand-2)}.vp-doc strong{font-weight:600}.vp-doc ul,.vp-doc ol{padding-left:1.25rem;margin:16px 0}.vp-doc ul{list-style:disc}.vp-doc ol{list-style:decimal}.vp-doc li+li{margin-top:8px}.vp-doc li>ol,.vp-doc li>ul{margin:8px 0 0}.vp-doc table{display:block;border-collapse:collapse;margin:20px 0;overflow-x:auto}.vp-doc tr{background-color:var(--vp-c-bg);border-top:1px solid var(--vp-c-divider);transition:background-color .5s}.vp-doc tr:nth-child(2n){background-color:var(--vp-c-bg-soft)}.vp-doc th,.vp-doc td{border:1px solid var(--vp-c-divider);padding:8px 16px}.vp-doc th{text-align:left;font-size:14px;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-doc td{font-size:14px}.vp-doc hr{margin:16px 0;border:none;border-top:1px solid var(--vp-c-divider)}.vp-doc .custom-block{margin:16px 0}.vp-doc .custom-block p{margin:8px 0;line-height:24px}.vp-doc .custom-block p:first-child{margin:0}.vp-doc .custom-block div[class*=language-]{margin:8px 0;border-radius:8px}.vp-doc .custom-block div[class*=language-] code{font-weight:400;background-color:transparent}.vp-doc .custom-block .vp-code-group .tabs{margin:0;border-radius:8px 8px 0 0}.vp-doc :not(pre,h1,h2,h3,h4,h5,h6)>code{font-size:var(--vp-code-font-size);color:var(--vp-code-color)}.vp-doc :not(pre)>code{border-radius:4px;padding:3px 6px;background-color:var(--vp-code-bg);transition:color .25s,background-color .5s}.vp-doc a>code{color:var(--vp-code-link-color)}.vp-doc a:hover>code{color:var(--vp-code-link-hover-color)}.vp-doc h1>code,.vp-doc h2>code,.vp-doc h3>code,.vp-doc h4>code{font-size:.9em}.vp-doc div[class*=language-],.vp-block{position:relative;margin:16px -24px;background-color:var(--vp-code-block-bg);overflow-x:auto;transition:background-color .5s}@media (min-width: 640px){.vp-doc div[class*=language-],.vp-block{border-radius:8px;margin:16px 0}}@media (max-width: 639px){.vp-doc li div[class*=language-]{border-radius:8px 0 0 8px}}.vp-doc div[class*=language-]+div[class*=language-],.vp-doc div[class$=-api]+div[class*=language-],.vp-doc div[class*=language-]+div[class$=-api]>div[class*=language-]{margin-top:-8px}.vp-doc [class*=language-] pre,.vp-doc [class*=language-] code{direction:ltr;text-align:left;white-space:pre;word-spacing:normal;word-break:normal;word-wrap:normal;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-hyphens:none;-moz-hyphens:none;-ms-hyphens:none;hyphens:none}.vp-doc [class*=language-] pre{position:relative;z-index:1;margin:0;padding:20px 0;background:transparent;overflow-x:auto}.vp-doc [class*=language-] code{display:block;padding:0 24px;width:fit-content;min-width:100%;line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-block-color);transition:color .5s}.vp-doc [class*=language-] code .highlighted{background-color:var(--vp-code-line-highlight-color);transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .highlighted.error{background-color:var(--vp-code-line-error-color)}.vp-doc [class*=language-] code .highlighted.warning{background-color:var(--vp-code-line-warning-color)}.vp-doc [class*=language-] code .diff{transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .diff:before{position:absolute;left:10px}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){filter:blur(.095rem);opacity:.4;transition:filter .35s,opacity .35s}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){opacity:.7;transition:filter .35s,opacity .35s}.vp-doc [class*=language-]:hover .has-focused-lines .line:not(.has-focus){filter:blur(0);opacity:1}.vp-doc [class*=language-] code .diff.remove{background-color:var(--vp-code-line-diff-remove-color);opacity:.7}.vp-doc [class*=language-] code .diff.remove:before{content:"-";color:var(--vp-code-line-diff-remove-symbol-color)}.vp-doc [class*=language-] code .diff.add{background-color:var(--vp-code-line-diff-add-color)}.vp-doc [class*=language-] code .diff.add:before{content:"+";color:var(--vp-code-line-diff-add-symbol-color)}.vp-doc div[class*=language-].line-numbers-mode{padding-left:32px}.vp-doc .line-numbers-wrapper{position:absolute;top:0;bottom:0;left:0;z-index:3;border-right:1px solid var(--vp-code-block-divider-color);padding-top:20px;width:32px;text-align:center;font-family:var(--vp-font-family-mono);line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-line-number-color);transition:border-color .5s,color .5s}.vp-doc [class*=language-]>button.copy{direction:ltr;position:absolute;top:12px;right:12px;z-index:3;border:1px solid var(--vp-code-copy-code-border-color);border-radius:4px;width:40px;height:40px;background-color:var(--vp-code-copy-code-bg);opacity:0;cursor:pointer;background-image:var(--vp-icon-copy);background-position:50%;background-size:20px;background-repeat:no-repeat;transition:border-color .25s,background-color .25s,opacity .25s}.vp-doc [class*=language-]:hover>button.copy,.vp-doc [class*=language-]>button.copy:focus{opacity:1}.vp-doc [class*=language-]>button.copy:hover,.vp-doc [class*=language-]>button.copy.copied{border-color:var(--vp-code-copy-code-hover-border-color);background-color:var(--vp-code-copy-code-hover-bg)}.vp-doc [class*=language-]>button.copy.copied,.vp-doc [class*=language-]>button.copy:hover.copied{border-radius:0 4px 4px 0;background-color:var(--vp-code-copy-code-hover-bg);background-image:var(--vp-icon-copied)}.vp-doc [class*=language-]>button.copy.copied:before,.vp-doc [class*=language-]>button.copy:hover.copied:before{position:relative;top:-1px;transform:translate(calc(-100% - 1px));display:flex;justify-content:center;align-items:center;border:1px solid var(--vp-code-copy-code-hover-border-color);border-right:0;border-radius:4px 0 0 4px;padding:0 10px;width:fit-content;height:40px;text-align:center;font-size:12px;font-weight:500;color:var(--vp-code-copy-code-active-text);background-color:var(--vp-code-copy-code-hover-bg);white-space:nowrap;content:var(--vp-code-copy-copied-text-content)}.vp-doc [class*=language-]>span.lang{position:absolute;top:2px;right:8px;z-index:2;font-size:12px;font-weight:500;color:var(--vp-code-lang-color);transition:color .4s,opacity .4s}.vp-doc [class*=language-]:hover>button.copy+span.lang,.vp-doc [class*=language-]>button.copy:focus+span.lang{opacity:0}.vp-doc .VPTeamMembers{margin-top:24px}.vp-doc .VPTeamMembers.small.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}.vp-doc .VPTeamMembers.small.count-2 .container,.vp-doc .VPTeamMembers.small.count-3 .container{max-width:100%!important}.vp-doc .VPTeamMembers.medium.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}:is(.vp-external-link-icon,.vp-doc a[href*="://"],.vp-doc a[target=_blank]):not(.no-icon):after{display:inline-block;margin-top:-1px;margin-left:4px;width:11px;height:11px;background:currentColor;color:var(--vp-c-text-3);flex-shrink:0;--icon: url("data:image/svg+xml, %3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24' %3E%3Cpath d='M0 0h24v24H0V0z' fill='none' /%3E%3Cpath d='M9 5v2h6.59L4 18.59 5.41 20 17 8.41V15h2V5H9z' /%3E%3C/svg%3E");-webkit-mask-image:var(--icon);mask-image:var(--icon)}.vp-external-link-icon:after{content:""}.external-link-icon-enabled :is(.vp-doc a[href*="://"],.vp-doc a[target=_blank]):after{content:"";color:currentColor}.vp-sponsor{border-radius:16px;overflow:hidden}.vp-sponsor.aside{border-radius:12px}.vp-sponsor-section+.vp-sponsor-section{margin-top:4px}.vp-sponsor-tier{margin:0 0 4px!important;text-align:center;letter-spacing:1px!important;line-height:24px;width:100%;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-sponsor.normal .vp-sponsor-tier{padding:13px 0 11px;font-size:14px}.vp-sponsor.aside .vp-sponsor-tier{padding:9px 0 7px;font-size:12px}.vp-sponsor-grid+.vp-sponsor-tier{margin-top:4px}.vp-sponsor-grid{display:flex;flex-wrap:wrap;gap:4px}.vp-sponsor-grid.xmini .vp-sponsor-grid-link{height:64px}.vp-sponsor-grid.xmini .vp-sponsor-grid-image{max-width:64px;max-height:22px}.vp-sponsor-grid.mini .vp-sponsor-grid-link{height:72px}.vp-sponsor-grid.mini .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.small .vp-sponsor-grid-link{height:96px}.vp-sponsor-grid.small .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.medium .vp-sponsor-grid-link{height:112px}.vp-sponsor-grid.medium .vp-sponsor-grid-image{max-width:120px;max-height:36px}.vp-sponsor-grid.big .vp-sponsor-grid-link{height:184px}.vp-sponsor-grid.big .vp-sponsor-grid-image{max-width:192px;max-height:56px}.vp-sponsor-grid[data-vp-grid="2"] .vp-sponsor-grid-item{width:calc((100% - 4px)/2)}.vp-sponsor-grid[data-vp-grid="3"] .vp-sponsor-grid-item{width:calc((100% - 4px * 2) / 3)}.vp-sponsor-grid[data-vp-grid="4"] .vp-sponsor-grid-item{width:calc((100% - 12px)/4)}.vp-sponsor-grid[data-vp-grid="5"] .vp-sponsor-grid-item{width:calc((100% - 16px)/5)}.vp-sponsor-grid[data-vp-grid="6"] .vp-sponsor-grid-item{width:calc((100% - 4px * 5) / 6)}.vp-sponsor-grid-item{flex-shrink:0;width:100%;background-color:var(--vp-c-bg-soft);transition:background-color .25s}.vp-sponsor-grid-item:hover{background-color:var(--vp-c-default-soft)}.vp-sponsor-grid-item:hover .vp-sponsor-grid-image{filter:grayscale(0) invert(0)}.vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.dark .vp-sponsor-grid-item:hover{background-color:var(--vp-c-white)}.dark .vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.vp-sponsor-grid-link{display:flex}.vp-sponsor-grid-box{display:flex;justify-content:center;align-items:center;width:100%}.vp-sponsor-grid-image{max-width:100%;filter:grayscale(1);transition:filter .25s}.dark .vp-sponsor-grid-image{filter:grayscale(1) invert(1)}.VPBadge{display:inline-block;margin-left:2px;border:1px solid transparent;border-radius:12px;padding:0 10px;line-height:22px;font-size:12px;font-weight:500;transform:translateY(-2px)}.VPBadge.small{padding:0 6px;line-height:18px;font-size:10px;transform:translateY(-8px)}.VPDocFooter .VPBadge{display:none}.vp-doc h1>.VPBadge{margin-top:4px;vertical-align:top}.vp-doc h2>.VPBadge{margin-top:3px;padding:0 8px;vertical-align:top}.vp-doc h3>.VPBadge{vertical-align:middle}.vp-doc h4>.VPBadge,.vp-doc h5>.VPBadge,.vp-doc h6>.VPBadge{vertical-align:middle;line-height:18px}.VPBadge.info{border-color:var(--vp-badge-info-border);color:var(--vp-badge-info-text);background-color:var(--vp-badge-info-bg)}.VPBadge.tip{border-color:var(--vp-badge-tip-border);color:var(--vp-badge-tip-text);background-color:var(--vp-badge-tip-bg)}.VPBadge.warning{border-color:var(--vp-badge-warning-border);color:var(--vp-badge-warning-text);background-color:var(--vp-badge-warning-bg)}.VPBadge.danger{border-color:var(--vp-badge-danger-border);color:var(--vp-badge-danger-text);background-color:var(--vp-badge-danger-bg)}.VPBackdrop[data-v-daa1937f]{position:fixed;top:0;right:0;bottom:0;left:0;z-index:var(--vp-z-index-backdrop);background:var(--vp-backdrop-bg-color);transition:opacity .5s}.VPBackdrop.fade-enter-from[data-v-daa1937f],.VPBackdrop.fade-leave-to[data-v-daa1937f]{opacity:0}.VPBackdrop.fade-leave-active[data-v-daa1937f]{transition-duration:.25s}@media (min-width: 1280px){.VPBackdrop[data-v-daa1937f]{display:none}}.NotFound[data-v-2aa14331]{padding:64px 24px 96px;text-align:center}@media (min-width: 768px){.NotFound[data-v-2aa14331]{padding:96px 32px 168px}}.code[data-v-2aa14331]{line-height:64px;font-size:64px;font-weight:600}.title[data-v-2aa14331]{padding-top:12px;letter-spacing:2px;line-height:20px;font-size:20px;font-weight:700}.divider[data-v-2aa14331]{margin:24px auto 18px;width:64px;height:1px;background-color:var(--vp-c-divider)}.quote[data-v-2aa14331]{margin:0 auto;max-width:256px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.action[data-v-2aa14331]{padding-top:20px}.link[data-v-2aa14331]{display:inline-block;border:1px solid var(--vp-c-brand-1);border-radius:16px;padding:3px 16px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:border-color .25s,color .25s}.link[data-v-2aa14331]:hover{border-color:var(--vp-c-brand-2);color:var(--vp-c-brand-2)}.root[data-v-b9c884bb]{position:relative;z-index:1}.nested[data-v-b9c884bb]{padding-right:16px;padding-left:16px}.outline-link[data-v-b9c884bb]{display:block;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-2);white-space:nowrap;overflow:hidden;text-overflow:ellipsis;transition:color .5s}.outline-link[data-v-b9c884bb]:hover,.outline-link.active[data-v-b9c884bb]{color:var(--vp-c-text-1);transition:color .25s}.outline-link.nested[data-v-b9c884bb]{padding-left:13px}.VPDocAsideOutline[data-v-d34649dc]{display:none}.VPDocAsideOutline.has-outline[data-v-d34649dc]{display:block}.content[data-v-d34649dc]{position:relative;border-left:1px solid var(--vp-c-divider);padding-left:16px;font-size:13px;font-weight:500}.outline-marker[data-v-d34649dc]{position:absolute;top:32px;left:-1px;z-index:0;opacity:0;width:2px;border-radius:2px;height:18px;background-color:var(--vp-c-brand-1);transition:top .25s cubic-bezier(0,1,.5,1),background-color .5s,opacity .25s}.outline-title[data-v-d34649dc]{line-height:32px;font-size:14px;font-weight:600}.VPDocAside[data-v-8951c20f]{display:flex;flex-direction:column;flex-grow:1}.spacer[data-v-8951c20f]{flex-grow:1}.VPDocAside[data-v-8951c20f] .spacer+.VPDocAsideSponsors,.VPDocAside[data-v-8951c20f] .spacer+.VPDocAsideCarbonAds{margin-top:24px}.VPDocAside[data-v-8951c20f] .VPDocAsideSponsors+.VPDocAsideCarbonAds{margin-top:16px}.VPLastUpdated[data-v-19bf19fb]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 640px){.VPLastUpdated[data-v-19bf19fb]{line-height:32px;font-size:14px;font-weight:500}}.VPDocFooter[data-v-28deee4a]{margin-top:64px}.edit-info[data-v-28deee4a]{padding-bottom:18px}@media (min-width: 640px){.edit-info[data-v-28deee4a]{display:flex;justify-content:space-between;align-items:center;padding-bottom:14px}}.edit-link-button[data-v-28deee4a]{display:flex;align-items:center;border:0;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.edit-link-button[data-v-28deee4a]:hover{color:var(--vp-c-brand-2)}.edit-link-icon[data-v-28deee4a]{margin-right:8px}.prev-next[data-v-28deee4a]{border-top:1px solid var(--vp-c-divider);padding-top:24px;display:grid;grid-row-gap:8px}@media (min-width: 640px){.prev-next[data-v-28deee4a]{grid-template-columns:repeat(2,1fr);grid-column-gap:16px}}.pager-link[data-v-28deee4a]{display:block;border:1px solid var(--vp-c-divider);border-radius:8px;padding:11px 16px 13px;width:100%;height:100%;transition:border-color .25s}.pager-link[data-v-28deee4a]:hover{border-color:var(--vp-c-brand-1)}.pager-link.next[data-v-28deee4a]{margin-left:auto;text-align:right}.desc[data-v-28deee4a]{display:block;line-height:20px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.title[data-v-28deee4a]{display:block;line-height:20px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.VPDoc[data-v-01c90815]{padding:32px 24px 96px;width:100%}@media (min-width: 768px){.VPDoc[data-v-01c90815]{padding:48px 32px 128px}}@media (min-width: 960px){.VPDoc[data-v-01c90815]{padding:48px 32px 0}.VPDoc:not(.has-sidebar) .container[data-v-01c90815]{display:flex;justify-content:center;max-width:992px}.VPDoc:not(.has-sidebar) .content[data-v-01c90815]{max-width:752px}}@media (min-width: 1280px){.VPDoc .container[data-v-01c90815]{display:flex;justify-content:center}.VPDoc .aside[data-v-01c90815]{display:block}}@media (min-width: 1440px){.VPDoc:not(.has-sidebar) .content[data-v-01c90815]{max-width:784px}.VPDoc:not(.has-sidebar) .container[data-v-01c90815]{max-width:1104px}}.container[data-v-01c90815]{margin:0 auto;width:100%}.aside[data-v-01c90815]{position:relative;display:none;order:2;flex-grow:1;padding-left:32px;width:100%;max-width:256px}.left-aside[data-v-01c90815]{order:1;padding-left:unset;padding-right:32px}.aside-container[data-v-01c90815]{position:fixed;top:0;padding-top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + var(--vp-doc-top-height, 0px) + 48px);width:224px;height:100vh;overflow-x:hidden;overflow-y:auto;scrollbar-width:none}.aside-container[data-v-01c90815]::-webkit-scrollbar{display:none}.aside-curtain[data-v-01c90815]{position:fixed;bottom:0;z-index:10;width:224px;height:32px;background:linear-gradient(transparent,var(--vp-c-bg) 70%)}.aside-content[data-v-01c90815]{display:flex;flex-direction:column;min-height:calc(100vh - (var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px));padding-bottom:32px}.content[data-v-01c90815]{position:relative;margin:0 auto;width:100%}@media (min-width: 960px){.content[data-v-01c90815]{padding:0 32px 128px}}@media (min-width: 1280px){.content[data-v-01c90815]{order:1;margin:0;min-width:640px}}.content-container[data-v-01c90815]{margin:0 auto}.VPDoc.has-aside .content-container[data-v-01c90815]{max-width:688px}.VPButton[data-v-f549f0f3]{display:inline-block;border:1px solid transparent;text-align:center;font-weight:600;white-space:nowrap;transition:color .25s,border-color .25s,background-color .25s}.VPButton[data-v-f549f0f3]:active{transition:color .1s,border-color .1s,background-color .1s}.VPButton.medium[data-v-f549f0f3]{border-radius:20px;padding:0 20px;line-height:38px;font-size:14px}.VPButton.big[data-v-f549f0f3]{border-radius:24px;padding:0 24px;line-height:46px;font-size:16px}.VPButton.brand[data-v-f549f0f3]{border-color:var(--vp-button-brand-border);color:var(--vp-button-brand-text);background-color:var(--vp-button-brand-bg)}.VPButton.brand[data-v-f549f0f3]:hover{border-color:var(--vp-button-brand-hover-border);color:var(--vp-button-brand-hover-text);background-color:var(--vp-button-brand-hover-bg)}.VPButton.brand[data-v-f549f0f3]:active{border-color:var(--vp-button-brand-active-border);color:var(--vp-button-brand-active-text);background-color:var(--vp-button-brand-active-bg)}.VPButton.alt[data-v-f549f0f3]{border-color:var(--vp-button-alt-border);color:var(--vp-button-alt-text);background-color:var(--vp-button-alt-bg)}.VPButton.alt[data-v-f549f0f3]:hover{border-color:var(--vp-button-alt-hover-border);color:var(--vp-button-alt-hover-text);background-color:var(--vp-button-alt-hover-bg)}.VPButton.alt[data-v-f549f0f3]:active{border-color:var(--vp-button-alt-active-border);color:var(--vp-button-alt-active-text);background-color:var(--vp-button-alt-active-bg)}.VPButton.sponsor[data-v-f549f0f3]{border-color:var(--vp-button-sponsor-border);color:var(--vp-button-sponsor-text);background-color:var(--vp-button-sponsor-bg)}.VPButton.sponsor[data-v-f549f0f3]:hover{border-color:var(--vp-button-sponsor-hover-border);color:var(--vp-button-sponsor-hover-text);background-color:var(--vp-button-sponsor-hover-bg)}.VPButton.sponsor[data-v-f549f0f3]:active{border-color:var(--vp-button-sponsor-active-border);color:var(--vp-button-sponsor-active-text);background-color:var(--vp-button-sponsor-active-bg)}html:not(.dark) .VPImage.dark[data-v-cc63e071]{display:none}.dark .VPImage.light[data-v-cc63e071]{display:none}.VPHero[data-v-e302b8ce]{margin-top:calc((var(--vp-nav-height) + var(--vp-layout-top-height, 0px)) * -1);padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px) 24px 48px}@media (min-width: 640px){.VPHero[data-v-e302b8ce]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 48px 64px}}@media (min-width: 960px){.VPHero[data-v-e302b8ce]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 64px 64px}}.container[data-v-e302b8ce]{display:flex;flex-direction:column;margin:0 auto;max-width:1152px}@media (min-width: 960px){.container[data-v-e302b8ce]{flex-direction:row}}.main[data-v-e302b8ce]{position:relative;z-index:10;order:2;flex-grow:1;flex-shrink:0}.VPHero.has-image .container[data-v-e302b8ce]{text-align:center}@media (min-width: 960px){.VPHero.has-image .container[data-v-e302b8ce]{text-align:left}}@media (min-width: 960px){.main[data-v-e302b8ce]{order:1;width:calc((100% / 3) * 2)}.VPHero.has-image .main[data-v-e302b8ce]{max-width:592px}}.name[data-v-e302b8ce],.text[data-v-e302b8ce]{max-width:392px;letter-spacing:-.4px;line-height:40px;font-size:32px;font-weight:700;white-space:pre-wrap}.VPHero.has-image .name[data-v-e302b8ce],.VPHero.has-image .text[data-v-e302b8ce]{margin:0 auto}.name[data-v-e302b8ce]{color:var(--vp-home-hero-name-color)}.clip[data-v-e302b8ce]{background:var(--vp-home-hero-name-background);-webkit-background-clip:text;background-clip:text;-webkit-text-fill-color:var(--vp-home-hero-name-color)}@media (min-width: 640px){.name[data-v-e302b8ce],.text[data-v-e302b8ce]{max-width:576px;line-height:56px;font-size:48px}}@media (min-width: 960px){.name[data-v-e302b8ce],.text[data-v-e302b8ce]{line-height:64px;font-size:56px}.VPHero.has-image .name[data-v-e302b8ce],.VPHero.has-image .text[data-v-e302b8ce]{margin:0}}.tagline[data-v-e302b8ce]{padding-top:8px;max-width:392px;line-height:28px;font-size:18px;font-weight:500;white-space:pre-wrap;color:var(--vp-c-text-2)}.VPHero.has-image .tagline[data-v-e302b8ce]{margin:0 auto}@media (min-width: 640px){.tagline[data-v-e302b8ce]{padding-top:12px;max-width:576px;line-height:32px;font-size:20px}}@media (min-width: 960px){.tagline[data-v-e302b8ce]{line-height:36px;font-size:24px}.VPHero.has-image .tagline[data-v-e302b8ce]{margin:0}}.actions[data-v-e302b8ce]{display:flex;flex-wrap:wrap;margin:-6px;padding-top:24px}.VPHero.has-image .actions[data-v-e302b8ce]{justify-content:center}@media (min-width: 640px){.actions[data-v-e302b8ce]{padding-top:32px}}@media (min-width: 960px){.VPHero.has-image .actions[data-v-e302b8ce]{justify-content:flex-start}}.action[data-v-e302b8ce]{flex-shrink:0;padding:6px}.image[data-v-e302b8ce]{order:1;margin:-76px -24px -48px}@media (min-width: 640px){.image[data-v-e302b8ce]{margin:-108px -24px -48px}}@media (min-width: 960px){.image[data-v-e302b8ce]{flex-grow:1;order:2;margin:0;min-height:100%}}.image-container[data-v-e302b8ce]{position:relative;margin:0 auto;width:320px;height:320px}@media (min-width: 640px){.image-container[data-v-e302b8ce]{width:392px;height:392px}}@media (min-width: 960px){.image-container[data-v-e302b8ce]{display:flex;justify-content:center;align-items:center;width:100%;height:100%;transform:translate(-32px,-32px)}}.image-bg[data-v-e302b8ce]{position:absolute;top:50%;left:50%;border-radius:50%;width:192px;height:192px;background-image:var(--vp-home-hero-image-background-image);filter:var(--vp-home-hero-image-filter);transform:translate(-50%,-50%)}@media (min-width: 640px){.image-bg[data-v-e302b8ce]{width:256px;height:256px}}@media (min-width: 960px){.image-bg[data-v-e302b8ce]{width:320px;height:320px}}[data-v-e302b8ce] .image-src{position:absolute;top:50%;left:50%;max-width:192px;max-height:192px;transform:translate(-50%,-50%)}@media (min-width: 640px){[data-v-e302b8ce] .image-src{max-width:256px;max-height:256px}}@media (min-width: 960px){[data-v-e302b8ce] .image-src{max-width:320px;max-height:320px}}.VPFeature[data-v-f77e80b4]{display:block;border:1px solid var(--vp-c-bg-soft);border-radius:12px;height:100%;background-color:var(--vp-c-bg-soft);transition:border-color .25s,background-color .25s}.VPFeature.link[data-v-f77e80b4]:hover{border-color:var(--vp-c-brand-1)}.box[data-v-f77e80b4]{display:flex;flex-direction:column;padding:24px;height:100%}.box[data-v-f77e80b4]>.VPImage{margin-bottom:20px}.icon[data-v-f77e80b4]{display:flex;justify-content:center;align-items:center;margin-bottom:20px;border-radius:6px;background-color:var(--vp-c-default-soft);width:48px;height:48px;font-size:24px;transition:background-color .25s}.title[data-v-f77e80b4]{line-height:24px;font-size:16px;font-weight:600}.details[data-v-f77e80b4]{flex-grow:1;padding-top:8px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.link-text[data-v-f77e80b4]{padding-top:8px}.link-text-value[data-v-f77e80b4]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.link-text-icon[data-v-f77e80b4]{margin-left:6px}.VPFeatures[data-v-8e833103]{position:relative;padding:0 24px}@media (min-width: 640px){.VPFeatures[data-v-8e833103]{padding:0 48px}}@media (min-width: 960px){.VPFeatures[data-v-8e833103]{padding:0 64px}}.container[data-v-8e833103]{margin:0 auto;max-width:1152px}.items[data-v-8e833103]{display:flex;flex-wrap:wrap;margin:-8px}.item[data-v-8e833103]{padding:8px;width:100%}@media (min-width: 640px){.item.grid-2[data-v-8e833103],.item.grid-4[data-v-8e833103],.item.grid-6[data-v-8e833103]{width:50%}}@media (min-width: 768px){.item.grid-2[data-v-8e833103],.item.grid-4[data-v-8e833103]{width:50%}.item.grid-3[data-v-8e833103],.item.grid-6[data-v-8e833103]{width:calc(100% / 3)}}@media (min-width: 960px){.item.grid-4[data-v-8e833103]{width:25%}}.container[data-v-90605523]{margin:auto;width:100%;max-width:1280px;padding:0 24px}@media (min-width: 640px){.container[data-v-90605523]{padding:0 48px}}@media (min-width: 960px){.container[data-v-90605523]{width:100%;padding:0 64px}}.vp-doc[data-v-90605523] .VPHomeSponsors,.vp-doc[data-v-90605523] .VPTeamPage{margin-left:var(--vp-offset, calc(50% - 50vw) );margin-right:var(--vp-offset, calc(50% - 50vw) )}.vp-doc[data-v-90605523] .VPHomeSponsors h2{border-top:none;letter-spacing:normal}.vp-doc[data-v-90605523] .VPHomeSponsors a,.vp-doc[data-v-90605523] .VPTeamPage a{text-decoration:none}.VPHome[data-v-55977d12]{margin-bottom:96px}@media (min-width: 768px){.VPHome[data-v-55977d12]{margin-bottom:128px}}.VPContent[data-v-fc04087f]{flex-grow:1;flex-shrink:0;margin:var(--vp-layout-top-height, 0px) auto 0;width:100%}.VPContent.is-home[data-v-fc04087f]{width:100%;max-width:100%}.VPContent.has-sidebar[data-v-fc04087f]{margin:0}@media (min-width: 960px){.VPContent[data-v-fc04087f]{padding-top:var(--vp-nav-height)}.VPContent.has-sidebar[data-v-fc04087f]{margin:var(--vp-layout-top-height, 0px) 0 0;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPContent.has-sidebar[data-v-fc04087f]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.VPFooter[data-v-d69bcf5d]{position:relative;z-index:var(--vp-z-index-footer);border-top:1px solid var(--vp-c-gutter);padding:32px 24px;background-color:var(--vp-c-bg)}.VPFooter.has-sidebar[data-v-d69bcf5d]{display:none}.VPFooter[data-v-d69bcf5d] a{text-decoration-line:underline;text-underline-offset:2px;transition:color .25s}.VPFooter[data-v-d69bcf5d] a:hover{color:var(--vp-c-text-1)}@media (min-width: 768px){.VPFooter[data-v-d69bcf5d]{padding:32px}}.container[data-v-d69bcf5d]{margin:0 auto;max-width:var(--vp-layout-max-width);text-align:center}.message[data-v-d69bcf5d],.copyright[data-v-d69bcf5d]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.VPLocalNavOutlineDropdown[data-v-9dd5e197]{padding:12px 20px 11px}@media (min-width: 960px){.VPLocalNavOutlineDropdown[data-v-9dd5e197]{padding:12px 36px 11px}}.VPLocalNavOutlineDropdown button[data-v-9dd5e197]{display:block;font-size:12px;font-weight:500;line-height:24px;color:var(--vp-c-text-2);transition:color .5s;position:relative}.VPLocalNavOutlineDropdown button[data-v-9dd5e197]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPLocalNavOutlineDropdown button.open[data-v-9dd5e197]{color:var(--vp-c-text-1)}.icon[data-v-9dd5e197]{display:inline-block;vertical-align:middle;margin-left:2px;font-size:14px;transform:rotate(0);transition:transform .25s}@media (min-width: 960px){.VPLocalNavOutlineDropdown button[data-v-9dd5e197]{font-size:14px}.icon[data-v-9dd5e197]{font-size:16px}}.open>.icon[data-v-9dd5e197]{transform:rotate(90deg)}.items[data-v-9dd5e197]{position:absolute;top:40px;right:16px;left:16px;display:grid;gap:1px;border:1px solid var(--vp-c-border);border-radius:8px;background-color:var(--vp-c-gutter);max-height:calc(var(--vp-vh, 100vh) - 86px);overflow:hidden auto;box-shadow:var(--vp-shadow-3)}@media (min-width: 960px){.items[data-v-9dd5e197]{right:auto;left:calc(var(--vp-sidebar-width) + 32px);width:320px}}.header[data-v-9dd5e197]{background-color:var(--vp-c-bg-soft)}.top-link[data-v-9dd5e197]{display:block;padding:0 16px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.outline[data-v-9dd5e197]{padding:8px 0;background-color:var(--vp-c-bg-soft)}.flyout-enter-active[data-v-9dd5e197]{transition:all .2s ease-out}.flyout-leave-active[data-v-9dd5e197]{transition:all .15s ease-in}.flyout-enter-from[data-v-9dd5e197],.flyout-leave-to[data-v-9dd5e197]{opacity:0;transform:translateY(-16px)}.VPLocalNav[data-v-9c649187]{position:sticky;top:0;left:0;z-index:var(--vp-z-index-local-nav);border-bottom:1px solid var(--vp-c-gutter);padding-top:var(--vp-layout-top-height, 0px);width:100%;background-color:var(--vp-local-nav-bg-color)}.VPLocalNav.fixed[data-v-9c649187]{position:fixed}@media (min-width: 960px){.VPLocalNav[data-v-9c649187]{top:var(--vp-nav-height)}.VPLocalNav.has-sidebar[data-v-9c649187]{padding-left:var(--vp-sidebar-width)}.VPLocalNav.empty[data-v-9c649187]{display:none}}@media (min-width: 1280px){.VPLocalNav[data-v-9c649187]{display:none}}@media (min-width: 1440px){.VPLocalNav.has-sidebar[data-v-9c649187]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.container[data-v-9c649187]{display:flex;justify-content:space-between;align-items:center}.menu[data-v-9c649187]{display:flex;align-items:center;padding:12px 24px 11px;line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.menu[data-v-9c649187]:hover{color:var(--vp-c-text-1);transition:color .25s}@media (min-width: 768px){.menu[data-v-9c649187]{padding:0 32px}}@media (min-width: 960px){.menu[data-v-9c649187]{display:none}}.menu-icon[data-v-9c649187]{margin-right:8px;font-size:14px}.VPOutlineDropdown[data-v-9c649187]{padding:12px 24px 11px}@media (min-width: 768px){.VPOutlineDropdown[data-v-9c649187]{padding:12px 32px 11px}}.VPSwitch[data-v-846fe538]{position:relative;border-radius:11px;display:block;width:40px;height:22px;flex-shrink:0;border:1px solid var(--vp-input-border-color);background-color:var(--vp-input-switch-bg-color);transition:border-color .25s!important}.VPSwitch[data-v-846fe538]:hover{border-color:var(--vp-c-brand-1)}.check[data-v-846fe538]{position:absolute;top:1px;left:1px;width:18px;height:18px;border-radius:50%;background-color:var(--vp-c-neutral-inverse);box-shadow:var(--vp-shadow-1);transition:transform .25s!important}.icon[data-v-846fe538]{position:relative;display:block;width:18px;height:18px;border-radius:50%;overflow:hidden}.icon[data-v-846fe538] [class^=vpi-]{position:absolute;top:3px;left:3px;width:12px;height:12px;color:var(--vp-c-text-2)}.dark .icon[data-v-846fe538] [class^=vpi-]{color:var(--vp-c-text-1);transition:opacity .25s!important}.sun[data-v-3125216b]{opacity:1}.moon[data-v-3125216b],.dark .sun[data-v-3125216b]{opacity:0}.dark .moon[data-v-3125216b]{opacity:1}.dark .VPSwitchAppearance[data-v-3125216b] .check{transform:translate(18px)}.VPNavBarAppearance[data-v-864d2abc]{display:none}@media (min-width: 1280px){.VPNavBarAppearance[data-v-864d2abc]{display:flex;align-items:center}}.VPMenuGroup+.VPMenuLink[data-v-25a54821]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.link[data-v-25a54821]{display:block;border-radius:6px;padding:0 12px;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);white-space:nowrap;transition:background-color .25s,color .25s}.link[data-v-25a54821]:hover{color:var(--vp-c-brand-1);background-color:var(--vp-c-default-soft)}.link.active[data-v-25a54821]{color:var(--vp-c-brand-1)}.VPMenuGroup[data-v-4dd03e28]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.VPMenuGroup[data-v-4dd03e28]:first-child{margin-top:0;border-top:0;padding-top:0}.VPMenuGroup+.VPMenuGroup[data-v-4dd03e28]{margin-top:12px;border-top:1px solid var(--vp-c-divider)}.title[data-v-4dd03e28]{padding:0 12px;line-height:32px;font-size:14px;font-weight:600;color:var(--vp-c-text-2);white-space:nowrap;transition:color .25s}.VPMenu[data-v-809b8af7]{border-radius:12px;padding:12px;min-width:128px;border:1px solid var(--vp-c-divider);background-color:var(--vp-c-bg-elv);box-shadow:var(--vp-shadow-3);transition:background-color .5s;max-height:calc(100vh - var(--vp-nav-height));overflow-y:auto}.VPMenu[data-v-809b8af7] .group{margin:0 -12px;padding:0 12px 12px}.VPMenu[data-v-809b8af7] .group+.group{border-top:1px solid var(--vp-c-divider);padding:11px 12px 12px}.VPMenu[data-v-809b8af7] .group:last-child{padding-bottom:0}.VPMenu[data-v-809b8af7] .group+.item{border-top:1px solid var(--vp-c-divider);padding:11px 16px 0}.VPMenu[data-v-809b8af7] .item{padding:0 16px;white-space:nowrap}.VPMenu[data-v-809b8af7] .label{flex-grow:1;line-height:28px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.VPMenu[data-v-809b8af7] .action{padding-left:24px}.VPFlyout[data-v-00660109]{position:relative}.VPFlyout[data-v-00660109]:hover{color:var(--vp-c-brand-1);transition:color .25s}.VPFlyout:hover .text[data-v-00660109]{color:var(--vp-c-text-2)}.VPFlyout:hover .icon[data-v-00660109]{fill:var(--vp-c-text-2)}.VPFlyout.active .text[data-v-00660109]{color:var(--vp-c-brand-1)}.VPFlyout.active:hover .text[data-v-00660109]{color:var(--vp-c-brand-2)}.VPFlyout:hover .menu[data-v-00660109],.button[aria-expanded=true]+.menu[data-v-00660109]{opacity:1;visibility:visible;transform:translateY(0)}.button[aria-expanded=false]+.menu[data-v-00660109]{opacity:0;visibility:hidden;transform:translateY(0)}.button[data-v-00660109]{display:flex;align-items:center;padding:0 12px;height:var(--vp-nav-height);color:var(--vp-c-text-1);transition:color .5s}.text[data-v-00660109]{display:flex;align-items:center;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.option-icon[data-v-00660109]{margin-right:0;font-size:16px}.text-icon[data-v-00660109]{margin-left:4px;font-size:14px}.icon[data-v-00660109]{font-size:20px;transition:fill .25s}.menu[data-v-00660109]{position:absolute;top:calc(var(--vp-nav-height) / 2 + 20px);right:0;opacity:0;visibility:hidden;transition:opacity .25s,visibility .25s,transform .25s}.VPSocialLink[data-v-15a5c40e]{display:flex;justify-content:center;align-items:center;width:36px;height:36px;color:var(--vp-c-text-2);transition:color .5s}.VPSocialLink[data-v-15a5c40e]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPSocialLink[data-v-15a5c40e]>svg,.VPSocialLink[data-v-15a5c40e]>[class^=vpi-social-]{width:20px;height:20px;fill:currentColor}.VPSocialLinks[data-v-100434c4]{display:flex;justify-content:center}.VPNavBarExtra[data-v-60cefd62]{display:none;margin-right:-12px}@media (min-width: 768px){.VPNavBarExtra[data-v-60cefd62]{display:block}}@media (min-width: 1280px){.VPNavBarExtra[data-v-60cefd62]{display:none}}.trans-title[data-v-60cefd62]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.item.appearance[data-v-60cefd62],.item.social-links[data-v-60cefd62]{display:flex;align-items:center;padding:0 12px}.item.appearance[data-v-60cefd62]{min-width:176px}.appearance-action[data-v-60cefd62]{margin-right:-2px}.social-links-list[data-v-60cefd62]{margin:-4px -8px}.VPNavBarHamburger[data-v-e047a1f2]{display:flex;justify-content:center;align-items:center;width:48px;height:var(--vp-nav-height)}@media (min-width: 768px){.VPNavBarHamburger[data-v-e047a1f2]{display:none}}.container[data-v-e047a1f2]{position:relative;width:16px;height:14px;overflow:hidden}.VPNavBarHamburger:hover .top[data-v-e047a1f2]{top:0;left:0;transform:translate(4px)}.VPNavBarHamburger:hover .middle[data-v-e047a1f2]{top:6px;left:0;transform:translate(0)}.VPNavBarHamburger:hover .bottom[data-v-e047a1f2]{top:12px;left:0;transform:translate(8px)}.VPNavBarHamburger.active .top[data-v-e047a1f2]{top:6px;transform:translate(0) rotate(225deg)}.VPNavBarHamburger.active .middle[data-v-e047a1f2]{top:6px;transform:translate(16px)}.VPNavBarHamburger.active .bottom[data-v-e047a1f2]{top:6px;transform:translate(0) rotate(135deg)}.VPNavBarHamburger.active:hover .top[data-v-e047a1f2],.VPNavBarHamburger.active:hover .middle[data-v-e047a1f2],.VPNavBarHamburger.active:hover .bottom[data-v-e047a1f2]{background-color:var(--vp-c-text-2);transition:top .25s,background-color .25s,transform .25s}.top[data-v-e047a1f2],.middle[data-v-e047a1f2],.bottom[data-v-e047a1f2]{position:absolute;width:16px;height:2px;background-color:var(--vp-c-text-1);transition:top .25s,background-color .5s,transform .25s}.top[data-v-e047a1f2]{top:0;left:0;transform:translate(0)}.middle[data-v-e047a1f2]{top:6px;left:0;transform:translate(8px)}.bottom[data-v-e047a1f2]{top:12px;left:0;transform:translate(4px)}.VPNavBarMenuLink[data-v-9a0da802]{display:flex;align-items:center;padding:0 12px;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.VPNavBarMenuLink.active[data-v-9a0da802],.VPNavBarMenuLink[data-v-9a0da802]:hover{color:var(--vp-c-brand-1)}.VPNavBarMenu[data-v-bf53b681]{display:none}@media (min-width: 768px){.VPNavBarMenu[data-v-bf53b681]{display:flex}}/*! @docsearch/css 3.6.1 | MIT License | © Algolia, Inc. and contributors | https://docsearch.algolia.com */:root{--docsearch-primary-color:#5468ff;--docsearch-text-color:#1c1e21;--docsearch-spacing:12px;--docsearch-icon-stroke-width:1.4;--docsearch-highlight-color:var(--docsearch-primary-color);--docsearch-muted-color:#969faf;--docsearch-container-background:rgba(101,108,133,.8);--docsearch-logo-color:#5468ff;--docsearch-modal-width:560px;--docsearch-modal-height:600px;--docsearch-modal-background:#f5f6f7;--docsearch-modal-shadow:inset 1px 1px 0 0 hsla(0,0%,100%,.5),0 3px 8px 0 #555a64;--docsearch-searchbox-height:56px;--docsearch-searchbox-background:#ebedf0;--docsearch-searchbox-focus-background:#fff;--docsearch-searchbox-shadow:inset 0 0 0 2px var(--docsearch-primary-color);--docsearch-hit-height:56px;--docsearch-hit-color:#444950;--docsearch-hit-active-color:#fff;--docsearch-hit-background:#fff;--docsearch-hit-shadow:0 1px 3px 0 #d4d9e1;--docsearch-key-gradient:linear-gradient(-225deg,#d5dbe4,#f8f8f8);--docsearch-key-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 2px 1px rgba(30,35,90,.4);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 1px 0 rgba(30,35,90,.4);--docsearch-footer-height:44px;--docsearch-footer-background:#fff;--docsearch-footer-shadow:0 -1px 0 0 #e0e3e8,0 -3px 6px 0 rgba(69,98,155,.12)}html[data-theme=dark]{--docsearch-text-color:#f5f6f7;--docsearch-container-background:rgba(9,10,17,.8);--docsearch-modal-background:#15172a;--docsearch-modal-shadow:inset 1px 1px 0 0 #2c2e40,0 3px 8px 0 #000309;--docsearch-searchbox-background:#090a11;--docsearch-searchbox-focus-background:#000;--docsearch-hit-color:#bec3c9;--docsearch-hit-shadow:none;--docsearch-hit-background:#090a11;--docsearch-key-gradient:linear-gradient(-26.5deg,#565872,#31355b);--docsearch-key-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 2px 2px 0 rgba(3,4,9,.3);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 1px 1px 0 rgba(3,4,9,.30196078431372547);--docsearch-footer-background:#1e2136;--docsearch-footer-shadow:inset 0 1px 0 0 rgba(73,76,106,.5),0 -4px 8px 0 rgba(0,0,0,.2);--docsearch-logo-color:#fff;--docsearch-muted-color:#7f8497}.DocSearch-Button{align-items:center;background:var(--docsearch-searchbox-background);border:0;border-radius:40px;color:var(--docsearch-muted-color);cursor:pointer;display:flex;font-weight:500;height:36px;justify-content:space-between;margin:0 0 0 16px;padding:0 8px;-webkit-user-select:none;user-select:none}.DocSearch-Button:active,.DocSearch-Button:focus,.DocSearch-Button:hover{background:var(--docsearch-searchbox-focus-background);box-shadow:var(--docsearch-searchbox-shadow);color:var(--docsearch-text-color);outline:none}.DocSearch-Button-Container{align-items:center;display:flex}.DocSearch-Search-Icon{stroke-width:1.6}.DocSearch-Button .DocSearch-Search-Icon{color:var(--docsearch-text-color)}.DocSearch-Button-Placeholder{font-size:1rem;padding:0 12px 0 6px}.DocSearch-Button-Keys{display:flex;min-width:calc(40px + .8em)}.DocSearch-Button-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:3px;box-shadow:var(--docsearch-key-shadow);color:var(--docsearch-muted-color);display:flex;height:18px;justify-content:center;margin-right:.4em;position:relative;padding:0 0 2px;border:0;top:-1px;width:20px}.DocSearch-Button-Key--pressed{transform:translate3d(0,1px,0);box-shadow:var(--docsearch-key-pressed-shadow)}@media (max-width:768px){.DocSearch-Button-Keys,.DocSearch-Button-Placeholder{display:none}}.DocSearch--active{overflow:hidden!important}.DocSearch-Container,.DocSearch-Container *{box-sizing:border-box}.DocSearch-Container{background-color:var(--docsearch-container-background);height:100vh;left:0;position:fixed;top:0;width:100vw;z-index:200}.DocSearch-Container a{text-decoration:none}.DocSearch-Link{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;font:inherit;margin:0;padding:0}.DocSearch-Modal{background:var(--docsearch-modal-background);border-radius:6px;box-shadow:var(--docsearch-modal-shadow);flex-direction:column;margin:60px auto auto;max-width:var(--docsearch-modal-width);position:relative}.DocSearch-SearchBar{display:flex;padding:var(--docsearch-spacing) var(--docsearch-spacing) 0}.DocSearch-Form{align-items:center;background:var(--docsearch-searchbox-focus-background);border-radius:4px;box-shadow:var(--docsearch-searchbox-shadow);display:flex;height:var(--docsearch-searchbox-height);margin:0;padding:0 var(--docsearch-spacing);position:relative;width:100%}.DocSearch-Input{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:transparent;border:0;color:var(--docsearch-text-color);flex:1;font:inherit;font-size:1.2em;height:100%;outline:none;padding:0 0 0 8px;width:80%}.DocSearch-Input::placeholder{color:var(--docsearch-muted-color);opacity:1}.DocSearch-Input::-webkit-search-cancel-button,.DocSearch-Input::-webkit-search-decoration,.DocSearch-Input::-webkit-search-results-button,.DocSearch-Input::-webkit-search-results-decoration{display:none}.DocSearch-LoadingIndicator,.DocSearch-MagnifierLabel,.DocSearch-Reset{margin:0;padding:0}.DocSearch-MagnifierLabel,.DocSearch-Reset{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}.DocSearch-Container--Stalled .DocSearch-MagnifierLabel,.DocSearch-LoadingIndicator{display:none}.DocSearch-Container--Stalled .DocSearch-LoadingIndicator{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Reset{animation:none;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;right:0;stroke-width:var(--docsearch-icon-stroke-width)}}.DocSearch-Reset{animation:fade-in .1s ease-in forwards;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;padding:2px;right:0;stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Reset[hidden]{display:none}.DocSearch-Reset:hover{color:var(--docsearch-highlight-color)}.DocSearch-LoadingIndicator svg,.DocSearch-MagnifierLabel svg{height:24px;width:24px}.DocSearch-Cancel{display:none}.DocSearch-Dropdown{max-height:calc(var(--docsearch-modal-height) - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height));min-height:var(--docsearch-spacing);overflow-y:auto;overflow-y:overlay;padding:0 var(--docsearch-spacing);scrollbar-color:var(--docsearch-muted-color) var(--docsearch-modal-background);scrollbar-width:thin}.DocSearch-Dropdown::-webkit-scrollbar{width:12px}.DocSearch-Dropdown::-webkit-scrollbar-track{background:transparent}.DocSearch-Dropdown::-webkit-scrollbar-thumb{background-color:var(--docsearch-muted-color);border:3px solid var(--docsearch-modal-background);border-radius:20px}.DocSearch-Dropdown ul{list-style:none;margin:0;padding:0}.DocSearch-Label{font-size:.75em;line-height:1.6em}.DocSearch-Help,.DocSearch-Label{color:var(--docsearch-muted-color)}.DocSearch-Help{font-size:.9em;margin:0;-webkit-user-select:none;user-select:none}.DocSearch-Title{font-size:1.2em}.DocSearch-Logo a{display:flex}.DocSearch-Logo svg{color:var(--docsearch-logo-color);margin-left:8px}.DocSearch-Hits:last-of-type{margin-bottom:24px}.DocSearch-Hits mark{background:none;color:var(--docsearch-highlight-color)}.DocSearch-HitsFooter{color:var(--docsearch-muted-color);display:flex;font-size:.85em;justify-content:center;margin-bottom:var(--docsearch-spacing);padding:var(--docsearch-spacing)}.DocSearch-HitsFooter a{border-bottom:1px solid;color:inherit}.DocSearch-Hit{border-radius:4px;display:flex;padding-bottom:4px;position:relative}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--deleting{transition:none}}.DocSearch-Hit--deleting{opacity:0;transition:all .25s linear}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--favoriting{transition:none}}.DocSearch-Hit--favoriting{transform:scale(0);transform-origin:top center;transition:all .25s linear;transition-delay:.25s}.DocSearch-Hit a{background:var(--docsearch-hit-background);border-radius:4px;box-shadow:var(--docsearch-hit-shadow);display:block;padding-left:var(--docsearch-spacing);width:100%}.DocSearch-Hit-source{background:var(--docsearch-modal-background);color:var(--docsearch-highlight-color);font-size:.85em;font-weight:600;line-height:32px;margin:0 -4px;padding:8px 4px 0;position:sticky;top:0;z-index:10}.DocSearch-Hit-Tree{color:var(--docsearch-muted-color);height:var(--docsearch-hit-height);opacity:.5;stroke-width:var(--docsearch-icon-stroke-width);width:24px}.DocSearch-Hit[aria-selected=true] a{background-color:var(--docsearch-highlight-color)}.DocSearch-Hit[aria-selected=true] mark{text-decoration:underline}.DocSearch-Hit-Container{align-items:center;color:var(--docsearch-hit-color);display:flex;flex-direction:row;height:var(--docsearch-hit-height);padding:0 var(--docsearch-spacing) 0 0}.DocSearch-Hit-icon{height:20px;width:20px}.DocSearch-Hit-action,.DocSearch-Hit-icon{color:var(--docsearch-muted-color);stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Hit-action{align-items:center;display:flex;height:22px;width:22px}.DocSearch-Hit-action svg{display:block;height:18px;width:18px}.DocSearch-Hit-action+.DocSearch-Hit-action{margin-left:6px}.DocSearch-Hit-action-button{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:inherit;cursor:pointer;padding:2px}svg.DocSearch-Hit-Select-Icon{display:none}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Select-Icon{display:block}.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:background-color .1s ease-in}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{transition:none}}.DocSearch-Hit-action-button:focus path,.DocSearch-Hit-action-button:hover path{fill:#fff}.DocSearch-Hit-content-wrapper{display:flex;flex:1 1 auto;flex-direction:column;font-weight:500;justify-content:center;line-height:1.2em;margin:0 8px;overflow-x:hidden;position:relative;text-overflow:ellipsis;white-space:nowrap;width:80%}.DocSearch-Hit-title{font-size:.9em}.DocSearch-Hit-path{color:var(--docsearch-muted-color);font-size:.75em}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-action,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-icon,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-path,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-text,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-title,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Tree,.DocSearch-Hit[aria-selected=true] mark{color:var(--docsearch-hit-active-color)!important}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:none}}.DocSearch-ErrorScreen,.DocSearch-NoResults,.DocSearch-StartScreen{font-size:.9em;margin:0 auto;padding:36px 0;text-align:center;width:80%}.DocSearch-Screen-Icon{color:var(--docsearch-muted-color);padding-bottom:12px}.DocSearch-NoResults-Prefill-List{display:inline-block;padding-bottom:24px;text-align:left}.DocSearch-NoResults-Prefill-List ul{display:inline-block;padding:8px 0 0}.DocSearch-NoResults-Prefill-List li{list-style-position:inside;list-style-type:"» "}.DocSearch-Prefill{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:1em;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;font-size:1em;font-weight:700;padding:0}.DocSearch-Prefill:focus,.DocSearch-Prefill:hover{outline:none;text-decoration:underline}.DocSearch-Footer{align-items:center;background:var(--docsearch-footer-background);border-radius:0 0 8px 8px;box-shadow:var(--docsearch-footer-shadow);display:flex;flex-direction:row-reverse;flex-shrink:0;height:var(--docsearch-footer-height);justify-content:space-between;padding:0 var(--docsearch-spacing);position:relative;-webkit-user-select:none;user-select:none;width:100%;z-index:300}.DocSearch-Commands{color:var(--docsearch-muted-color);display:flex;list-style:none;margin:0;padding:0}.DocSearch-Commands li{align-items:center;display:flex}.DocSearch-Commands li:not(:last-of-type){margin-right:.8em}.DocSearch-Commands-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:2px;box-shadow:var(--docsearch-key-shadow);display:flex;height:18px;justify-content:center;margin-right:.4em;padding:0 0 1px;color:var(--docsearch-muted-color);border:0;width:20px}.DocSearch-VisuallyHiddenForAccessibility{clip:rect(0 0 0 0);clip-path:inset(50%);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}@media (max-width:768px){:root{--docsearch-spacing:10px;--docsearch-footer-height:40px}.DocSearch-Dropdown{height:100%}.DocSearch-Container{height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);position:absolute}.DocSearch-Footer{border-radius:0;bottom:0;position:absolute}.DocSearch-Hit-content-wrapper{display:flex;position:relative;width:80%}.DocSearch-Modal{border-radius:0;box-shadow:none;height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);margin:0;max-width:100%;width:100%}.DocSearch-Dropdown{max-height:calc(var(--docsearch-vh, 1vh)*100 - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height))}.DocSearch-Cancel{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;flex:none;font:inherit;font-size:1em;font-weight:500;margin-left:var(--docsearch-spacing);outline:none;overflow:hidden;padding:0;-webkit-user-select:none;user-select:none;white-space:nowrap}.DocSearch-Commands,.DocSearch-Hit-Tree{display:none}}@keyframes fade-in{0%{opacity:0}to{opacity:1}}[class*=DocSearch]{--docsearch-primary-color: var(--vp-c-brand-1);--docsearch-highlight-color: var(--docsearch-primary-color);--docsearch-text-color: var(--vp-c-text-1);--docsearch-muted-color: var(--vp-c-text-2);--docsearch-searchbox-shadow: none;--docsearch-searchbox-background: transparent;--docsearch-searchbox-focus-background: transparent;--docsearch-key-gradient: transparent;--docsearch-key-shadow: none;--docsearch-modal-background: var(--vp-c-bg-soft);--docsearch-footer-background: var(--vp-c-bg)}.dark [class*=DocSearch]{--docsearch-modal-shadow: none;--docsearch-footer-shadow: none;--docsearch-logo-color: var(--vp-c-text-2);--docsearch-hit-background: var(--vp-c-default-soft);--docsearch-hit-color: var(--vp-c-text-2);--docsearch-hit-shadow: none}.DocSearch-Button{display:flex;justify-content:center;align-items:center;margin:0;padding:0;width:48px;height:55px;background:transparent;transition:border-color .25s}.DocSearch-Button:hover{background:transparent}.DocSearch-Button:focus{outline:1px dotted;outline:5px auto -webkit-focus-ring-color}.DocSearch-Button-Key--pressed{transform:none;box-shadow:none}.DocSearch-Button:focus:not(:focus-visible){outline:none!important}@media (min-width: 768px){.DocSearch-Button{justify-content:flex-start;border:1px solid transparent;border-radius:8px;padding:0 10px 0 12px;width:100%;height:40px;background-color:var(--vp-c-bg-alt)}.DocSearch-Button:hover{border-color:var(--vp-c-brand-1);background:var(--vp-c-bg-alt)}}.DocSearch-Button .DocSearch-Button-Container{display:flex;align-items:center}.DocSearch-Button .DocSearch-Search-Icon{position:relative;width:16px;height:16px;color:var(--vp-c-text-1);fill:currentColor;transition:color .5s}.DocSearch-Button:hover .DocSearch-Search-Icon{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Search-Icon{top:1px;margin-right:8px;width:14px;height:14px;color:var(--vp-c-text-2)}}.DocSearch-Button .DocSearch-Button-Placeholder{display:none;margin-top:2px;padding:0 16px 0 0;font-size:13px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.DocSearch-Button:hover .DocSearch-Button-Placeholder{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Placeholder{display:inline-block}}.DocSearch-Button .DocSearch-Button-Keys{direction:ltr;display:none;min-width:auto}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Keys{display:flex;align-items:center}}.DocSearch-Button .DocSearch-Button-Key{display:block;margin:2px 0 0;border:1px solid var(--vp-c-divider);border-right:none;border-radius:4px 0 0 4px;padding-left:6px;min-width:0;width:auto;height:22px;line-height:22px;font-family:var(--vp-font-family-base);font-size:12px;font-weight:500;transition:color .5s,border-color .5s}.DocSearch-Button .DocSearch-Button-Key+.DocSearch-Button-Key{border-right:1px solid var(--vp-c-divider);border-left:none;border-radius:0 4px 4px 0;padding-left:2px;padding-right:6px}.DocSearch-Button .DocSearch-Button-Key:first-child{font-size:0!important}.DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"Ctrl";font-size:12px;letter-spacing:normal;color:var(--docsearch-muted-color)}.mac .DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"⌘"}.DocSearch-Button .DocSearch-Button-Key:first-child>*{display:none}.DocSearch-Search-Icon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' stroke-width='1.6' viewBox='0 0 20 20'%3E%3Cpath fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' d='m14.386 14.386 4.088 4.088-4.088-4.088A7.533 7.533 0 1 1 3.733 3.733a7.533 7.533 0 0 1 10.653 10.653z'/%3E%3C/svg%3E")}.VPNavBarSearch{display:flex;align-items:center}@media (min-width: 768px){.VPNavBarSearch{flex-grow:1;padding-left:24px}}@media (min-width: 960px){.VPNavBarSearch{padding-left:32px}}.dark .DocSearch-Footer{border-top:1px solid var(--vp-c-divider)}.DocSearch-Form{border:1px solid var(--vp-c-brand-1);background-color:var(--vp-c-white)}.dark .DocSearch-Form{background-color:var(--vp-c-default-soft)}.DocSearch-Screen-Icon>svg{margin:auto}.VPNavBarSocialLinks[data-v-2c606308]{display:none}@media (min-width: 1280px){.VPNavBarSocialLinks[data-v-2c606308]{display:flex;align-items:center}}.title[data-v-606a7e0f]{display:flex;align-items:center;border-bottom:1px solid transparent;width:100%;height:var(--vp-nav-height);font-size:16px;font-weight:600;color:var(--vp-c-text-1);transition:opacity .25s}@media (min-width: 960px){.title[data-v-606a7e0f]{flex-shrink:0}.VPNavBarTitle.has-sidebar .title[data-v-606a7e0f]{border-bottom-color:var(--vp-c-divider)}}[data-v-606a7e0f] .logo{margin-right:8px;height:var(--vp-nav-logo-height)}.VPNavBarTranslations[data-v-912817b1]{display:none}@media (min-width: 1280px){.VPNavBarTranslations[data-v-912817b1]{display:flex;align-items:center}}.title[data-v-912817b1]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.VPNavBar[data-v-da0688be]{position:relative;height:var(--vp-nav-height);pointer-events:none;white-space:nowrap;transition:background-color .25s}.VPNavBar.screen-open[data-v-da0688be]{transition:none;background-color:var(--vp-nav-bg-color);border-bottom:1px solid var(--vp-c-divider)}.VPNavBar[data-v-da0688be]:not(.home){background-color:var(--vp-nav-bg-color)}@media (min-width: 960px){.VPNavBar[data-v-da0688be]:not(.home){background-color:transparent}.VPNavBar[data-v-da0688be]:not(.has-sidebar):not(.home.top){background-color:var(--vp-nav-bg-color)}}.wrapper[data-v-da0688be]{padding:0 8px 0 24px}@media (min-width: 768px){.wrapper[data-v-da0688be]{padding:0 32px}}@media (min-width: 960px){.VPNavBar.has-sidebar .wrapper[data-v-da0688be]{padding:0}}.container[data-v-da0688be]{display:flex;justify-content:space-between;margin:0 auto;max-width:calc(var(--vp-layout-max-width) - 64px);height:var(--vp-nav-height);pointer-events:none}.container>.title[data-v-da0688be],.container>.content[data-v-da0688be]{pointer-events:none}.container[data-v-da0688be] *{pointer-events:auto}@media (min-width: 960px){.VPNavBar.has-sidebar .container[data-v-da0688be]{max-width:100%}}.title[data-v-da0688be]{flex-shrink:0;height:calc(var(--vp-nav-height) - 1px);transition:background-color .5s}@media (min-width: 960px){.VPNavBar.has-sidebar .title[data-v-da0688be]{position:absolute;top:0;left:0;z-index:2;padding:0 32px;width:var(--vp-sidebar-width);height:var(--vp-nav-height);background-color:transparent}}@media (min-width: 1440px){.VPNavBar.has-sidebar .title[data-v-da0688be]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}.content[data-v-da0688be]{flex-grow:1}@media (min-width: 960px){.VPNavBar.has-sidebar .content[data-v-da0688be]{position:relative;z-index:1;padding-right:32px;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .content[data-v-da0688be]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2 + 32px);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.content-body[data-v-da0688be]{display:flex;justify-content:flex-end;align-items:center;height:var(--vp-nav-height);transition:background-color .5s}@media (min-width: 960px){.VPNavBar:not(.home.top) .content-body[data-v-da0688be]{position:relative;background-color:var(--vp-nav-bg-color)}.VPNavBar:not(.has-sidebar):not(.home.top) .content-body[data-v-da0688be]{background-color:transparent}}@media (max-width: 767px){.content-body[data-v-da0688be]{column-gap:.5rem}}.menu+.translations[data-v-da0688be]:before,.menu+.appearance[data-v-da0688be]:before,.menu+.social-links[data-v-da0688be]:before,.translations+.appearance[data-v-da0688be]:before,.appearance+.social-links[data-v-da0688be]:before{margin-right:8px;margin-left:8px;width:1px;height:24px;background-color:var(--vp-c-divider);content:""}.menu+.appearance[data-v-da0688be]:before,.translations+.appearance[data-v-da0688be]:before{margin-right:16px}.appearance+.social-links[data-v-da0688be]:before{margin-left:16px}.social-links[data-v-da0688be]{margin-right:-8px}.divider[data-v-da0688be]{width:100%;height:1px}@media (min-width: 960px){.VPNavBar.has-sidebar .divider[data-v-da0688be]{padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .divider[data-v-da0688be]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.divider-line[data-v-da0688be]{width:100%;height:1px;transition:background-color .5s}.VPNavBar:not(.home) .divider-line[data-v-da0688be]{background-color:var(--vp-c-gutter)}@media (min-width: 960px){.VPNavBar:not(.home.top) .divider-line[data-v-da0688be]{background-color:var(--vp-c-gutter)}.VPNavBar:not(.has-sidebar):not(.home.top) .divider[data-v-da0688be]{background-color:var(--vp-c-gutter)}}.VPNavScreenAppearance[data-v-dfcc1536]{display:flex;justify-content:space-between;align-items:center;border-radius:8px;padding:12px 14px 12px 16px;background-color:var(--vp-c-bg-soft)}.text[data-v-dfcc1536]{line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.VPNavScreenMenuLink[data-v-8cd41455]{display:block;border-bottom:1px solid var(--vp-c-divider);padding:12px 0 11px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:border-color .25s,color .25s}.VPNavScreenMenuLink[data-v-8cd41455]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupLink[data-v-b8c7c580]{display:block;margin-left:12px;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-1);transition:color .25s}.VPNavScreenMenuGroupLink[data-v-b8c7c580]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupSection[data-v-a3e7a51c]{display:block}.title[data-v-a3e7a51c]{line-height:32px;font-size:13px;font-weight:700;color:var(--vp-c-text-2);transition:color .25s}.VPNavScreenMenuGroup[data-v-90f695a2]{border-bottom:1px solid var(--vp-c-divider);height:48px;overflow:hidden;transition:border-color .5s}.VPNavScreenMenuGroup .items[data-v-90f695a2]{visibility:hidden}.VPNavScreenMenuGroup.open .items[data-v-90f695a2]{visibility:visible}.VPNavScreenMenuGroup.open[data-v-90f695a2]{padding-bottom:10px;height:auto}.VPNavScreenMenuGroup.open .button[data-v-90f695a2]{padding-bottom:6px;color:var(--vp-c-brand-1)}.VPNavScreenMenuGroup.open .button-icon[data-v-90f695a2]{transform:rotate(45deg)}.button[data-v-90f695a2]{display:flex;justify-content:space-between;align-items:center;padding:12px 4px 11px 0;width:100%;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.button[data-v-90f695a2]:hover{color:var(--vp-c-brand-1)}.button-icon[data-v-90f695a2]{transition:transform .25s}.group[data-v-90f695a2]:first-child{padding-top:0}.group+.group[data-v-90f695a2],.group+.item[data-v-90f695a2]{padding-top:4px}.VPNavScreenTranslations[data-v-95c61444]{height:24px;overflow:hidden}.VPNavScreenTranslations.open[data-v-95c61444]{height:auto}.title[data-v-95c61444]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-text-1)}.icon[data-v-95c61444]{font-size:16px}.icon.lang[data-v-95c61444]{margin-right:8px}.icon.chevron[data-v-95c61444]{margin-left:4px}.list[data-v-95c61444]{padding:4px 0 0 24px}.link[data-v-95c61444]{line-height:32px;font-size:13px;color:var(--vp-c-text-1)}.VPNavScreen[data-v-c14c1e21]{position:fixed;top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px));right:0;bottom:0;left:0;padding:0 32px;width:100%;background-color:var(--vp-nav-screen-bg-color);overflow-y:auto;transition:background-color .25s;pointer-events:auto}.VPNavScreen.fade-enter-active[data-v-c14c1e21],.VPNavScreen.fade-leave-active[data-v-c14c1e21]{transition:opacity .25s}.VPNavScreen.fade-enter-active .container[data-v-c14c1e21],.VPNavScreen.fade-leave-active .container[data-v-c14c1e21]{transition:transform .25s ease}.VPNavScreen.fade-enter-from[data-v-c14c1e21],.VPNavScreen.fade-leave-to[data-v-c14c1e21]{opacity:0}.VPNavScreen.fade-enter-from .container[data-v-c14c1e21],.VPNavScreen.fade-leave-to .container[data-v-c14c1e21]{transform:translateY(-8px)}@media (min-width: 768px){.VPNavScreen[data-v-c14c1e21]{display:none}}.container[data-v-c14c1e21]{margin:0 auto;padding:24px 0 96px;max-width:288px}.menu+.translations[data-v-c14c1e21],.menu+.appearance[data-v-c14c1e21],.translations+.appearance[data-v-c14c1e21]{margin-top:24px}.menu+.social-links[data-v-c14c1e21]{margin-top:16px}.appearance+.social-links[data-v-c14c1e21]{margin-top:16px}.VPNav[data-v-e823d444]{position:relative;top:var(--vp-layout-top-height, 0px);left:0;z-index:var(--vp-z-index-nav);width:100%;pointer-events:none;transition:background-color .5s}@media (min-width: 960px){.VPNav[data-v-e823d444]{position:fixed}}.VPSidebarItem.level-0[data-v-a9cdba99]{padding-bottom:24px}.VPSidebarItem.collapsed.level-0[data-v-a9cdba99]{padding-bottom:10px}.item[data-v-a9cdba99]{position:relative;display:flex;width:100%}.VPSidebarItem.collapsible>.item[data-v-a9cdba99]{cursor:pointer}.indicator[data-v-a9cdba99]{position:absolute;top:6px;bottom:6px;left:-17px;width:2px;border-radius:2px;transition:background-color .25s}.VPSidebarItem.level-2.is-active>.item>.indicator[data-v-a9cdba99],.VPSidebarItem.level-3.is-active>.item>.indicator[data-v-a9cdba99],.VPSidebarItem.level-4.is-active>.item>.indicator[data-v-a9cdba99],.VPSidebarItem.level-5.is-active>.item>.indicator[data-v-a9cdba99]{background-color:var(--vp-c-brand-1)}.link[data-v-a9cdba99]{display:flex;align-items:center;flex-grow:1}.text[data-v-a9cdba99]{flex-grow:1;padding:4px 0;line-height:24px;font-size:14px;transition:color .25s}.VPSidebarItem.level-0 .text[data-v-a9cdba99]{font-weight:700;color:var(--vp-c-text-1)}.VPSidebarItem.level-1 .text[data-v-a9cdba99],.VPSidebarItem.level-2 .text[data-v-a9cdba99],.VPSidebarItem.level-3 .text[data-v-a9cdba99],.VPSidebarItem.level-4 .text[data-v-a9cdba99],.VPSidebarItem.level-5 .text[data-v-a9cdba99]{font-weight:500;color:var(--vp-c-text-2)}.VPSidebarItem.level-0.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-1.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-2.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-3.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-4.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-5.is-link>.item>.link:hover .text[data-v-a9cdba99]{color:var(--vp-c-brand-1)}.VPSidebarItem.level-0.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-1.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-2.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-3.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-4.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-5.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-0.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-1.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-2.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-3.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-4.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-5.has-active>.item>.link>.text[data-v-a9cdba99]{color:var(--vp-c-text-1)}.VPSidebarItem.level-0.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-1.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-2.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-3.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-4.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-5.is-active>.item .link>.text[data-v-a9cdba99]{color:var(--vp-c-brand-1)}.caret[data-v-a9cdba99]{display:flex;justify-content:center;align-items:center;margin-right:-7px;width:32px;height:32px;color:var(--vp-c-text-3);cursor:pointer;transition:color .25s;flex-shrink:0}.item:hover .caret[data-v-a9cdba99]{color:var(--vp-c-text-2)}.item:hover .caret[data-v-a9cdba99]:hover{color:var(--vp-c-text-1)}.caret-icon[data-v-a9cdba99]{font-size:18px;transform:rotate(90deg);transition:transform .25s}.VPSidebarItem.collapsed .caret-icon[data-v-a9cdba99]{transform:rotate(0)}.VPSidebarItem.level-1 .items[data-v-a9cdba99],.VPSidebarItem.level-2 .items[data-v-a9cdba99],.VPSidebarItem.level-3 .items[data-v-a9cdba99],.VPSidebarItem.level-4 .items[data-v-a9cdba99],.VPSidebarItem.level-5 .items[data-v-a9cdba99]{border-left:1px solid var(--vp-c-divider);padding-left:16px}.VPSidebarItem.collapsed .items[data-v-a9cdba99]{display:none}.no-transition[data-v-72c67ed4] .caret-icon{transition:none}.group+.group[data-v-72c67ed4]{border-top:1px solid var(--vp-c-divider);padding-top:10px}@media (min-width: 960px){.group[data-v-72c67ed4]{padding-top:10px;width:calc(var(--vp-sidebar-width) - 64px)}}.VPSidebar[data-v-59ceefa4]{position:fixed;top:var(--vp-layout-top-height, 0px);bottom:0;left:0;z-index:var(--vp-z-index-sidebar);padding:32px 32px 96px;width:calc(100vw - 64px);max-width:320px;background-color:var(--vp-sidebar-bg-color);opacity:0;box-shadow:var(--vp-c-shadow-3);overflow-x:hidden;overflow-y:auto;transform:translate(-100%);transition:opacity .5s,transform .25s ease;overscroll-behavior:contain}.VPSidebar.open[data-v-59ceefa4]{opacity:1;visibility:visible;transform:translate(0);transition:opacity .25s,transform .5s cubic-bezier(.19,1,.22,1)}.dark .VPSidebar[data-v-59ceefa4]{box-shadow:var(--vp-shadow-1)}@media (min-width: 960px){.VPSidebar[data-v-59ceefa4]{padding-top:var(--vp-nav-height);width:var(--vp-sidebar-width);max-width:100%;background-color:var(--vp-sidebar-bg-color);opacity:1;visibility:visible;box-shadow:none;transform:translate(0)}}@media (min-width: 1440px){.VPSidebar[data-v-59ceefa4]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}@media (min-width: 960px){.curtain[data-v-59ceefa4]{position:sticky;top:-64px;left:0;z-index:1;margin-top:calc(var(--vp-nav-height) * -1);margin-right:-32px;margin-left:-32px;height:var(--vp-nav-height);background-color:var(--vp-sidebar-bg-color)}}.nav[data-v-59ceefa4]{outline:0}.VPSkipLink[data-v-e813112c]{top:8px;left:8px;padding:8px 16px;z-index:999;border-radius:8px;font-size:12px;font-weight:700;text-decoration:none;color:var(--vp-c-brand-1);box-shadow:var(--vp-shadow-3);background-color:var(--vp-c-bg)}.VPSkipLink[data-v-e813112c]:focus{height:auto;width:auto;clip:auto;clip-path:none}@media (min-width: 1280px){.VPSkipLink[data-v-e813112c]{top:14px;left:16px}}.Layout[data-v-3b4648ff]{display:flex;flex-direction:column;min-height:100vh}.VPHomeSponsors[data-v-e06ca32a]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPHomeSponsors[data-v-e06ca32a]{margin:96px 0}@media (min-width: 768px){.VPHomeSponsors[data-v-e06ca32a]{margin:128px 0}}.VPHomeSponsors[data-v-e06ca32a]{padding:0 24px}@media (min-width: 768px){.VPHomeSponsors[data-v-e06ca32a]{padding:0 48px}}@media (min-width: 960px){.VPHomeSponsors[data-v-e06ca32a]{padding:0 64px}}.container[data-v-e06ca32a]{margin:0 auto;max-width:1152px}.love[data-v-e06ca32a]{margin:0 auto;width:fit-content;font-size:28px;color:var(--vp-c-text-3)}.icon[data-v-e06ca32a]{display:inline-block}.message[data-v-e06ca32a]{margin:0 auto;padding-top:10px;max-width:320px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.sponsors[data-v-e06ca32a]{padding-top:32px}.action[data-v-e06ca32a]{padding-top:40px;text-align:center}.VPTeamPage[data-v-b1db0dbf]{margin:96px 0}@media (min-width: 768px){.VPTeamPage[data-v-b1db0dbf]{margin:128px 0}}.VPHome .VPTeamPageTitle[data-v-b1db0dbf-s]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPTeamPageSection+.VPTeamPageSection[data-v-b1db0dbf-s],.VPTeamMembers+.VPTeamPageSection[data-v-b1db0dbf-s]{margin-top:64px}.VPTeamMembers+.VPTeamMembers[data-v-b1db0dbf-s]{margin-top:24px}@media (min-width: 768px){.VPTeamPageTitle+.VPTeamPageSection[data-v-b1db0dbf-s]{margin-top:16px}.VPTeamPageSection+.VPTeamPageSection[data-v-b1db0dbf-s],.VPTeamMembers+.VPTeamPageSection[data-v-b1db0dbf-s]{margin-top:96px}}.VPTeamMembers[data-v-b1db0dbf-s]{padding:0 24px}@media (min-width: 768px){.VPTeamMembers[data-v-b1db0dbf-s]{padding:0 48px}}@media (min-width: 960px){.VPTeamMembers[data-v-b1db0dbf-s]{padding:0 64px}}.VPTeamPageTitle[data-v-67e2507a]{padding:48px 32px;text-align:center}@media (min-width: 768px){.VPTeamPageTitle[data-v-67e2507a]{padding:64px 48px 48px}}@media (min-width: 960px){.VPTeamPageTitle[data-v-67e2507a]{padding:80px 64px 48px}}.title[data-v-67e2507a]{letter-spacing:0;line-height:44px;font-size:36px;font-weight:500}@media (min-width: 768px){.title[data-v-67e2507a]{letter-spacing:-.5px;line-height:56px;font-size:48px}}.lead[data-v-67e2507a]{margin:0 auto;max-width:512px;padding-top:12px;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 768px){.lead[data-v-67e2507a]{max-width:592px;letter-spacing:.15px;line-height:28px;font-size:20px}}.VPTeamPageSection[data-v-848babf0]{padding:0 32px}@media (min-width: 768px){.VPTeamPageSection[data-v-848babf0]{padding:0 48px}}@media (min-width: 960px){.VPTeamPageSection[data-v-848babf0]{padding:0 64px}}.title[data-v-848babf0]{position:relative;margin:0 auto;max-width:1152px;text-align:center;color:var(--vp-c-text-2)}.title-line[data-v-848babf0]{position:absolute;top:16px;left:0;width:100%;height:1px;background-color:var(--vp-c-divider)}.title-text[data-v-848babf0]{position:relative;display:inline-block;padding:0 24px;letter-spacing:0;line-height:32px;font-size:20px;font-weight:500;background-color:var(--vp-c-bg)}.lead[data-v-848babf0]{margin:0 auto;max-width:480px;padding-top:12px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.members[data-v-848babf0]{padding-top:40px}.VPTeamMembersItem[data-v-990ef11d]{display:flex;flex-direction:column;gap:2px;border-radius:12px;width:100%;height:100%;overflow:hidden}.VPTeamMembersItem.small .profile[data-v-990ef11d]{padding:32px}.VPTeamMembersItem.small .data[data-v-990ef11d]{padding-top:20px}.VPTeamMembersItem.small .avatar[data-v-990ef11d]{width:64px;height:64px}.VPTeamMembersItem.small .name[data-v-990ef11d]{line-height:24px;font-size:16px}.VPTeamMembersItem.small .affiliation[data-v-990ef11d]{padding-top:4px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .desc[data-v-990ef11d]{padding-top:12px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .links[data-v-990ef11d]{margin:0 -16px -20px;padding:10px 0 0}.VPTeamMembersItem.medium .profile[data-v-990ef11d]{padding:48px 32px}.VPTeamMembersItem.medium .data[data-v-990ef11d]{padding-top:24px;text-align:center}.VPTeamMembersItem.medium .avatar[data-v-990ef11d]{width:96px;height:96px}.VPTeamMembersItem.medium .name[data-v-990ef11d]{letter-spacing:.15px;line-height:28px;font-size:20px}.VPTeamMembersItem.medium .affiliation[data-v-990ef11d]{padding-top:4px;font-size:16px}.VPTeamMembersItem.medium .desc[data-v-990ef11d]{padding-top:16px;max-width:288px;font-size:16px}.VPTeamMembersItem.medium .links[data-v-990ef11d]{margin:0 -16px -12px;padding:16px 12px 0}.profile[data-v-990ef11d]{flex-grow:1;background-color:var(--vp-c-bg-soft)}.data[data-v-990ef11d]{text-align:center}.avatar[data-v-990ef11d]{position:relative;flex-shrink:0;margin:0 auto;border-radius:50%;box-shadow:var(--vp-shadow-3)}.avatar-img[data-v-990ef11d]{position:absolute;top:0;right:0;bottom:0;left:0;border-radius:50%;object-fit:cover}.name[data-v-990ef11d]{margin:0;font-weight:600}.affiliation[data-v-990ef11d]{margin:0;font-weight:500;color:var(--vp-c-text-2)}.org.link[data-v-990ef11d]{color:var(--vp-c-text-2);transition:color .25s}.org.link[data-v-990ef11d]:hover{color:var(--vp-c-brand-1)}.desc[data-v-990ef11d]{margin:0 auto}.desc[data-v-990ef11d] a{font-weight:500;color:var(--vp-c-brand-1);text-decoration-style:dotted;transition:color .25s}.links[data-v-990ef11d]{display:flex;justify-content:center;height:56px}.sp-link[data-v-990ef11d]{display:flex;justify-content:center;align-items:center;text-align:center;padding:16px;font-size:14px;font-weight:500;color:var(--vp-c-sponsor);background-color:var(--vp-c-bg-soft);transition:color .25s,background-color .25s}.sp .sp-link.link[data-v-990ef11d]:hover,.sp .sp-link.link[data-v-990ef11d]:focus{outline:none;color:var(--vp-c-white);background-color:var(--vp-c-sponsor)}.sp-icon[data-v-990ef11d]{margin-right:8px;font-size:16px}.VPTeamMembers.small .container[data-v-387893a3]{grid-template-columns:repeat(auto-fit,minmax(224px,1fr))}.VPTeamMembers.small.count-1 .container[data-v-387893a3]{max-width:276px}.VPTeamMembers.small.count-2 .container[data-v-387893a3]{max-width:576px}.VPTeamMembers.small.count-3 .container[data-v-387893a3]{max-width:876px}.VPTeamMembers.medium .container[data-v-387893a3]{grid-template-columns:repeat(auto-fit,minmax(256px,1fr))}@media (min-width: 375px){.VPTeamMembers.medium .container[data-v-387893a3]{grid-template-columns:repeat(auto-fit,minmax(288px,1fr))}}.VPTeamMembers.medium.count-1 .container[data-v-387893a3]{max-width:368px}.VPTeamMembers.medium.count-2 .container[data-v-387893a3]{max-width:760px}.container[data-v-387893a3]{display:grid;gap:24px;margin:0 auto;max-width:1152px}:root{--vp-font-family-base: "Poppins", "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: "Cousine", monospace}:root{--vp-home-hero-name-color: transparent;--vp-home-hero-name-background: -webkit-linear-gradient(120deg, #bd34fe 30%, #41d1ff)}@media (min-width: 640px){:root{--vp-home-hero-image-filter: blur(56px)}}@media (min-width: 960px){:root{--vp-home-hero-image-filter: blur(68px)}}.VPLocalSearchBox[data-v-6120c6bd]{position:fixed;z-index:100;top:0;right:0;bottom:0;left:0;display:flex}.backdrop[data-v-6120c6bd]{position:absolute;top:0;right:0;bottom:0;left:0;background:var(--vp-backdrop-bg-color);transition:opacity .5s}.shell[data-v-6120c6bd]{position:relative;padding:12px;margin:64px auto;display:flex;flex-direction:column;gap:16px;background:var(--vp-local-search-bg);width:min(100vw - 60px,900px);height:min-content;max-height:min(100vh - 128px,900px);border-radius:6px}@media (max-width: 767px){.shell[data-v-6120c6bd]{margin:0;width:100vw;height:100vh;max-height:none;border-radius:0}}.search-bar[data-v-6120c6bd]{border:1px solid var(--vp-c-divider);border-radius:4px;display:flex;align-items:center;padding:0 12px;cursor:text}@media (max-width: 767px){.search-bar[data-v-6120c6bd]{padding:0 8px}}.search-bar[data-v-6120c6bd]:focus-within{border-color:var(--vp-c-brand-1)}.local-search-icon[data-v-6120c6bd]{display:block;font-size:18px}.navigate-icon[data-v-6120c6bd]{display:block;font-size:14px}.search-icon[data-v-6120c6bd]{margin:8px}@media (max-width: 767px){.search-icon[data-v-6120c6bd]{display:none}}.search-input[data-v-6120c6bd]{padding:6px 12px;font-size:inherit;width:100%}@media (max-width: 767px){.search-input[data-v-6120c6bd]{padding:6px 4px}}.search-actions[data-v-6120c6bd]{display:flex;gap:4px}@media (any-pointer: coarse){.search-actions[data-v-6120c6bd]{gap:8px}}@media (min-width: 769px){.search-actions.before[data-v-6120c6bd]{display:none}}.search-actions button[data-v-6120c6bd]{padding:8px}.search-actions button[data-v-6120c6bd]:not([disabled]):hover,.toggle-layout-button.detailed-list[data-v-6120c6bd]{color:var(--vp-c-brand-1)}.search-actions button.clear-button[data-v-6120c6bd]:disabled{opacity:.37}.search-keyboard-shortcuts[data-v-6120c6bd]{font-size:.8rem;opacity:75%;display:flex;flex-wrap:wrap;gap:16px;line-height:14px}.search-keyboard-shortcuts span[data-v-6120c6bd]{display:flex;align-items:center;gap:4px}@media (max-width: 767px){.search-keyboard-shortcuts[data-v-6120c6bd]{display:none}}.search-keyboard-shortcuts kbd[data-v-6120c6bd]{background:#8080801a;border-radius:4px;padding:3px 6px;min-width:24px;display:inline-block;text-align:center;vertical-align:middle;border:1px solid rgba(128,128,128,.15);box-shadow:0 2px 2px #0000001a}.results[data-v-6120c6bd]{display:flex;flex-direction:column;gap:6px;overflow-x:hidden;overflow-y:auto;overscroll-behavior:contain}.result[data-v-6120c6bd]{display:flex;align-items:center;gap:8px;border-radius:4px;transition:none;line-height:1rem;border:solid 2px var(--vp-local-search-result-border);outline:none}.result>div[data-v-6120c6bd]{margin:12px;width:100%;overflow:hidden}@media (max-width: 767px){.result>div[data-v-6120c6bd]{margin:8px}}.titles[data-v-6120c6bd]{display:flex;flex-wrap:wrap;gap:4px;position:relative;z-index:1001;padding:2px 0}.title[data-v-6120c6bd]{display:flex;align-items:center;gap:4px}.title.main[data-v-6120c6bd]{font-weight:500}.title-icon[data-v-6120c6bd]{opacity:.5;font-weight:500;color:var(--vp-c-brand-1)}.title svg[data-v-6120c6bd]{opacity:.5}.result.selected[data-v-6120c6bd]{--vp-local-search-result-bg: var(--vp-local-search-result-selected-bg);border-color:var(--vp-local-search-result-selected-border)}.excerpt-wrapper[data-v-6120c6bd]{position:relative}.excerpt[data-v-6120c6bd]{opacity:50%;pointer-events:none;max-height:140px;overflow:hidden;position:relative;margin-top:4px}.result.selected .excerpt[data-v-6120c6bd]{opacity:1}.excerpt[data-v-6120c6bd] *{font-size:.8rem!important;line-height:130%!important}.titles[data-v-6120c6bd] mark,.excerpt[data-v-6120c6bd] mark{background-color:var(--vp-local-search-highlight-bg);color:var(--vp-local-search-highlight-text);border-radius:2px;padding:0 2px}.excerpt[data-v-6120c6bd] .vp-code-group .tabs{display:none}.excerpt[data-v-6120c6bd] .vp-code-group div[class*=language-]{border-radius:8px!important}.excerpt-gradient-bottom[data-v-6120c6bd]{position:absolute;bottom:-1px;left:0;width:100%;height:8px;background:linear-gradient(transparent,var(--vp-local-search-result-bg));z-index:1000}.excerpt-gradient-top[data-v-6120c6bd]{position:absolute;top:-1px;left:0;width:100%;height:8px;background:linear-gradient(var(--vp-local-search-result-bg),transparent);z-index:1000}.result.selected .titles[data-v-6120c6bd],.result.selected .title-icon[data-v-6120c6bd]{color:var(--vp-c-brand-1)!important}.no-results[data-v-6120c6bd]{font-size:.9rem;text-align:center;padding:12px}svg[data-v-6120c6bd]{flex:none}
diff --git a/assets/style.Czi07tLB.css b/assets/style.Czi07tLB.css
new file mode 100644
index 0000000..a75a21f
--- /dev/null
+++ b/assets/style.Czi07tLB.css
@@ -0,0 +1 @@
+:root{--vp-home-hero-name-color: transparent;--vp-home-hero-name-background: -webkit-linear-gradient(120deg, #bd34fe 30%, #41d1ff)}@media (min-width: 640px){:root{--vp-home-hero-image-filter: blur(56px)}}@media (min-width: 960px){:root{--vp-home-hero-image-filter: blur(68px)}}:root{--vp-c-white: #ffffff;--vp-c-black: #000000;--vp-c-neutral: var(--vp-c-black);--vp-c-neutral-inverse: var(--vp-c-white)}.dark{--vp-c-neutral: var(--vp-c-white);--vp-c-neutral-inverse: var(--vp-c-black)}:root{--vp-c-gray-1: #dddde3;--vp-c-gray-2: #e4e4e9;--vp-c-gray-3: #ebebef;--vp-c-gray-soft: rgba(142, 150, 170, .14);--vp-c-indigo-1: #3451b2;--vp-c-indigo-2: #3a5ccc;--vp-c-indigo-3: #5672cd;--vp-c-indigo-soft: rgba(100, 108, 255, .14);--vp-c-purple-1: #6f42c1;--vp-c-purple-2: #7e4cc9;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .14);--vp-c-green-1: #18794e;--vp-c-green-2: #299764;--vp-c-green-3: #30a46c;--vp-c-green-soft: rgba(16, 185, 129, .14);--vp-c-yellow-1: #915930;--vp-c-yellow-2: #946300;--vp-c-yellow-3: #9f6a00;--vp-c-yellow-soft: rgba(234, 179, 8, .14);--vp-c-red-1: #b8272c;--vp-c-red-2: #d5393e;--vp-c-red-3: #e0575b;--vp-c-red-soft: rgba(244, 63, 94, .14);--vp-c-sponsor: #db2777}.dark{--vp-c-gray-1: #515c67;--vp-c-gray-2: #414853;--vp-c-gray-3: #32363f;--vp-c-gray-soft: rgba(101, 117, 133, .16);--vp-c-indigo-1: #a8b1ff;--vp-c-indigo-2: #5c73e7;--vp-c-indigo-3: #3e63dd;--vp-c-indigo-soft: rgba(100, 108, 255, .16);--vp-c-purple-1: #c8abfa;--vp-c-purple-2: #a879e6;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .16);--vp-c-green-1: #3dd68c;--vp-c-green-2: #30a46c;--vp-c-green-3: #298459;--vp-c-green-soft: rgba(16, 185, 129, .16);--vp-c-yellow-1: #f9b44e;--vp-c-yellow-2: #da8b17;--vp-c-yellow-3: #a46a0a;--vp-c-yellow-soft: rgba(234, 179, 8, .16);--vp-c-red-1: #f66f81;--vp-c-red-2: #f14158;--vp-c-red-3: #b62a3c;--vp-c-red-soft: rgba(244, 63, 94, .16)}:root{--vp-c-bg: #ffffff;--vp-c-bg-alt: #f6f6f7;--vp-c-bg-elv: #ffffff;--vp-c-bg-soft: #f6f6f7}.dark{--vp-c-bg: #1b1b1f;--vp-c-bg-alt: #161618;--vp-c-bg-elv: #202127;--vp-c-bg-soft: #202127}:root{--vp-c-border: #c2c2c4;--vp-c-divider: #e2e2e3;--vp-c-gutter: #e2e2e3}.dark{--vp-c-border: #3c3f44;--vp-c-divider: #2e2e32;--vp-c-gutter: #000000}:root{--vp-c-text-1: rgba(60, 60, 67);--vp-c-text-2: rgba(60, 60, 67, .78);--vp-c-text-3: rgba(60, 60, 67, .56)}.dark{--vp-c-text-1: rgba(255, 255, 245, .86);--vp-c-text-2: rgba(235, 235, 245, .6);--vp-c-text-3: rgba(235, 235, 245, .38)}:root{--vp-c-default-1: var(--vp-c-gray-1);--vp-c-default-2: var(--vp-c-gray-2);--vp-c-default-3: var(--vp-c-gray-3);--vp-c-default-soft: var(--vp-c-gray-soft);--vp-c-brand-1: var(--vp-c-indigo-1);--vp-c-brand-2: var(--vp-c-indigo-2);--vp-c-brand-3: var(--vp-c-indigo-3);--vp-c-brand-soft: var(--vp-c-indigo-soft);--vp-c-brand: var(--vp-c-brand-1);--vp-c-tip-1: var(--vp-c-brand-1);--vp-c-tip-2: var(--vp-c-brand-2);--vp-c-tip-3: var(--vp-c-brand-3);--vp-c-tip-soft: var(--vp-c-brand-soft);--vp-c-note-1: var(--vp-c-brand-1);--vp-c-note-2: var(--vp-c-brand-2);--vp-c-note-3: var(--vp-c-brand-3);--vp-c-note-soft: var(--vp-c-brand-soft);--vp-c-success-1: var(--vp-c-green-1);--vp-c-success-2: var(--vp-c-green-2);--vp-c-success-3: var(--vp-c-green-3);--vp-c-success-soft: var(--vp-c-green-soft);--vp-c-important-1: var(--vp-c-purple-1);--vp-c-important-2: var(--vp-c-purple-2);--vp-c-important-3: var(--vp-c-purple-3);--vp-c-important-soft: var(--vp-c-purple-soft);--vp-c-warning-1: var(--vp-c-yellow-1);--vp-c-warning-2: var(--vp-c-yellow-2);--vp-c-warning-3: var(--vp-c-yellow-3);--vp-c-warning-soft: var(--vp-c-yellow-soft);--vp-c-danger-1: var(--vp-c-red-1);--vp-c-danger-2: var(--vp-c-red-2);--vp-c-danger-3: var(--vp-c-red-3);--vp-c-danger-soft: var(--vp-c-red-soft);--vp-c-caution-1: var(--vp-c-red-1);--vp-c-caution-2: var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, "Menlo", "Monaco", "Consolas", "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root:where(:lang(zh)){--vp-font-family-base: "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: var(--vp-c-text-1);--vp-custom-block-warning-bg: var(--vp-c-warning-soft);--vp-custom-block-warning-code-bg: var(--vp-c-warning-soft);--vp-custom-block-danger-border: transparent;--vp-custom-block-danger-text: var(--vp-c-text-1);--vp-custom-block-danger-bg: var(--vp-c-danger-soft);--vp-custom-block-danger-code-bg: var(--vp-c-danger-soft);--vp-custom-block-caution-border: transparent;--vp-custom-block-caution-text: var(--vp-c-text-1);--vp-custom-block-caution-bg: var(--vp-c-caution-soft);--vp-custom-block-caution-code-bg: var(--vp-c-caution-soft);--vp-custom-block-details-border: var(--vp-custom-block-info-border);--vp-custom-block-details-text: var(--vp-custom-block-info-text);--vp-custom-block-details-bg: var(--vp-custom-block-info-bg);--vp-custom-block-details-code-bg: var(--vp-custom-block-info-code-bg)}:root{--vp-input-border-color: var(--vp-c-border);--vp-input-bg-color: var(--vp-c-bg-alt);--vp-input-switch-bg-color: var(--vp-c-default-soft)}:root{--vp-nav-height: 64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: var(--vp-c-bg);--vp-local-search-result-bg: var(--vp-c-bg);--vp-local-search-result-border: var(--vp-c-divider);--vp-local-search-result-selected-bg: var(--vp-c-bg);--vp-local-search-result-selected-border: var(--vp-c-brand-1);--vp-local-search-highlight-bg: var(--vp-c-brand-1);--vp-local-search-highlight-text: var(--vp-c-neutral-inverse)}@media (prefers-reduced-motion: reduce){*,:before,:after{animation-delay:-1ms!important;animation-duration:1ms!important;animation-iteration-count:1!important;background-attachment:initial!important;scroll-behavior:auto!important;transition-duration:0s!important;transition-delay:0s!important}}*,:before,:after{box-sizing:border-box}html{line-height:1.4;font-size:16px;-webkit-text-size-adjust:100%}html.dark{color-scheme:dark}body{margin:0;width:100%;min-width:320px;min-height:100vh;line-height:24px;font-family:var(--vp-font-family-base);font-size:16px;font-weight:400;color:var(--vp-c-text-1);background-color:var(--vp-c-bg);font-synthesis:style;text-rendering:optimizeLegibility;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale}main{display:block}h1,h2,h3,h4,h5,h6{margin:0;line-height:24px;font-size:16px;font-weight:400}p{margin:0}strong,b{font-weight:600}a,area,button,[role=button],input,label,select,summary,textarea{touch-action:manipulation}a{color:inherit;text-decoration:inherit}ol,ul{list-style:none;margin:0;padding:0}blockquote{margin:0}pre,code,kbd,samp{font-family:var(--vp-font-family-mono)}img,svg,video,canvas,audio,iframe,embed,object{display:block}figure{margin:0}img,video{max-width:100%;height:auto}button,input,optgroup,select,textarea{border:0;padding:0;line-height:inherit;color:inherit}button{padding:0;font-family:inherit;background-color:transparent;background-image:none}button:enabled,[role=button]:enabled{cursor:pointer}button:focus,button:focus-visible{outline:1px dotted;outline:4px auto -webkit-focus-ring-color}button:focus:not(:focus-visible){outline:none!important}input:focus,textarea:focus,select:focus{outline:none}table{border-collapse:collapse}input{background-color:transparent}input:-ms-input-placeholder,textarea:-ms-input-placeholder{color:var(--vp-c-text-3)}input::-ms-input-placeholder,textarea::-ms-input-placeholder{color:var(--vp-c-text-3)}input::placeholder,textarea::placeholder{color:var(--vp-c-text-3)}input::-webkit-outer-spin-button,input::-webkit-inner-spin-button{-webkit-appearance:none;margin:0}input[type=number]{-moz-appearance:textfield}textarea{resize:vertical}select{-webkit-appearance:none}fieldset{margin:0;padding:0}h1,h2,h3,h4,h5,h6,li,p{overflow-wrap:break-word}vite-error-overlay{z-index:9999}mjx-container{overflow-x:auto}mjx-container>svg{display:inline-block;margin:auto}[class^=vpi-],[class*=" vpi-"],.vp-icon{width:1em;height:1em}[class^=vpi-].bg,[class*=" vpi-"].bg,.vp-icon.bg{background-size:100% 100%;background-color:transparent}[class^=vpi-]:not(.bg),[class*=" vpi-"]:not(.bg),.vp-icon:not(.bg){-webkit-mask:var(--icon) no-repeat;mask:var(--icon) no-repeat;-webkit-mask-size:100% 100%;mask-size:100% 100%;background-color:currentColor;color:inherit}.vpi-align-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M21 6H3M15 12H3M17 18H3'/%3E%3C/svg%3E")}.vpi-arrow-right,.vpi-arrow-down,.vpi-arrow-left,.vpi-arrow-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5l7 7-7 7'/%3E%3C/svg%3E")}.vpi-chevron-right,.vpi-chevron-down,.vpi-chevron-left,.vpi-chevron-up{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 18 6-6-6-6'/%3E%3C/svg%3E")}.vpi-chevron-down,.vpi-arrow-down{transform:rotate(90deg)}.vpi-chevron-left,.vpi-arrow-left{transform:rotate(180deg)}.vpi-chevron-up,.vpi-arrow-up{transform:rotate(-90deg)}.vpi-square-pen{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3H5a2 2 0 0 0-2 2v14a2 2 0 0 0 2 2h14a2 2 0 0 0 2-2v-7'/%3E%3Cpath d='M18.375 2.625a2.121 2.121 0 1 1 3 3L12 15l-4 1 1-4Z'/%3E%3C/svg%3E")}.vpi-plus{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M5 12h14M12 5v14'/%3E%3C/svg%3E")}.vpi-sun{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='4'/%3E%3Cpath d='M12 2v2M12 20v2M4.93 4.93l1.41 1.41M17.66 17.66l1.41 1.41M2 12h2M20 12h2M6.34 17.66l-1.41 1.41M19.07 4.93l-1.41 1.41'/%3E%3C/svg%3E")}.vpi-moon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M12 3a6 6 0 0 0 9 9 9 9 0 1 1-9-9Z'/%3E%3C/svg%3E")}.vpi-more-horizontal{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='12' cy='12' r='1'/%3E%3Ccircle cx='19' cy='12' r='1'/%3E%3Ccircle cx='5' cy='12' r='1'/%3E%3C/svg%3E")}.vpi-languages{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m5 8 6 6M4 14l6-6 2-3M2 5h12M7 2h1M22 22l-5-10-5 10M14 18h6'/%3E%3C/svg%3E")}.vpi-heart{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M19 14c1.49-1.46 3-3.21 3-5.5A5.5 5.5 0 0 0 16.5 3c-1.76 0-3 .5-4.5 2-1.5-1.5-2.74-2-4.5-2A5.5 5.5 0 0 0 2 8.5c0 2.3 1.5 4.05 3 5.5l7 7Z'/%3E%3C/svg%3E")}.vpi-search{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Ccircle cx='11' cy='11' r='8'/%3E%3Cpath d='m21 21-4.3-4.3'/%3E%3C/svg%3E")}.vpi-layout-list{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='7' height='7' x='3' y='3' rx='1'/%3E%3Crect width='7' height='7' x='3' y='14' rx='1'/%3E%3Cpath d='M14 4h7M14 9h7M14 15h7M14 20h7'/%3E%3C/svg%3E")}.vpi-delete{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='M20 5H9l-7 7 7 7h11a2 2 0 0 0 2-2V7a2 2 0 0 0-2-2ZM18 9l-6 6M12 9l6 6'/%3E%3C/svg%3E")}.vpi-corner-down-left{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Cpath d='m9 10-5 5 5 5'/%3E%3Cpath d='M20 4v7a4 4 0 0 1-4 4H4'/%3E%3C/svg%3E")}:root{--vp-icon-copy: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3C/svg%3E");--vp-icon-copied: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='none' stroke='rgba(128,128,128,1)' stroke-linecap='round' stroke-linejoin='round' stroke-width='2' viewBox='0 0 24 24'%3E%3Crect width='8' height='4' x='8' y='2' rx='1' ry='1'/%3E%3Cpath d='M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2'/%3E%3Cpath d='m9 14 2 2 4-4'/%3E%3C/svg%3E")}.vpi-social-discord{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.317 4.37a19.791 19.791 0 0 0-4.885-1.515.074.074 0 0 0-.079.037c-.21.375-.444.864-.608 1.25a18.27 18.27 0 0 0-5.487 0 12.64 12.64 0 0 0-.617-1.25.077.077 0 0 0-.079-.037A19.736 19.736 0 0 0 3.677 4.37a.07.07 0 0 0-.032.027C.533 9.046-.32 13.58.099 18.057a.082.082 0 0 0 .031.057 19.9 19.9 0 0 0 5.993 3.03.078.078 0 0 0 .084-.028c.462-.63.874-1.295 1.226-1.994a.076.076 0 0 0-.041-.106 13.107 13.107 0 0 1-1.872-.892.077.077 0 0 1-.008-.128 10.2 10.2 0 0 0 .372-.292.074.074 0 0 1 .077-.01c3.928 1.793 8.18 1.793 12.062 0a.074.074 0 0 1 .078.01c.12.098.246.198.373.292a.077.077 0 0 1-.006.127 12.299 12.299 0 0 1-1.873.892.077.077 0 0 0-.041.107c.36.698.772 1.362 1.225 1.993a.076.076 0 0 0 .084.028 19.839 19.839 0 0 0 6.002-3.03.077.077 0 0 0 .032-.054c.5-5.177-.838-9.674-3.549-13.66a.061.061 0 0 0-.031-.03zM8.02 15.33c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.956-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.956 2.418-2.157 2.418zm7.975 0c-1.183 0-2.157-1.085-2.157-2.419 0-1.333.955-2.419 2.157-2.419 1.21 0 2.176 1.096 2.157 2.42 0 1.333-.946 2.418-2.157 2.418Z'/%3E%3C/svg%3E")}.vpi-social-facebook{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M9.101 23.691v-7.98H6.627v-3.667h2.474v-1.58c0-4.085 1.848-5.978 5.858-5.978.401 0 .955.042 1.468.103a8.68 8.68 0 0 1 1.141.195v3.325a8.623 8.623 0 0 0-.653-.036 26.805 26.805 0 0 0-.733-.009c-.707 0-1.259.096-1.675.309a1.686 1.686 0 0 0-.679.622c-.258.42-.374.995-.374 1.752v1.297h3.919l-.386 2.103-.287 1.564h-3.246v8.245C19.396 23.238 24 18.179 24 12.044c0-6.627-5.373-12-12-12s-12 5.373-12 12c0 5.628 3.874 10.35 9.101 11.647Z'/%3E%3C/svg%3E")}.vpi-social-github{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12'/%3E%3C/svg%3E")}.vpi-social-instagram{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M7.03.084c-1.277.06-2.149.264-2.91.563a5.874 5.874 0 0 0-2.124 1.388 5.878 5.878 0 0 0-1.38 2.127C.321 4.926.12 5.8.064 7.076.008 8.354-.005 8.764.001 12.023c.007 3.259.021 3.667.083 4.947.061 1.277.264 2.149.563 2.911.308.789.72 1.457 1.388 2.123a5.872 5.872 0 0 0 2.129 1.38c.763.295 1.636.496 2.913.552 1.278.056 1.689.069 4.947.063 3.257-.007 3.668-.021 4.947-.082 1.28-.06 2.147-.265 2.91-.563a5.881 5.881 0 0 0 2.123-1.388 5.881 5.881 0 0 0 1.38-2.129c.295-.763.496-1.636.551-2.912.056-1.28.07-1.69.063-4.948-.006-3.258-.02-3.667-.081-4.947-.06-1.28-.264-2.148-.564-2.911a5.892 5.892 0 0 0-1.387-2.123 5.857 5.857 0 0 0-2.128-1.38C19.074.322 18.202.12 16.924.066 15.647.009 15.236-.006 11.977 0 8.718.008 8.31.021 7.03.084m.14 21.693c-1.17-.05-1.805-.245-2.228-.408a3.736 3.736 0 0 1-1.382-.895 3.695 3.695 0 0 1-.9-1.378c-.165-.423-.363-1.058-.417-2.228-.06-1.264-.072-1.644-.08-4.848-.006-3.204.006-3.583.061-4.848.05-1.169.246-1.805.408-2.228.216-.561.477-.96.895-1.382a3.705 3.705 0 0 1 1.379-.9c.423-.165 1.057-.361 2.227-.417 1.265-.06 1.644-.072 4.848-.08 3.203-.006 3.583.006 4.85.062 1.168.05 1.804.244 2.227.408.56.216.96.475 1.382.895.421.42.681.817.9 1.378.165.422.362 1.056.417 2.227.06 1.265.074 1.645.08 4.848.005 3.203-.006 3.583-.061 4.848-.051 1.17-.245 1.805-.408 2.23-.216.56-.477.96-.896 1.38a3.705 3.705 0 0 1-1.378.9c-.422.165-1.058.362-2.226.418-1.266.06-1.645.072-4.85.079-3.204.007-3.582-.006-4.848-.06m9.783-16.192a1.44 1.44 0 1 0 1.437-1.442 1.44 1.44 0 0 0-1.437 1.442M5.839 12.012a6.161 6.161 0 1 0 12.323-.024 6.162 6.162 0 0 0-12.323.024M8 12.008A4 4 0 1 1 12.008 16 4 4 0 0 1 8 12.008'/%3E%3C/svg%3E")}.vpi-social-linkedin{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M20.447 20.452h-3.554v-5.569c0-1.328-.027-3.037-1.852-3.037-1.853 0-2.136 1.445-2.136 2.939v5.667H9.351V9h3.414v1.561h.046c.477-.9 1.637-1.85 3.37-1.85 3.601 0 4.267 2.37 4.267 5.455v6.286zM5.337 7.433a2.062 2.062 0 0 1-2.063-2.065 2.064 2.064 0 1 1 2.063 2.065zm1.782 13.019H3.555V9h3.564v11.452zM22.225 0H1.771C.792 0 0 .774 0 1.729v20.542C0 23.227.792 24 1.771 24h20.451C23.2 24 24 23.227 24 22.271V1.729C24 .774 23.2 0 22.222 0h.003z'/%3E%3C/svg%3E")}.vpi-social-mastodon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.268 5.313c-.35-2.578-2.617-4.61-5.304-5.004C17.51.242 15.792 0 11.813 0h-.03c-3.98 0-4.835.242-5.288.309C3.882.692 1.496 2.518.917 5.127.64 6.412.61 7.837.661 9.143c.074 1.874.088 3.745.26 5.611.118 1.24.325 2.47.62 3.68.55 2.237 2.777 4.098 4.96 4.857 2.336.792 4.849.923 7.256.38.265-.061.527-.132.786-.213.585-.184 1.27-.39 1.774-.753a.057.057 0 0 0 .023-.043v-1.809a.052.052 0 0 0-.02-.041.053.053 0 0 0-.046-.01 20.282 20.282 0 0 1-4.709.545c-2.73 0-3.463-1.284-3.674-1.818a5.593 5.593 0 0 1-.319-1.433.053.053 0 0 1 .066-.054c1.517.363 3.072.546 4.632.546.376 0 .75 0 1.125-.01 1.57-.044 3.224-.124 4.768-.422.038-.008.077-.015.11-.024 2.435-.464 4.753-1.92 4.989-5.604.008-.145.03-1.52.03-1.67.002-.512.167-3.63-.024-5.545zm-3.748 9.195h-2.561V8.29c0-1.309-.55-1.976-1.67-1.976-1.23 0-1.846.79-1.846 2.35v3.403h-2.546V8.663c0-1.56-.617-2.35-1.848-2.35-1.112 0-1.668.668-1.67 1.977v6.218H4.822V8.102c0-1.31.337-2.35 1.011-3.12.696-.77 1.608-1.164 2.74-1.164 1.311 0 2.302.5 2.962 1.498l.638 1.06.638-1.06c.66-.999 1.65-1.498 2.96-1.498 1.13 0 2.043.395 2.74 1.164.675.77 1.012 1.81 1.012 3.12z'/%3E%3C/svg%3E")}.vpi-social-npm{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M1.763 0C.786 0 0 .786 0 1.763v20.474C0 23.214.786 24 1.763 24h20.474c.977 0 1.763-.786 1.763-1.763V1.763C24 .786 23.214 0 22.237 0zM5.13 5.323l13.837.019-.009 13.836h-3.464l.01-10.382h-3.456L12.04 19.17H5.113z'/%3E%3C/svg%3E")}.vpi-social-slack{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M5.042 15.165a2.528 2.528 0 0 1-2.52 2.523A2.528 2.528 0 0 1 0 15.165a2.527 2.527 0 0 1 2.522-2.52h2.52v2.52zm1.271 0a2.527 2.527 0 0 1 2.521-2.52 2.527 2.527 0 0 1 2.521 2.52v6.313A2.528 2.528 0 0 1 8.834 24a2.528 2.528 0 0 1-2.521-2.522v-6.313zM8.834 5.042a2.528 2.528 0 0 1-2.521-2.52A2.528 2.528 0 0 1 8.834 0a2.528 2.528 0 0 1 2.521 2.522v2.52H8.834zm0 1.271a2.528 2.528 0 0 1 2.521 2.521 2.528 2.528 0 0 1-2.521 2.521H2.522A2.528 2.528 0 0 1 0 8.834a2.528 2.528 0 0 1 2.522-2.521h6.312zm10.122 2.521a2.528 2.528 0 0 1 2.522-2.521A2.528 2.528 0 0 1 24 8.834a2.528 2.528 0 0 1-2.522 2.521h-2.522V8.834zm-1.268 0a2.528 2.528 0 0 1-2.523 2.521 2.527 2.527 0 0 1-2.52-2.521V2.522A2.527 2.527 0 0 1 15.165 0a2.528 2.528 0 0 1 2.523 2.522v6.312zm-2.523 10.122a2.528 2.528 0 0 1 2.523 2.522A2.528 2.528 0 0 1 15.165 24a2.527 2.527 0 0 1-2.52-2.522v-2.522h2.52zm0-1.268a2.527 2.527 0 0 1-2.52-2.523 2.526 2.526 0 0 1 2.52-2.52h6.313A2.527 2.527 0 0 1 24 15.165a2.528 2.528 0 0 1-2.522 2.523h-6.313z'/%3E%3C/svg%3E")}.vpi-social-twitter,.vpi-social-x{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M18.901 1.153h3.68l-8.04 9.19L24 22.846h-7.406l-5.8-7.584-6.638 7.584H.474l8.6-9.83L0 1.154h7.594l5.243 6.932ZM17.61 20.644h2.039L6.486 3.24H4.298Z'/%3E%3C/svg%3E")}.vpi-social-youtube{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24'%3E%3Cpath d='M23.498 6.186a3.016 3.016 0 0 0-2.122-2.136C19.505 3.545 12 3.545 12 3.545s-7.505 0-9.377.505A3.017 3.017 0 0 0 .502 6.186C0 8.07 0 12 0 12s0 3.93.502 5.814a3.016 3.016 0 0 0 2.122 2.136c1.871.505 9.376.505 9.376.505s7.505 0 9.377-.505a3.015 3.015 0 0 0 2.122-2.136C24 15.93 24 12 24 12s0-3.93-.502-5.814zM9.545 15.568V8.432L15.818 12l-6.273 3.568z'/%3E%3C/svg%3E")}.visually-hidden{position:absolute;width:1px;height:1px;white-space:nowrap;clip:rect(0 0 0 0);clip-path:inset(50%);overflow:hidden}.custom-block{border:1px solid transparent;border-radius:8px;padding:16px 16px 8px;line-height:24px;font-size:var(--vp-custom-block-font-size);color:var(--vp-c-text-2)}.custom-block.info{border-color:var(--vp-custom-block-info-border);color:var(--vp-custom-block-info-text);background-color:var(--vp-custom-block-info-bg)}.custom-block.info a,.custom-block.info code{color:var(--vp-c-brand-1)}.custom-block.info a:hover,.custom-block.info a:hover>code{color:var(--vp-c-brand-2)}.custom-block.info code{background-color:var(--vp-custom-block-info-code-bg)}.custom-block.note{border-color:var(--vp-custom-block-note-border);color:var(--vp-custom-block-note-text);background-color:var(--vp-custom-block-note-bg)}.custom-block.note a,.custom-block.note code{color:var(--vp-c-brand-1)}.custom-block.note a:hover,.custom-block.note a:hover>code{color:var(--vp-c-brand-2)}.custom-block.note code{background-color:var(--vp-custom-block-note-code-bg)}.custom-block.tip{border-color:var(--vp-custom-block-tip-border);color:var(--vp-custom-block-tip-text);background-color:var(--vp-custom-block-tip-bg)}.custom-block.tip a,.custom-block.tip code{color:var(--vp-c-tip-1)}.custom-block.tip a:hover,.custom-block.tip a:hover>code{color:var(--vp-c-tip-2)}.custom-block.tip code{background-color:var(--vp-custom-block-tip-code-bg)}.custom-block.important{border-color:var(--vp-custom-block-important-border);color:var(--vp-custom-block-important-text);background-color:var(--vp-custom-block-important-bg)}.custom-block.important a,.custom-block.important code{color:var(--vp-c-important-1)}.custom-block.important a:hover,.custom-block.important a:hover>code{color:var(--vp-c-important-2)}.custom-block.important code{background-color:var(--vp-custom-block-important-code-bg)}.custom-block.warning{border-color:var(--vp-custom-block-warning-border);color:var(--vp-custom-block-warning-text);background-color:var(--vp-custom-block-warning-bg)}.custom-block.warning a,.custom-block.warning code{color:var(--vp-c-warning-1)}.custom-block.warning a:hover,.custom-block.warning a:hover>code{color:var(--vp-c-warning-2)}.custom-block.warning code{background-color:var(--vp-custom-block-warning-code-bg)}.custom-block.danger{border-color:var(--vp-custom-block-danger-border);color:var(--vp-custom-block-danger-text);background-color:var(--vp-custom-block-danger-bg)}.custom-block.danger a,.custom-block.danger code{color:var(--vp-c-danger-1)}.custom-block.danger a:hover,.custom-block.danger a:hover>code{color:var(--vp-c-danger-2)}.custom-block.danger code{background-color:var(--vp-custom-block-danger-code-bg)}.custom-block.caution{border-color:var(--vp-custom-block-caution-border);color:var(--vp-custom-block-caution-text);background-color:var(--vp-custom-block-caution-bg)}.custom-block.caution a,.custom-block.caution code{color:var(--vp-c-caution-1)}.custom-block.caution a:hover,.custom-block.caution a:hover>code{color:var(--vp-c-caution-2)}.custom-block.caution code{background-color:var(--vp-custom-block-caution-code-bg)}.custom-block.details{border-color:var(--vp-custom-block-details-border);color:var(--vp-custom-block-details-text);background-color:var(--vp-custom-block-details-bg)}.custom-block.details a{color:var(--vp-c-brand-1)}.custom-block.details a:hover,.custom-block.details a:hover>code{color:var(--vp-c-brand-2)}.custom-block.details code{background-color:var(--vp-custom-block-details-code-bg)}.custom-block-title{font-weight:600}.custom-block p+p{margin:8px 0}.custom-block.details summary{margin:0 0 8px;font-weight:700;cursor:pointer;-webkit-user-select:none;user-select:none}.custom-block.details summary+p{margin:8px 0}.custom-block a{color:inherit;font-weight:600;text-decoration:underline;text-underline-offset:2px;transition:opacity .25s}.custom-block a:hover{opacity:.75}.custom-block code{font-size:var(--vp-custom-block-code-font-size)}.custom-block.custom-block th,.custom-block.custom-block blockquote>p{font-size:var(--vp-custom-block-font-size);color:inherit}.dark .vp-code span{color:var(--shiki-dark, inherit)}html:not(.dark) .vp-code span{color:var(--shiki-light, inherit)}.vp-code-group{margin-top:16px}.vp-code-group .tabs{position:relative;display:flex;margin-right:-24px;margin-left:-24px;padding:0 12px;background-color:var(--vp-code-tab-bg);overflow-x:auto;overflow-y:hidden;box-shadow:inset 0 -1px var(--vp-code-tab-divider)}@media (min-width: 640px){.vp-code-group .tabs{margin-right:0;margin-left:0;border-radius:8px 8px 0 0}}.vp-code-group .tabs input{position:fixed;opacity:0;pointer-events:none}.vp-code-group .tabs label{position:relative;display:inline-block;border-bottom:1px solid transparent;padding:0 12px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-code-tab-text-color);white-space:nowrap;cursor:pointer;transition:color .25s}.vp-code-group .tabs label:after{position:absolute;right:8px;bottom:-1px;left:8px;z-index:1;height:2px;border-radius:2px;content:"";background-color:transparent;transition:background-color .25s}.vp-code-group label:hover{color:var(--vp-code-tab-hover-text-color)}.vp-code-group input:checked+label{color:var(--vp-code-tab-active-text-color)}.vp-code-group input:checked+label:after{background-color:var(--vp-code-tab-active-bar-color)}.vp-code-group div[class*=language-],.vp-block{display:none;margin-top:0!important;border-top-left-radius:0!important;border-top-right-radius:0!important}.vp-code-group div[class*=language-].active,.vp-block.active{display:block}.vp-block{padding:20px 24px}.vp-doc h1,.vp-doc h2,.vp-doc h3,.vp-doc h4,.vp-doc h5,.vp-doc h6{position:relative;font-weight:600;outline:none}.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:28px}.vp-doc h2{margin:48px 0 16px;border-top:1px solid var(--vp-c-divider);padding-top:24px;letter-spacing:-.02em;line-height:32px;font-size:24px}.vp-doc h3{margin:32px 0 0;letter-spacing:-.01em;line-height:28px;font-size:20px}.vp-doc h4{margin:24px 0 0;letter-spacing:-.01em;line-height:24px;font-size:18px}.vp-doc .header-anchor{position:absolute;top:0;left:0;margin-left:-.87em;font-weight:500;-webkit-user-select:none;user-select:none;opacity:0;text-decoration:none;transition:color .25s,opacity .25s}.vp-doc .header-anchor:before{content:var(--vp-header-anchor-symbol)}.vp-doc h1:hover .header-anchor,.vp-doc h1 .header-anchor:focus,.vp-doc h2:hover .header-anchor,.vp-doc h2 .header-anchor:focus,.vp-doc h3:hover .header-anchor,.vp-doc h3 .header-anchor:focus,.vp-doc h4:hover .header-anchor,.vp-doc h4 .header-anchor:focus,.vp-doc h5:hover .header-anchor,.vp-doc h5 .header-anchor:focus,.vp-doc h6:hover .header-anchor,.vp-doc h6 .header-anchor:focus{opacity:1}@media (min-width: 768px){.vp-doc h1{letter-spacing:-.02em;line-height:40px;font-size:32px}}.vp-doc h2 .header-anchor{top:24px}.vp-doc p,.vp-doc summary{margin:16px 0}.vp-doc p{line-height:28px}.vp-doc blockquote{margin:16px 0;border-left:2px solid var(--vp-c-divider);padding-left:16px;transition:border-color .5s;color:var(--vp-c-text-2)}.vp-doc blockquote>p{margin:0;font-size:16px;transition:color .5s}.vp-doc a{font-weight:500;color:var(--vp-c-brand-1);text-decoration:underline;text-underline-offset:2px;transition:color .25s,opacity .25s}.vp-doc a:hover{color:var(--vp-c-brand-2)}.vp-doc strong{font-weight:600}.vp-doc ul,.vp-doc ol{padding-left:1.25rem;margin:16px 0}.vp-doc ul{list-style:disc}.vp-doc ol{list-style:decimal}.vp-doc li+li{margin-top:8px}.vp-doc li>ol,.vp-doc li>ul{margin:8px 0 0}.vp-doc table{display:block;border-collapse:collapse;margin:20px 0;overflow-x:auto}.vp-doc tr{background-color:var(--vp-c-bg);border-top:1px solid var(--vp-c-divider);transition:background-color .5s}.vp-doc tr:nth-child(2n){background-color:var(--vp-c-bg-soft)}.vp-doc th,.vp-doc td{border:1px solid var(--vp-c-divider);padding:8px 16px}.vp-doc th{text-align:left;font-size:14px;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-doc td{font-size:14px}.vp-doc hr{margin:16px 0;border:none;border-top:1px solid var(--vp-c-divider)}.vp-doc .custom-block{margin:16px 0}.vp-doc .custom-block p{margin:8px 0;line-height:24px}.vp-doc .custom-block p:first-child{margin:0}.vp-doc .custom-block div[class*=language-]{margin:8px 0;border-radius:8px}.vp-doc .custom-block div[class*=language-] code{font-weight:400;background-color:transparent}.vp-doc .custom-block .vp-code-group .tabs{margin:0;border-radius:8px 8px 0 0}.vp-doc :not(pre,h1,h2,h3,h4,h5,h6)>code{font-size:var(--vp-code-font-size);color:var(--vp-code-color)}.vp-doc :not(pre)>code{border-radius:4px;padding:3px 6px;background-color:var(--vp-code-bg);transition:color .25s,background-color .5s}.vp-doc a>code{color:var(--vp-code-link-color)}.vp-doc a:hover>code{color:var(--vp-code-link-hover-color)}.vp-doc h1>code,.vp-doc h2>code,.vp-doc h3>code,.vp-doc h4>code{font-size:.9em}.vp-doc div[class*=language-],.vp-block{position:relative;margin:16px -24px;background-color:var(--vp-code-block-bg);overflow-x:auto;transition:background-color .5s}@media (min-width: 640px){.vp-doc div[class*=language-],.vp-block{border-radius:8px;margin:16px 0}}@media (max-width: 639px){.vp-doc li div[class*=language-]{border-radius:8px 0 0 8px}}.vp-doc div[class*=language-]+div[class*=language-],.vp-doc div[class$=-api]+div[class*=language-],.vp-doc div[class*=language-]+div[class$=-api]>div[class*=language-]{margin-top:-8px}.vp-doc [class*=language-] pre,.vp-doc [class*=language-] code{direction:ltr;text-align:left;white-space:pre;word-spacing:normal;word-break:normal;word-wrap:normal;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-hyphens:none;-moz-hyphens:none;-ms-hyphens:none;hyphens:none}.vp-doc [class*=language-] pre{position:relative;z-index:1;margin:0;padding:20px 0;background:transparent;overflow-x:auto}.vp-doc [class*=language-] code{display:block;padding:0 24px;width:fit-content;min-width:100%;line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-block-color);transition:color .5s}.vp-doc [class*=language-] code .highlighted{background-color:var(--vp-code-line-highlight-color);transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .highlighted.error{background-color:var(--vp-code-line-error-color)}.vp-doc [class*=language-] code .highlighted.warning{background-color:var(--vp-code-line-warning-color)}.vp-doc [class*=language-] code .diff{transition:background-color .5s;margin:0 -24px;padding:0 24px;width:calc(100% + 48px);display:inline-block}.vp-doc [class*=language-] code .diff:before{position:absolute;left:10px}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){filter:blur(.095rem);opacity:.4;transition:filter .35s,opacity .35s}.vp-doc [class*=language-] .has-focused-lines .line:not(.has-focus){opacity:.7;transition:filter .35s,opacity .35s}.vp-doc [class*=language-]:hover .has-focused-lines .line:not(.has-focus){filter:blur(0);opacity:1}.vp-doc [class*=language-] code .diff.remove{background-color:var(--vp-code-line-diff-remove-color);opacity:.7}.vp-doc [class*=language-] code .diff.remove:before{content:"-";color:var(--vp-code-line-diff-remove-symbol-color)}.vp-doc [class*=language-] code .diff.add{background-color:var(--vp-code-line-diff-add-color)}.vp-doc [class*=language-] code .diff.add:before{content:"+";color:var(--vp-code-line-diff-add-symbol-color)}.vp-doc div[class*=language-].line-numbers-mode{padding-left:32px}.vp-doc .line-numbers-wrapper{position:absolute;top:0;bottom:0;left:0;z-index:3;border-right:1px solid var(--vp-code-block-divider-color);padding-top:20px;width:32px;text-align:center;font-family:var(--vp-font-family-mono);line-height:var(--vp-code-line-height);font-size:var(--vp-code-font-size);color:var(--vp-code-line-number-color);transition:border-color .5s,color .5s}.vp-doc [class*=language-]>button.copy{direction:ltr;position:absolute;top:12px;right:12px;z-index:3;border:1px solid var(--vp-code-copy-code-border-color);border-radius:4px;width:40px;height:40px;background-color:var(--vp-code-copy-code-bg);opacity:0;cursor:pointer;background-image:var(--vp-icon-copy);background-position:50%;background-size:20px;background-repeat:no-repeat;transition:border-color .25s,background-color .25s,opacity .25s}.vp-doc [class*=language-]:hover>button.copy,.vp-doc [class*=language-]>button.copy:focus{opacity:1}.vp-doc [class*=language-]>button.copy:hover,.vp-doc [class*=language-]>button.copy.copied{border-color:var(--vp-code-copy-code-hover-border-color);background-color:var(--vp-code-copy-code-hover-bg)}.vp-doc [class*=language-]>button.copy.copied,.vp-doc [class*=language-]>button.copy:hover.copied{border-radius:0 4px 4px 0;background-color:var(--vp-code-copy-code-hover-bg);background-image:var(--vp-icon-copied)}.vp-doc [class*=language-]>button.copy.copied:before,.vp-doc [class*=language-]>button.copy:hover.copied:before{position:relative;top:-1px;transform:translate(calc(-100% - 1px));display:flex;justify-content:center;align-items:center;border:1px solid var(--vp-code-copy-code-hover-border-color);border-right:0;border-radius:4px 0 0 4px;padding:0 10px;width:fit-content;height:40px;text-align:center;font-size:12px;font-weight:500;color:var(--vp-code-copy-code-active-text);background-color:var(--vp-code-copy-code-hover-bg);white-space:nowrap;content:var(--vp-code-copy-copied-text-content)}.vp-doc [class*=language-]>span.lang{position:absolute;top:2px;right:8px;z-index:2;font-size:12px;font-weight:500;color:var(--vp-code-lang-color);transition:color .4s,opacity .4s}.vp-doc [class*=language-]:hover>button.copy+span.lang,.vp-doc [class*=language-]>button.copy:focus+span.lang{opacity:0}.vp-doc .VPTeamMembers{margin-top:24px}.vp-doc .VPTeamMembers.small.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}.vp-doc .VPTeamMembers.small.count-2 .container,.vp-doc .VPTeamMembers.small.count-3 .container{max-width:100%!important}.vp-doc .VPTeamMembers.medium.count-1 .container{margin:0!important;max-width:calc((100% - 24px)/2)!important}:is(.vp-external-link-icon,.vp-doc a[href*="://"],.vp-doc a[target=_blank]):not(.no-icon):after{display:inline-block;margin-top:-1px;margin-left:4px;width:11px;height:11px;background:currentColor;color:var(--vp-c-text-3);flex-shrink:0;--icon: url("data:image/svg+xml, %3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 24 24' %3E%3Cpath d='M0 0h24v24H0V0z' fill='none' /%3E%3Cpath d='M9 5v2h6.59L4 18.59 5.41 20 17 8.41V15h2V5H9z' /%3E%3C/svg%3E");-webkit-mask-image:var(--icon);mask-image:var(--icon)}.vp-external-link-icon:after{content:""}.external-link-icon-enabled :is(.vp-doc a[href*="://"],.vp-doc a[target=_blank]):after{content:"";color:currentColor}.vp-sponsor{border-radius:16px;overflow:hidden}.vp-sponsor.aside{border-radius:12px}.vp-sponsor-section+.vp-sponsor-section{margin-top:4px}.vp-sponsor-tier{margin:0 0 4px!important;text-align:center;letter-spacing:1px!important;line-height:24px;width:100%;font-weight:600;color:var(--vp-c-text-2);background-color:var(--vp-c-bg-soft)}.vp-sponsor.normal .vp-sponsor-tier{padding:13px 0 11px;font-size:14px}.vp-sponsor.aside .vp-sponsor-tier{padding:9px 0 7px;font-size:12px}.vp-sponsor-grid+.vp-sponsor-tier{margin-top:4px}.vp-sponsor-grid{display:flex;flex-wrap:wrap;gap:4px}.vp-sponsor-grid.xmini .vp-sponsor-grid-link{height:64px}.vp-sponsor-grid.xmini .vp-sponsor-grid-image{max-width:64px;max-height:22px}.vp-sponsor-grid.mini .vp-sponsor-grid-link{height:72px}.vp-sponsor-grid.mini .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.small .vp-sponsor-grid-link{height:96px}.vp-sponsor-grid.small .vp-sponsor-grid-image{max-width:96px;max-height:24px}.vp-sponsor-grid.medium .vp-sponsor-grid-link{height:112px}.vp-sponsor-grid.medium .vp-sponsor-grid-image{max-width:120px;max-height:36px}.vp-sponsor-grid.big .vp-sponsor-grid-link{height:184px}.vp-sponsor-grid.big .vp-sponsor-grid-image{max-width:192px;max-height:56px}.vp-sponsor-grid[data-vp-grid="2"] .vp-sponsor-grid-item{width:calc((100% - 4px)/2)}.vp-sponsor-grid[data-vp-grid="3"] .vp-sponsor-grid-item{width:calc((100% - 4px * 2) / 3)}.vp-sponsor-grid[data-vp-grid="4"] .vp-sponsor-grid-item{width:calc((100% - 12px)/4)}.vp-sponsor-grid[data-vp-grid="5"] .vp-sponsor-grid-item{width:calc((100% - 16px)/5)}.vp-sponsor-grid[data-vp-grid="6"] .vp-sponsor-grid-item{width:calc((100% - 4px * 5) / 6)}.vp-sponsor-grid-item{flex-shrink:0;width:100%;background-color:var(--vp-c-bg-soft);transition:background-color .25s}.vp-sponsor-grid-item:hover{background-color:var(--vp-c-default-soft)}.vp-sponsor-grid-item:hover .vp-sponsor-grid-image{filter:grayscale(0) invert(0)}.vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.dark .vp-sponsor-grid-item:hover{background-color:var(--vp-c-white)}.dark .vp-sponsor-grid-item.empty:hover{background-color:var(--vp-c-bg-soft)}.vp-sponsor-grid-link{display:flex}.vp-sponsor-grid-box{display:flex;justify-content:center;align-items:center;width:100%}.vp-sponsor-grid-image{max-width:100%;filter:grayscale(1);transition:filter .25s}.dark .vp-sponsor-grid-image{filter:grayscale(1) invert(1)}.VPBadge{display:inline-block;margin-left:2px;border:1px solid transparent;border-radius:12px;padding:0 10px;line-height:22px;font-size:12px;font-weight:500;transform:translateY(-2px)}.VPBadge.small{padding:0 6px;line-height:18px;font-size:10px;transform:translateY(-8px)}.VPDocFooter .VPBadge{display:none}.vp-doc h1>.VPBadge{margin-top:4px;vertical-align:top}.vp-doc h2>.VPBadge{margin-top:3px;padding:0 8px;vertical-align:top}.vp-doc h3>.VPBadge{vertical-align:middle}.vp-doc h4>.VPBadge,.vp-doc h5>.VPBadge,.vp-doc h6>.VPBadge{vertical-align:middle;line-height:18px}.VPBadge.info{border-color:var(--vp-badge-info-border);color:var(--vp-badge-info-text);background-color:var(--vp-badge-info-bg)}.VPBadge.tip{border-color:var(--vp-badge-tip-border);color:var(--vp-badge-tip-text);background-color:var(--vp-badge-tip-bg)}.VPBadge.warning{border-color:var(--vp-badge-warning-border);color:var(--vp-badge-warning-text);background-color:var(--vp-badge-warning-bg)}.VPBadge.danger{border-color:var(--vp-badge-danger-border);color:var(--vp-badge-danger-text);background-color:var(--vp-badge-danger-bg)}.VPBackdrop[data-v-daa1937f]{position:fixed;top:0;right:0;bottom:0;left:0;z-index:var(--vp-z-index-backdrop);background:var(--vp-backdrop-bg-color);transition:opacity .5s}.VPBackdrop.fade-enter-from[data-v-daa1937f],.VPBackdrop.fade-leave-to[data-v-daa1937f]{opacity:0}.VPBackdrop.fade-leave-active[data-v-daa1937f]{transition-duration:.25s}@media (min-width: 1280px){.VPBackdrop[data-v-daa1937f]{display:none}}.NotFound[data-v-2aa14331]{padding:64px 24px 96px;text-align:center}@media (min-width: 768px){.NotFound[data-v-2aa14331]{padding:96px 32px 168px}}.code[data-v-2aa14331]{line-height:64px;font-size:64px;font-weight:600}.title[data-v-2aa14331]{padding-top:12px;letter-spacing:2px;line-height:20px;font-size:20px;font-weight:700}.divider[data-v-2aa14331]{margin:24px auto 18px;width:64px;height:1px;background-color:var(--vp-c-divider)}.quote[data-v-2aa14331]{margin:0 auto;max-width:256px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.action[data-v-2aa14331]{padding-top:20px}.link[data-v-2aa14331]{display:inline-block;border:1px solid var(--vp-c-brand-1);border-radius:16px;padding:3px 16px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:border-color .25s,color .25s}.link[data-v-2aa14331]:hover{border-color:var(--vp-c-brand-2);color:var(--vp-c-brand-2)}.root[data-v-b9c884bb]{position:relative;z-index:1}.nested[data-v-b9c884bb]{padding-right:16px;padding-left:16px}.outline-link[data-v-b9c884bb]{display:block;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-2);white-space:nowrap;overflow:hidden;text-overflow:ellipsis;transition:color .5s}.outline-link[data-v-b9c884bb]:hover,.outline-link.active[data-v-b9c884bb]{color:var(--vp-c-text-1);transition:color .25s}.outline-link.nested[data-v-b9c884bb]{padding-left:13px}.VPDocAsideOutline[data-v-d34649dc]{display:none}.VPDocAsideOutline.has-outline[data-v-d34649dc]{display:block}.content[data-v-d34649dc]{position:relative;border-left:1px solid var(--vp-c-divider);padding-left:16px;font-size:13px;font-weight:500}.outline-marker[data-v-d34649dc]{position:absolute;top:32px;left:-1px;z-index:0;opacity:0;width:2px;border-radius:2px;height:18px;background-color:var(--vp-c-brand-1);transition:top .25s cubic-bezier(0,1,.5,1),background-color .5s,opacity .25s}.outline-title[data-v-d34649dc]{line-height:32px;font-size:14px;font-weight:600}.VPDocAside[data-v-8951c20f]{display:flex;flex-direction:column;flex-grow:1}.spacer[data-v-8951c20f]{flex-grow:1}.VPDocAside[data-v-8951c20f] .spacer+.VPDocAsideSponsors,.VPDocAside[data-v-8951c20f] .spacer+.VPDocAsideCarbonAds{margin-top:24px}.VPDocAside[data-v-8951c20f] .VPDocAsideSponsors+.VPDocAsideCarbonAds{margin-top:16px}.VPLastUpdated[data-v-19bf19fb]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 640px){.VPLastUpdated[data-v-19bf19fb]{line-height:32px;font-size:14px;font-weight:500}}.VPDocFooter[data-v-28deee4a]{margin-top:64px}.edit-info[data-v-28deee4a]{padding-bottom:18px}@media (min-width: 640px){.edit-info[data-v-28deee4a]{display:flex;justify-content:space-between;align-items:center;padding-bottom:14px}}.edit-link-button[data-v-28deee4a]{display:flex;align-items:center;border:0;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.edit-link-button[data-v-28deee4a]:hover{color:var(--vp-c-brand-2)}.edit-link-icon[data-v-28deee4a]{margin-right:8px}.prev-next[data-v-28deee4a]{border-top:1px solid var(--vp-c-divider);padding-top:24px;display:grid;grid-row-gap:8px}@media (min-width: 640px){.prev-next[data-v-28deee4a]{grid-template-columns:repeat(2,1fr);grid-column-gap:16px}}.pager-link[data-v-28deee4a]{display:block;border:1px solid var(--vp-c-divider);border-radius:8px;padding:11px 16px 13px;width:100%;height:100%;transition:border-color .25s}.pager-link[data-v-28deee4a]:hover{border-color:var(--vp-c-brand-1)}.pager-link.next[data-v-28deee4a]{margin-left:auto;text-align:right}.desc[data-v-28deee4a]{display:block;line-height:20px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.title[data-v-28deee4a]{display:block;line-height:20px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1);transition:color .25s}.VPDoc[data-v-01c90815]{padding:32px 24px 96px;width:100%}@media (min-width: 768px){.VPDoc[data-v-01c90815]{padding:48px 32px 128px}}@media (min-width: 960px){.VPDoc[data-v-01c90815]{padding:48px 32px 0}.VPDoc:not(.has-sidebar) .container[data-v-01c90815]{display:flex;justify-content:center;max-width:992px}.VPDoc:not(.has-sidebar) .content[data-v-01c90815]{max-width:752px}}@media (min-width: 1280px){.VPDoc .container[data-v-01c90815]{display:flex;justify-content:center}.VPDoc .aside[data-v-01c90815]{display:block}}@media (min-width: 1440px){.VPDoc:not(.has-sidebar) .content[data-v-01c90815]{max-width:784px}.VPDoc:not(.has-sidebar) .container[data-v-01c90815]{max-width:1104px}}.container[data-v-01c90815]{margin:0 auto;width:100%}.aside[data-v-01c90815]{position:relative;display:none;order:2;flex-grow:1;padding-left:32px;width:100%;max-width:256px}.left-aside[data-v-01c90815]{order:1;padding-left:unset;padding-right:32px}.aside-container[data-v-01c90815]{position:fixed;top:0;padding-top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + var(--vp-doc-top-height, 0px) + 48px);width:224px;height:100vh;overflow-x:hidden;overflow-y:auto;scrollbar-width:none}.aside-container[data-v-01c90815]::-webkit-scrollbar{display:none}.aside-curtain[data-v-01c90815]{position:fixed;bottom:0;z-index:10;width:224px;height:32px;background:linear-gradient(transparent,var(--vp-c-bg) 70%)}.aside-content[data-v-01c90815]{display:flex;flex-direction:column;min-height:calc(100vh - (var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px));padding-bottom:32px}.content[data-v-01c90815]{position:relative;margin:0 auto;width:100%}@media (min-width: 960px){.content[data-v-01c90815]{padding:0 32px 128px}}@media (min-width: 1280px){.content[data-v-01c90815]{order:1;margin:0;min-width:640px}}.content-container[data-v-01c90815]{margin:0 auto}.VPDoc.has-aside .content-container[data-v-01c90815]{max-width:688px}.VPButton[data-v-f549f0f3]{display:inline-block;border:1px solid transparent;text-align:center;font-weight:600;white-space:nowrap;transition:color .25s,border-color .25s,background-color .25s}.VPButton[data-v-f549f0f3]:active{transition:color .1s,border-color .1s,background-color .1s}.VPButton.medium[data-v-f549f0f3]{border-radius:20px;padding:0 20px;line-height:38px;font-size:14px}.VPButton.big[data-v-f549f0f3]{border-radius:24px;padding:0 24px;line-height:46px;font-size:16px}.VPButton.brand[data-v-f549f0f3]{border-color:var(--vp-button-brand-border);color:var(--vp-button-brand-text);background-color:var(--vp-button-brand-bg)}.VPButton.brand[data-v-f549f0f3]:hover{border-color:var(--vp-button-brand-hover-border);color:var(--vp-button-brand-hover-text);background-color:var(--vp-button-brand-hover-bg)}.VPButton.brand[data-v-f549f0f3]:active{border-color:var(--vp-button-brand-active-border);color:var(--vp-button-brand-active-text);background-color:var(--vp-button-brand-active-bg)}.VPButton.alt[data-v-f549f0f3]{border-color:var(--vp-button-alt-border);color:var(--vp-button-alt-text);background-color:var(--vp-button-alt-bg)}.VPButton.alt[data-v-f549f0f3]:hover{border-color:var(--vp-button-alt-hover-border);color:var(--vp-button-alt-hover-text);background-color:var(--vp-button-alt-hover-bg)}.VPButton.alt[data-v-f549f0f3]:active{border-color:var(--vp-button-alt-active-border);color:var(--vp-button-alt-active-text);background-color:var(--vp-button-alt-active-bg)}.VPButton.sponsor[data-v-f549f0f3]{border-color:var(--vp-button-sponsor-border);color:var(--vp-button-sponsor-text);background-color:var(--vp-button-sponsor-bg)}.VPButton.sponsor[data-v-f549f0f3]:hover{border-color:var(--vp-button-sponsor-hover-border);color:var(--vp-button-sponsor-hover-text);background-color:var(--vp-button-sponsor-hover-bg)}.VPButton.sponsor[data-v-f549f0f3]:active{border-color:var(--vp-button-sponsor-active-border);color:var(--vp-button-sponsor-active-text);background-color:var(--vp-button-sponsor-active-bg)}html:not(.dark) .VPImage.dark[data-v-cc63e071]{display:none}.dark .VPImage.light[data-v-cc63e071]{display:none}.VPHero[data-v-e302b8ce]{margin-top:calc((var(--vp-nav-height) + var(--vp-layout-top-height, 0px)) * -1);padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 48px) 24px 48px}@media (min-width: 640px){.VPHero[data-v-e302b8ce]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 48px 64px}}@media (min-width: 960px){.VPHero[data-v-e302b8ce]{padding:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px) + 80px) 64px 64px}}.container[data-v-e302b8ce]{display:flex;flex-direction:column;margin:0 auto;max-width:1152px}@media (min-width: 960px){.container[data-v-e302b8ce]{flex-direction:row}}.main[data-v-e302b8ce]{position:relative;z-index:10;order:2;flex-grow:1;flex-shrink:0}.VPHero.has-image .container[data-v-e302b8ce]{text-align:center}@media (min-width: 960px){.VPHero.has-image .container[data-v-e302b8ce]{text-align:left}}@media (min-width: 960px){.main[data-v-e302b8ce]{order:1;width:calc((100% / 3) * 2)}.VPHero.has-image .main[data-v-e302b8ce]{max-width:592px}}.name[data-v-e302b8ce],.text[data-v-e302b8ce]{max-width:392px;letter-spacing:-.4px;line-height:40px;font-size:32px;font-weight:700;white-space:pre-wrap}.VPHero.has-image .name[data-v-e302b8ce],.VPHero.has-image .text[data-v-e302b8ce]{margin:0 auto}.name[data-v-e302b8ce]{color:var(--vp-home-hero-name-color)}.clip[data-v-e302b8ce]{background:var(--vp-home-hero-name-background);-webkit-background-clip:text;background-clip:text;-webkit-text-fill-color:var(--vp-home-hero-name-color)}@media (min-width: 640px){.name[data-v-e302b8ce],.text[data-v-e302b8ce]{max-width:576px;line-height:56px;font-size:48px}}@media (min-width: 960px){.name[data-v-e302b8ce],.text[data-v-e302b8ce]{line-height:64px;font-size:56px}.VPHero.has-image .name[data-v-e302b8ce],.VPHero.has-image .text[data-v-e302b8ce]{margin:0}}.tagline[data-v-e302b8ce]{padding-top:8px;max-width:392px;line-height:28px;font-size:18px;font-weight:500;white-space:pre-wrap;color:var(--vp-c-text-2)}.VPHero.has-image .tagline[data-v-e302b8ce]{margin:0 auto}@media (min-width: 640px){.tagline[data-v-e302b8ce]{padding-top:12px;max-width:576px;line-height:32px;font-size:20px}}@media (min-width: 960px){.tagline[data-v-e302b8ce]{line-height:36px;font-size:24px}.VPHero.has-image .tagline[data-v-e302b8ce]{margin:0}}.actions[data-v-e302b8ce]{display:flex;flex-wrap:wrap;margin:-6px;padding-top:24px}.VPHero.has-image .actions[data-v-e302b8ce]{justify-content:center}@media (min-width: 640px){.actions[data-v-e302b8ce]{padding-top:32px}}@media (min-width: 960px){.VPHero.has-image .actions[data-v-e302b8ce]{justify-content:flex-start}}.action[data-v-e302b8ce]{flex-shrink:0;padding:6px}.image[data-v-e302b8ce]{order:1;margin:-76px -24px -48px}@media (min-width: 640px){.image[data-v-e302b8ce]{margin:-108px -24px -48px}}@media (min-width: 960px){.image[data-v-e302b8ce]{flex-grow:1;order:2;margin:0;min-height:100%}}.image-container[data-v-e302b8ce]{position:relative;margin:0 auto;width:320px;height:320px}@media (min-width: 640px){.image-container[data-v-e302b8ce]{width:392px;height:392px}}@media (min-width: 960px){.image-container[data-v-e302b8ce]{display:flex;justify-content:center;align-items:center;width:100%;height:100%;transform:translate(-32px,-32px)}}.image-bg[data-v-e302b8ce]{position:absolute;top:50%;left:50%;border-radius:50%;width:192px;height:192px;background-image:var(--vp-home-hero-image-background-image);filter:var(--vp-home-hero-image-filter);transform:translate(-50%,-50%)}@media (min-width: 640px){.image-bg[data-v-e302b8ce]{width:256px;height:256px}}@media (min-width: 960px){.image-bg[data-v-e302b8ce]{width:320px;height:320px}}[data-v-e302b8ce] .image-src{position:absolute;top:50%;left:50%;max-width:192px;max-height:192px;transform:translate(-50%,-50%)}@media (min-width: 640px){[data-v-e302b8ce] .image-src{max-width:256px;max-height:256px}}@media (min-width: 960px){[data-v-e302b8ce] .image-src{max-width:320px;max-height:320px}}.VPFeature[data-v-f77e80b4]{display:block;border:1px solid var(--vp-c-bg-soft);border-radius:12px;height:100%;background-color:var(--vp-c-bg-soft);transition:border-color .25s,background-color .25s}.VPFeature.link[data-v-f77e80b4]:hover{border-color:var(--vp-c-brand-1)}.box[data-v-f77e80b4]{display:flex;flex-direction:column;padding:24px;height:100%}.box[data-v-f77e80b4]>.VPImage{margin-bottom:20px}.icon[data-v-f77e80b4]{display:flex;justify-content:center;align-items:center;margin-bottom:20px;border-radius:6px;background-color:var(--vp-c-default-soft);width:48px;height:48px;font-size:24px;transition:background-color .25s}.title[data-v-f77e80b4]{line-height:24px;font-size:16px;font-weight:600}.details[data-v-f77e80b4]{flex-grow:1;padding-top:8px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.link-text[data-v-f77e80b4]{padding-top:8px}.link-text-value[data-v-f77e80b4]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.link-text-icon[data-v-f77e80b4]{margin-left:6px}.VPFeatures[data-v-8e833103]{position:relative;padding:0 24px}@media (min-width: 640px){.VPFeatures[data-v-8e833103]{padding:0 48px}}@media (min-width: 960px){.VPFeatures[data-v-8e833103]{padding:0 64px}}.container[data-v-8e833103]{margin:0 auto;max-width:1152px}.items[data-v-8e833103]{display:flex;flex-wrap:wrap;margin:-8px}.item[data-v-8e833103]{padding:8px;width:100%}@media (min-width: 640px){.item.grid-2[data-v-8e833103],.item.grid-4[data-v-8e833103],.item.grid-6[data-v-8e833103]{width:50%}}@media (min-width: 768px){.item.grid-2[data-v-8e833103],.item.grid-4[data-v-8e833103]{width:50%}.item.grid-3[data-v-8e833103],.item.grid-6[data-v-8e833103]{width:calc(100% / 3)}}@media (min-width: 960px){.item.grid-4[data-v-8e833103]{width:25%}}.container[data-v-90605523]{margin:auto;width:100%;max-width:1280px;padding:0 24px}@media (min-width: 640px){.container[data-v-90605523]{padding:0 48px}}@media (min-width: 960px){.container[data-v-90605523]{width:100%;padding:0 64px}}.vp-doc[data-v-90605523] .VPHomeSponsors,.vp-doc[data-v-90605523] .VPTeamPage{margin-left:var(--vp-offset, calc(50% - 50vw) );margin-right:var(--vp-offset, calc(50% - 50vw) )}.vp-doc[data-v-90605523] .VPHomeSponsors h2{border-top:none;letter-spacing:normal}.vp-doc[data-v-90605523] .VPHomeSponsors a,.vp-doc[data-v-90605523] .VPTeamPage a{text-decoration:none}.VPHome[data-v-55977d12]{margin-bottom:96px}@media (min-width: 768px){.VPHome[data-v-55977d12]{margin-bottom:128px}}.VPContent[data-v-fc04087f]{flex-grow:1;flex-shrink:0;margin:var(--vp-layout-top-height, 0px) auto 0;width:100%}.VPContent.is-home[data-v-fc04087f]{width:100%;max-width:100%}.VPContent.has-sidebar[data-v-fc04087f]{margin:0}@media (min-width: 960px){.VPContent[data-v-fc04087f]{padding-top:var(--vp-nav-height)}.VPContent.has-sidebar[data-v-fc04087f]{margin:var(--vp-layout-top-height, 0px) 0 0;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPContent.has-sidebar[data-v-fc04087f]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.VPFooter[data-v-d69bcf5d]{position:relative;z-index:var(--vp-z-index-footer);border-top:1px solid var(--vp-c-gutter);padding:32px 24px;background-color:var(--vp-c-bg)}.VPFooter.has-sidebar[data-v-d69bcf5d]{display:none}.VPFooter[data-v-d69bcf5d] a{text-decoration-line:underline;text-underline-offset:2px;transition:color .25s}.VPFooter[data-v-d69bcf5d] a:hover{color:var(--vp-c-text-1)}@media (min-width: 768px){.VPFooter[data-v-d69bcf5d]{padding:32px}}.container[data-v-d69bcf5d]{margin:0 auto;max-width:var(--vp-layout-max-width);text-align:center}.message[data-v-d69bcf5d],.copyright[data-v-d69bcf5d]{line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-2)}.VPLocalNavOutlineDropdown[data-v-9dd5e197]{padding:12px 20px 11px}@media (min-width: 960px){.VPLocalNavOutlineDropdown[data-v-9dd5e197]{padding:12px 36px 11px}}.VPLocalNavOutlineDropdown button[data-v-9dd5e197]{display:block;font-size:12px;font-weight:500;line-height:24px;color:var(--vp-c-text-2);transition:color .5s;position:relative}.VPLocalNavOutlineDropdown button[data-v-9dd5e197]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPLocalNavOutlineDropdown button.open[data-v-9dd5e197]{color:var(--vp-c-text-1)}.icon[data-v-9dd5e197]{display:inline-block;vertical-align:middle;margin-left:2px;font-size:14px;transform:rotate(0);transition:transform .25s}@media (min-width: 960px){.VPLocalNavOutlineDropdown button[data-v-9dd5e197]{font-size:14px}.icon[data-v-9dd5e197]{font-size:16px}}.open>.icon[data-v-9dd5e197]{transform:rotate(90deg)}.items[data-v-9dd5e197]{position:absolute;top:40px;right:16px;left:16px;display:grid;gap:1px;border:1px solid var(--vp-c-border);border-radius:8px;background-color:var(--vp-c-gutter);max-height:calc(var(--vp-vh, 100vh) - 86px);overflow:hidden auto;box-shadow:var(--vp-shadow-3)}@media (min-width: 960px){.items[data-v-9dd5e197]{right:auto;left:calc(var(--vp-sidebar-width) + 32px);width:320px}}.header[data-v-9dd5e197]{background-color:var(--vp-c-bg-soft)}.top-link[data-v-9dd5e197]{display:block;padding:0 16px;line-height:48px;font-size:14px;font-weight:500;color:var(--vp-c-brand-1)}.outline[data-v-9dd5e197]{padding:8px 0;background-color:var(--vp-c-bg-soft)}.flyout-enter-active[data-v-9dd5e197]{transition:all .2s ease-out}.flyout-leave-active[data-v-9dd5e197]{transition:all .15s ease-in}.flyout-enter-from[data-v-9dd5e197],.flyout-leave-to[data-v-9dd5e197]{opacity:0;transform:translateY(-16px)}.VPLocalNav[data-v-9c649187]{position:sticky;top:0;left:0;z-index:var(--vp-z-index-local-nav);border-bottom:1px solid var(--vp-c-gutter);padding-top:var(--vp-layout-top-height, 0px);width:100%;background-color:var(--vp-local-nav-bg-color)}.VPLocalNav.fixed[data-v-9c649187]{position:fixed}@media (min-width: 960px){.VPLocalNav[data-v-9c649187]{top:var(--vp-nav-height)}.VPLocalNav.has-sidebar[data-v-9c649187]{padding-left:var(--vp-sidebar-width)}.VPLocalNav.empty[data-v-9c649187]{display:none}}@media (min-width: 1280px){.VPLocalNav[data-v-9c649187]{display:none}}@media (min-width: 1440px){.VPLocalNav.has-sidebar[data-v-9c649187]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.container[data-v-9c649187]{display:flex;justify-content:space-between;align-items:center}.menu[data-v-9c649187]{display:flex;align-items:center;padding:12px 24px 11px;line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.menu[data-v-9c649187]:hover{color:var(--vp-c-text-1);transition:color .25s}@media (min-width: 768px){.menu[data-v-9c649187]{padding:0 32px}}@media (min-width: 960px){.menu[data-v-9c649187]{display:none}}.menu-icon[data-v-9c649187]{margin-right:8px;font-size:14px}.VPOutlineDropdown[data-v-9c649187]{padding:12px 24px 11px}@media (min-width: 768px){.VPOutlineDropdown[data-v-9c649187]{padding:12px 32px 11px}}.VPSwitch[data-v-846fe538]{position:relative;border-radius:11px;display:block;width:40px;height:22px;flex-shrink:0;border:1px solid var(--vp-input-border-color);background-color:var(--vp-input-switch-bg-color);transition:border-color .25s!important}.VPSwitch[data-v-846fe538]:hover{border-color:var(--vp-c-brand-1)}.check[data-v-846fe538]{position:absolute;top:1px;left:1px;width:18px;height:18px;border-radius:50%;background-color:var(--vp-c-neutral-inverse);box-shadow:var(--vp-shadow-1);transition:transform .25s!important}.icon[data-v-846fe538]{position:relative;display:block;width:18px;height:18px;border-radius:50%;overflow:hidden}.icon[data-v-846fe538] [class^=vpi-]{position:absolute;top:3px;left:3px;width:12px;height:12px;color:var(--vp-c-text-2)}.dark .icon[data-v-846fe538] [class^=vpi-]{color:var(--vp-c-text-1);transition:opacity .25s!important}.sun[data-v-3125216b]{opacity:1}.moon[data-v-3125216b],.dark .sun[data-v-3125216b]{opacity:0}.dark .moon[data-v-3125216b]{opacity:1}.dark .VPSwitchAppearance[data-v-3125216b] .check{transform:translate(18px)}.VPNavBarAppearance[data-v-864d2abc]{display:none}@media (min-width: 1280px){.VPNavBarAppearance[data-v-864d2abc]{display:flex;align-items:center}}.VPMenuGroup+.VPMenuLink[data-v-25a54821]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.link[data-v-25a54821]{display:block;border-radius:6px;padding:0 12px;line-height:32px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);white-space:nowrap;transition:background-color .25s,color .25s}.link[data-v-25a54821]:hover{color:var(--vp-c-brand-1);background-color:var(--vp-c-default-soft)}.link.active[data-v-25a54821]{color:var(--vp-c-brand-1)}.VPMenuGroup[data-v-4dd03e28]{margin:12px -12px 0;border-top:1px solid var(--vp-c-divider);padding:12px 12px 0}.VPMenuGroup[data-v-4dd03e28]:first-child{margin-top:0;border-top:0;padding-top:0}.VPMenuGroup+.VPMenuGroup[data-v-4dd03e28]{margin-top:12px;border-top:1px solid var(--vp-c-divider)}.title[data-v-4dd03e28]{padding:0 12px;line-height:32px;font-size:14px;font-weight:600;color:var(--vp-c-text-2);white-space:nowrap;transition:color .25s}.VPMenu[data-v-809b8af7]{border-radius:12px;padding:12px;min-width:128px;border:1px solid var(--vp-c-divider);background-color:var(--vp-c-bg-elv);box-shadow:var(--vp-shadow-3);transition:background-color .5s;max-height:calc(100vh - var(--vp-nav-height));overflow-y:auto}.VPMenu[data-v-809b8af7] .group{margin:0 -12px;padding:0 12px 12px}.VPMenu[data-v-809b8af7] .group+.group{border-top:1px solid var(--vp-c-divider);padding:11px 12px 12px}.VPMenu[data-v-809b8af7] .group:last-child{padding-bottom:0}.VPMenu[data-v-809b8af7] .group+.item{border-top:1px solid var(--vp-c-divider);padding:11px 16px 0}.VPMenu[data-v-809b8af7] .item{padding:0 16px;white-space:nowrap}.VPMenu[data-v-809b8af7] .label{flex-grow:1;line-height:28px;font-size:12px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.VPMenu[data-v-809b8af7] .action{padding-left:24px}.VPFlyout[data-v-00660109]{position:relative}.VPFlyout[data-v-00660109]:hover{color:var(--vp-c-brand-1);transition:color .25s}.VPFlyout:hover .text[data-v-00660109]{color:var(--vp-c-text-2)}.VPFlyout:hover .icon[data-v-00660109]{fill:var(--vp-c-text-2)}.VPFlyout.active .text[data-v-00660109]{color:var(--vp-c-brand-1)}.VPFlyout.active:hover .text[data-v-00660109]{color:var(--vp-c-brand-2)}.VPFlyout:hover .menu[data-v-00660109],.button[aria-expanded=true]+.menu[data-v-00660109]{opacity:1;visibility:visible;transform:translateY(0)}.button[aria-expanded=false]+.menu[data-v-00660109]{opacity:0;visibility:hidden;transform:translateY(0)}.button[data-v-00660109]{display:flex;align-items:center;padding:0 12px;height:var(--vp-nav-height);color:var(--vp-c-text-1);transition:color .5s}.text[data-v-00660109]{display:flex;align-items:center;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.option-icon[data-v-00660109]{margin-right:0;font-size:16px}.text-icon[data-v-00660109]{margin-left:4px;font-size:14px}.icon[data-v-00660109]{font-size:20px;transition:fill .25s}.menu[data-v-00660109]{position:absolute;top:calc(var(--vp-nav-height) / 2 + 20px);right:0;opacity:0;visibility:hidden;transition:opacity .25s,visibility .25s,transform .25s}.VPSocialLink[data-v-15a5c40e]{display:flex;justify-content:center;align-items:center;width:36px;height:36px;color:var(--vp-c-text-2);transition:color .5s}.VPSocialLink[data-v-15a5c40e]:hover{color:var(--vp-c-text-1);transition:color .25s}.VPSocialLink[data-v-15a5c40e]>svg,.VPSocialLink[data-v-15a5c40e]>[class^=vpi-social-]{width:20px;height:20px;fill:currentColor}.VPSocialLinks[data-v-100434c4]{display:flex;justify-content:center}.VPNavBarExtra[data-v-60cefd62]{display:none;margin-right:-12px}@media (min-width: 768px){.VPNavBarExtra[data-v-60cefd62]{display:block}}@media (min-width: 1280px){.VPNavBarExtra[data-v-60cefd62]{display:none}}.trans-title[data-v-60cefd62]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.item.appearance[data-v-60cefd62],.item.social-links[data-v-60cefd62]{display:flex;align-items:center;padding:0 12px}.item.appearance[data-v-60cefd62]{min-width:176px}.appearance-action[data-v-60cefd62]{margin-right:-2px}.social-links-list[data-v-60cefd62]{margin:-4px -8px}.VPNavBarHamburger[data-v-e047a1f2]{display:flex;justify-content:center;align-items:center;width:48px;height:var(--vp-nav-height)}@media (min-width: 768px){.VPNavBarHamburger[data-v-e047a1f2]{display:none}}.container[data-v-e047a1f2]{position:relative;width:16px;height:14px;overflow:hidden}.VPNavBarHamburger:hover .top[data-v-e047a1f2]{top:0;left:0;transform:translate(4px)}.VPNavBarHamburger:hover .middle[data-v-e047a1f2]{top:6px;left:0;transform:translate(0)}.VPNavBarHamburger:hover .bottom[data-v-e047a1f2]{top:12px;left:0;transform:translate(8px)}.VPNavBarHamburger.active .top[data-v-e047a1f2]{top:6px;transform:translate(0) rotate(225deg)}.VPNavBarHamburger.active .middle[data-v-e047a1f2]{top:6px;transform:translate(16px)}.VPNavBarHamburger.active .bottom[data-v-e047a1f2]{top:6px;transform:translate(0) rotate(135deg)}.VPNavBarHamburger.active:hover .top[data-v-e047a1f2],.VPNavBarHamburger.active:hover .middle[data-v-e047a1f2],.VPNavBarHamburger.active:hover .bottom[data-v-e047a1f2]{background-color:var(--vp-c-text-2);transition:top .25s,background-color .25s,transform .25s}.top[data-v-e047a1f2],.middle[data-v-e047a1f2],.bottom[data-v-e047a1f2]{position:absolute;width:16px;height:2px;background-color:var(--vp-c-text-1);transition:top .25s,background-color .5s,transform .25s}.top[data-v-e047a1f2]{top:0;left:0;transform:translate(0)}.middle[data-v-e047a1f2]{top:6px;left:0;transform:translate(8px)}.bottom[data-v-e047a1f2]{top:12px;left:0;transform:translate(4px)}.VPNavBarMenuLink[data-v-9a0da802]{display:flex;align-items:center;padding:0 12px;line-height:var(--vp-nav-height);font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.VPNavBarMenuLink.active[data-v-9a0da802],.VPNavBarMenuLink[data-v-9a0da802]:hover{color:var(--vp-c-brand-1)}.VPNavBarMenu[data-v-bf53b681]{display:none}@media (min-width: 768px){.VPNavBarMenu[data-v-bf53b681]{display:flex}}/*! @docsearch/css 3.6.1 | MIT License | © Algolia, Inc. and contributors | https://docsearch.algolia.com */:root{--docsearch-primary-color:#5468ff;--docsearch-text-color:#1c1e21;--docsearch-spacing:12px;--docsearch-icon-stroke-width:1.4;--docsearch-highlight-color:var(--docsearch-primary-color);--docsearch-muted-color:#969faf;--docsearch-container-background:rgba(101,108,133,.8);--docsearch-logo-color:#5468ff;--docsearch-modal-width:560px;--docsearch-modal-height:600px;--docsearch-modal-background:#f5f6f7;--docsearch-modal-shadow:inset 1px 1px 0 0 hsla(0,0%,100%,.5),0 3px 8px 0 #555a64;--docsearch-searchbox-height:56px;--docsearch-searchbox-background:#ebedf0;--docsearch-searchbox-focus-background:#fff;--docsearch-searchbox-shadow:inset 0 0 0 2px var(--docsearch-primary-color);--docsearch-hit-height:56px;--docsearch-hit-color:#444950;--docsearch-hit-active-color:#fff;--docsearch-hit-background:#fff;--docsearch-hit-shadow:0 1px 3px 0 #d4d9e1;--docsearch-key-gradient:linear-gradient(-225deg,#d5dbe4,#f8f8f8);--docsearch-key-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 2px 1px rgba(30,35,90,.4);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #cdcde6,inset 0 0 1px 1px #fff,0 1px 1px 0 rgba(30,35,90,.4);--docsearch-footer-height:44px;--docsearch-footer-background:#fff;--docsearch-footer-shadow:0 -1px 0 0 #e0e3e8,0 -3px 6px 0 rgba(69,98,155,.12)}html[data-theme=dark]{--docsearch-text-color:#f5f6f7;--docsearch-container-background:rgba(9,10,17,.8);--docsearch-modal-background:#15172a;--docsearch-modal-shadow:inset 1px 1px 0 0 #2c2e40,0 3px 8px 0 #000309;--docsearch-searchbox-background:#090a11;--docsearch-searchbox-focus-background:#000;--docsearch-hit-color:#bec3c9;--docsearch-hit-shadow:none;--docsearch-hit-background:#090a11;--docsearch-key-gradient:linear-gradient(-26.5deg,#565872,#31355b);--docsearch-key-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 2px 2px 0 rgba(3,4,9,.3);--docsearch-key-pressed-shadow:inset 0 -2px 0 0 #282d55,inset 0 0 1px 1px #51577d,0 1px 1px 0 rgba(3,4,9,.30196078431372547);--docsearch-footer-background:#1e2136;--docsearch-footer-shadow:inset 0 1px 0 0 rgba(73,76,106,.5),0 -4px 8px 0 rgba(0,0,0,.2);--docsearch-logo-color:#fff;--docsearch-muted-color:#7f8497}.DocSearch-Button{align-items:center;background:var(--docsearch-searchbox-background);border:0;border-radius:40px;color:var(--docsearch-muted-color);cursor:pointer;display:flex;font-weight:500;height:36px;justify-content:space-between;margin:0 0 0 16px;padding:0 8px;-webkit-user-select:none;user-select:none}.DocSearch-Button:active,.DocSearch-Button:focus,.DocSearch-Button:hover{background:var(--docsearch-searchbox-focus-background);box-shadow:var(--docsearch-searchbox-shadow);color:var(--docsearch-text-color);outline:none}.DocSearch-Button-Container{align-items:center;display:flex}.DocSearch-Search-Icon{stroke-width:1.6}.DocSearch-Button .DocSearch-Search-Icon{color:var(--docsearch-text-color)}.DocSearch-Button-Placeholder{font-size:1rem;padding:0 12px 0 6px}.DocSearch-Button-Keys{display:flex;min-width:calc(40px + .8em)}.DocSearch-Button-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:3px;box-shadow:var(--docsearch-key-shadow);color:var(--docsearch-muted-color);display:flex;height:18px;justify-content:center;margin-right:.4em;position:relative;padding:0 0 2px;border:0;top:-1px;width:20px}.DocSearch-Button-Key--pressed{transform:translate3d(0,1px,0);box-shadow:var(--docsearch-key-pressed-shadow)}@media (max-width:768px){.DocSearch-Button-Keys,.DocSearch-Button-Placeholder{display:none}}.DocSearch--active{overflow:hidden!important}.DocSearch-Container,.DocSearch-Container *{box-sizing:border-box}.DocSearch-Container{background-color:var(--docsearch-container-background);height:100vh;left:0;position:fixed;top:0;width:100vw;z-index:200}.DocSearch-Container a{text-decoration:none}.DocSearch-Link{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;font:inherit;margin:0;padding:0}.DocSearch-Modal{background:var(--docsearch-modal-background);border-radius:6px;box-shadow:var(--docsearch-modal-shadow);flex-direction:column;margin:60px auto auto;max-width:var(--docsearch-modal-width);position:relative}.DocSearch-SearchBar{display:flex;padding:var(--docsearch-spacing) var(--docsearch-spacing) 0}.DocSearch-Form{align-items:center;background:var(--docsearch-searchbox-focus-background);border-radius:4px;box-shadow:var(--docsearch-searchbox-shadow);display:flex;height:var(--docsearch-searchbox-height);margin:0;padding:0 var(--docsearch-spacing);position:relative;width:100%}.DocSearch-Input{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:transparent;border:0;color:var(--docsearch-text-color);flex:1;font:inherit;font-size:1.2em;height:100%;outline:none;padding:0 0 0 8px;width:80%}.DocSearch-Input::placeholder{color:var(--docsearch-muted-color);opacity:1}.DocSearch-Input::-webkit-search-cancel-button,.DocSearch-Input::-webkit-search-decoration,.DocSearch-Input::-webkit-search-results-button,.DocSearch-Input::-webkit-search-results-decoration{display:none}.DocSearch-LoadingIndicator,.DocSearch-MagnifierLabel,.DocSearch-Reset{margin:0;padding:0}.DocSearch-MagnifierLabel,.DocSearch-Reset{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}.DocSearch-Container--Stalled .DocSearch-MagnifierLabel,.DocSearch-LoadingIndicator{display:none}.DocSearch-Container--Stalled .DocSearch-LoadingIndicator{align-items:center;color:var(--docsearch-highlight-color);display:flex;justify-content:center}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Reset{animation:none;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;right:0;stroke-width:var(--docsearch-icon-stroke-width)}}.DocSearch-Reset{animation:fade-in .1s ease-in forwards;-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:var(--docsearch-icon-color);cursor:pointer;padding:2px;right:0;stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Reset[hidden]{display:none}.DocSearch-Reset:hover{color:var(--docsearch-highlight-color)}.DocSearch-LoadingIndicator svg,.DocSearch-MagnifierLabel svg{height:24px;width:24px}.DocSearch-Cancel{display:none}.DocSearch-Dropdown{max-height:calc(var(--docsearch-modal-height) - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height));min-height:var(--docsearch-spacing);overflow-y:auto;overflow-y:overlay;padding:0 var(--docsearch-spacing);scrollbar-color:var(--docsearch-muted-color) var(--docsearch-modal-background);scrollbar-width:thin}.DocSearch-Dropdown::-webkit-scrollbar{width:12px}.DocSearch-Dropdown::-webkit-scrollbar-track{background:transparent}.DocSearch-Dropdown::-webkit-scrollbar-thumb{background-color:var(--docsearch-muted-color);border:3px solid var(--docsearch-modal-background);border-radius:20px}.DocSearch-Dropdown ul{list-style:none;margin:0;padding:0}.DocSearch-Label{font-size:.75em;line-height:1.6em}.DocSearch-Help,.DocSearch-Label{color:var(--docsearch-muted-color)}.DocSearch-Help{font-size:.9em;margin:0;-webkit-user-select:none;user-select:none}.DocSearch-Title{font-size:1.2em}.DocSearch-Logo a{display:flex}.DocSearch-Logo svg{color:var(--docsearch-logo-color);margin-left:8px}.DocSearch-Hits:last-of-type{margin-bottom:24px}.DocSearch-Hits mark{background:none;color:var(--docsearch-highlight-color)}.DocSearch-HitsFooter{color:var(--docsearch-muted-color);display:flex;font-size:.85em;justify-content:center;margin-bottom:var(--docsearch-spacing);padding:var(--docsearch-spacing)}.DocSearch-HitsFooter a{border-bottom:1px solid;color:inherit}.DocSearch-Hit{border-radius:4px;display:flex;padding-bottom:4px;position:relative}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--deleting{transition:none}}.DocSearch-Hit--deleting{opacity:0;transition:all .25s linear}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit--favoriting{transition:none}}.DocSearch-Hit--favoriting{transform:scale(0);transform-origin:top center;transition:all .25s linear;transition-delay:.25s}.DocSearch-Hit a{background:var(--docsearch-hit-background);border-radius:4px;box-shadow:var(--docsearch-hit-shadow);display:block;padding-left:var(--docsearch-spacing);width:100%}.DocSearch-Hit-source{background:var(--docsearch-modal-background);color:var(--docsearch-highlight-color);font-size:.85em;font-weight:600;line-height:32px;margin:0 -4px;padding:8px 4px 0;position:sticky;top:0;z-index:10}.DocSearch-Hit-Tree{color:var(--docsearch-muted-color);height:var(--docsearch-hit-height);opacity:.5;stroke-width:var(--docsearch-icon-stroke-width);width:24px}.DocSearch-Hit[aria-selected=true] a{background-color:var(--docsearch-highlight-color)}.DocSearch-Hit[aria-selected=true] mark{text-decoration:underline}.DocSearch-Hit-Container{align-items:center;color:var(--docsearch-hit-color);display:flex;flex-direction:row;height:var(--docsearch-hit-height);padding:0 var(--docsearch-spacing) 0 0}.DocSearch-Hit-icon{height:20px;width:20px}.DocSearch-Hit-action,.DocSearch-Hit-icon{color:var(--docsearch-muted-color);stroke-width:var(--docsearch-icon-stroke-width)}.DocSearch-Hit-action{align-items:center;display:flex;height:22px;width:22px}.DocSearch-Hit-action svg{display:block;height:18px;width:18px}.DocSearch-Hit-action+.DocSearch-Hit-action{margin-left:6px}.DocSearch-Hit-action-button{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:50%;color:inherit;cursor:pointer;padding:2px}svg.DocSearch-Hit-Select-Icon{display:none}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Select-Icon{display:block}.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:background-color .1s ease-in}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{transition:none}}.DocSearch-Hit-action-button:focus path,.DocSearch-Hit-action-button:hover path{fill:#fff}.DocSearch-Hit-content-wrapper{display:flex;flex:1 1 auto;flex-direction:column;font-weight:500;justify-content:center;line-height:1.2em;margin:0 8px;overflow-x:hidden;position:relative;text-overflow:ellipsis;white-space:nowrap;width:80%}.DocSearch-Hit-title{font-size:.9em}.DocSearch-Hit-path{color:var(--docsearch-muted-color);font-size:.75em}.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-action,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-icon,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-path,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-text,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-title,.DocSearch-Hit[aria-selected=true] .DocSearch-Hit-Tree,.DocSearch-Hit[aria-selected=true] mark{color:var(--docsearch-hit-active-color)!important}@media screen and (prefers-reduced-motion:reduce){.DocSearch-Hit-action-button:focus,.DocSearch-Hit-action-button:hover{background:#0003;transition:none}}.DocSearch-ErrorScreen,.DocSearch-NoResults,.DocSearch-StartScreen{font-size:.9em;margin:0 auto;padding:36px 0;text-align:center;width:80%}.DocSearch-Screen-Icon{color:var(--docsearch-muted-color);padding-bottom:12px}.DocSearch-NoResults-Prefill-List{display:inline-block;padding-bottom:24px;text-align:left}.DocSearch-NoResults-Prefill-List ul{display:inline-block;padding:8px 0 0}.DocSearch-NoResults-Prefill-List li{list-style-position:inside;list-style-type:"» "}.DocSearch-Prefill{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;border-radius:1em;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;font-size:1em;font-weight:700;padding:0}.DocSearch-Prefill:focus,.DocSearch-Prefill:hover{outline:none;text-decoration:underline}.DocSearch-Footer{align-items:center;background:var(--docsearch-footer-background);border-radius:0 0 8px 8px;box-shadow:var(--docsearch-footer-shadow);display:flex;flex-direction:row-reverse;flex-shrink:0;height:var(--docsearch-footer-height);justify-content:space-between;padding:0 var(--docsearch-spacing);position:relative;-webkit-user-select:none;user-select:none;width:100%;z-index:300}.DocSearch-Commands{color:var(--docsearch-muted-color);display:flex;list-style:none;margin:0;padding:0}.DocSearch-Commands li{align-items:center;display:flex}.DocSearch-Commands li:not(:last-of-type){margin-right:.8em}.DocSearch-Commands-Key{align-items:center;background:var(--docsearch-key-gradient);border-radius:2px;box-shadow:var(--docsearch-key-shadow);display:flex;height:18px;justify-content:center;margin-right:.4em;padding:0 0 1px;color:var(--docsearch-muted-color);border:0;width:20px}.DocSearch-VisuallyHiddenForAccessibility{clip:rect(0 0 0 0);clip-path:inset(50%);height:1px;overflow:hidden;position:absolute;white-space:nowrap;width:1px}@media (max-width:768px){:root{--docsearch-spacing:10px;--docsearch-footer-height:40px}.DocSearch-Dropdown{height:100%}.DocSearch-Container{height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);position:absolute}.DocSearch-Footer{border-radius:0;bottom:0;position:absolute}.DocSearch-Hit-content-wrapper{display:flex;position:relative;width:80%}.DocSearch-Modal{border-radius:0;box-shadow:none;height:100vh;height:-webkit-fill-available;height:calc(var(--docsearch-vh, 1vh)*100);margin:0;max-width:100%;width:100%}.DocSearch-Dropdown{max-height:calc(var(--docsearch-vh, 1vh)*100 - var(--docsearch-searchbox-height) - var(--docsearch-spacing) - var(--docsearch-footer-height))}.DocSearch-Cancel{-webkit-appearance:none;-moz-appearance:none;appearance:none;background:none;border:0;color:var(--docsearch-highlight-color);cursor:pointer;display:inline-block;flex:none;font:inherit;font-size:1em;font-weight:500;margin-left:var(--docsearch-spacing);outline:none;overflow:hidden;padding:0;-webkit-user-select:none;user-select:none;white-space:nowrap}.DocSearch-Commands,.DocSearch-Hit-Tree{display:none}}@keyframes fade-in{0%{opacity:0}to{opacity:1}}[class*=DocSearch]{--docsearch-primary-color: var(--vp-c-brand-1);--docsearch-highlight-color: var(--docsearch-primary-color);--docsearch-text-color: var(--vp-c-text-1);--docsearch-muted-color: var(--vp-c-text-2);--docsearch-searchbox-shadow: none;--docsearch-searchbox-background: transparent;--docsearch-searchbox-focus-background: transparent;--docsearch-key-gradient: transparent;--docsearch-key-shadow: none;--docsearch-modal-background: var(--vp-c-bg-soft);--docsearch-footer-background: var(--vp-c-bg)}.dark [class*=DocSearch]{--docsearch-modal-shadow: none;--docsearch-footer-shadow: none;--docsearch-logo-color: var(--vp-c-text-2);--docsearch-hit-background: var(--vp-c-default-soft);--docsearch-hit-color: var(--vp-c-text-2);--docsearch-hit-shadow: none}.DocSearch-Button{display:flex;justify-content:center;align-items:center;margin:0;padding:0;width:48px;height:55px;background:transparent;transition:border-color .25s}.DocSearch-Button:hover{background:transparent}.DocSearch-Button:focus{outline:1px dotted;outline:5px auto -webkit-focus-ring-color}.DocSearch-Button-Key--pressed{transform:none;box-shadow:none}.DocSearch-Button:focus:not(:focus-visible){outline:none!important}@media (min-width: 768px){.DocSearch-Button{justify-content:flex-start;border:1px solid transparent;border-radius:8px;padding:0 10px 0 12px;width:100%;height:40px;background-color:var(--vp-c-bg-alt)}.DocSearch-Button:hover{border-color:var(--vp-c-brand-1);background:var(--vp-c-bg-alt)}}.DocSearch-Button .DocSearch-Button-Container{display:flex;align-items:center}.DocSearch-Button .DocSearch-Search-Icon{position:relative;width:16px;height:16px;color:var(--vp-c-text-1);fill:currentColor;transition:color .5s}.DocSearch-Button:hover .DocSearch-Search-Icon{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Search-Icon{top:1px;margin-right:8px;width:14px;height:14px;color:var(--vp-c-text-2)}}.DocSearch-Button .DocSearch-Button-Placeholder{display:none;margin-top:2px;padding:0 16px 0 0;font-size:13px;font-weight:500;color:var(--vp-c-text-2);transition:color .5s}.DocSearch-Button:hover .DocSearch-Button-Placeholder{color:var(--vp-c-text-1)}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Placeholder{display:inline-block}}.DocSearch-Button .DocSearch-Button-Keys{direction:ltr;display:none;min-width:auto}@media (min-width: 768px){.DocSearch-Button .DocSearch-Button-Keys{display:flex;align-items:center}}.DocSearch-Button .DocSearch-Button-Key{display:block;margin:2px 0 0;border:1px solid var(--vp-c-divider);border-right:none;border-radius:4px 0 0 4px;padding-left:6px;min-width:0;width:auto;height:22px;line-height:22px;font-family:var(--vp-font-family-base);font-size:12px;font-weight:500;transition:color .5s,border-color .5s}.DocSearch-Button .DocSearch-Button-Key+.DocSearch-Button-Key{border-right:1px solid var(--vp-c-divider);border-left:none;border-radius:0 4px 4px 0;padding-left:2px;padding-right:6px}.DocSearch-Button .DocSearch-Button-Key:first-child{font-size:0!important}.DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"Ctrl";font-size:12px;letter-spacing:normal;color:var(--docsearch-muted-color)}.mac .DocSearch-Button .DocSearch-Button-Key:first-child:after{content:"⌘"}.DocSearch-Button .DocSearch-Button-Key:first-child>*{display:none}.DocSearch-Search-Icon{--icon: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' stroke-width='1.6' viewBox='0 0 20 20'%3E%3Cpath fill='none' stroke='currentColor' stroke-linecap='round' stroke-linejoin='round' d='m14.386 14.386 4.088 4.088-4.088-4.088A7.533 7.533 0 1 1 3.733 3.733a7.533 7.533 0 0 1 10.653 10.653z'/%3E%3C/svg%3E")}.VPNavBarSearch{display:flex;align-items:center}@media (min-width: 768px){.VPNavBarSearch{flex-grow:1;padding-left:24px}}@media (min-width: 960px){.VPNavBarSearch{padding-left:32px}}.dark .DocSearch-Footer{border-top:1px solid var(--vp-c-divider)}.DocSearch-Form{border:1px solid var(--vp-c-brand-1);background-color:var(--vp-c-white)}.dark .DocSearch-Form{background-color:var(--vp-c-default-soft)}.DocSearch-Screen-Icon>svg{margin:auto}.VPNavBarSocialLinks[data-v-2c606308]{display:none}@media (min-width: 1280px){.VPNavBarSocialLinks[data-v-2c606308]{display:flex;align-items:center}}.title[data-v-606a7e0f]{display:flex;align-items:center;border-bottom:1px solid transparent;width:100%;height:var(--vp-nav-height);font-size:16px;font-weight:600;color:var(--vp-c-text-1);transition:opacity .25s}@media (min-width: 960px){.title[data-v-606a7e0f]{flex-shrink:0}.VPNavBarTitle.has-sidebar .title[data-v-606a7e0f]{border-bottom-color:var(--vp-c-divider)}}[data-v-606a7e0f] .logo{margin-right:8px;height:var(--vp-nav-logo-height)}.VPNavBarTranslations[data-v-912817b1]{display:none}@media (min-width: 1280px){.VPNavBarTranslations[data-v-912817b1]{display:flex;align-items:center}}.title[data-v-912817b1]{padding:0 24px 0 12px;line-height:32px;font-size:14px;font-weight:700;color:var(--vp-c-text-1)}.VPNavBar[data-v-da0688be]{position:relative;height:var(--vp-nav-height);pointer-events:none;white-space:nowrap;transition:background-color .25s}.VPNavBar.screen-open[data-v-da0688be]{transition:none;background-color:var(--vp-nav-bg-color);border-bottom:1px solid var(--vp-c-divider)}.VPNavBar[data-v-da0688be]:not(.home){background-color:var(--vp-nav-bg-color)}@media (min-width: 960px){.VPNavBar[data-v-da0688be]:not(.home){background-color:transparent}.VPNavBar[data-v-da0688be]:not(.has-sidebar):not(.home.top){background-color:var(--vp-nav-bg-color)}}.wrapper[data-v-da0688be]{padding:0 8px 0 24px}@media (min-width: 768px){.wrapper[data-v-da0688be]{padding:0 32px}}@media (min-width: 960px){.VPNavBar.has-sidebar .wrapper[data-v-da0688be]{padding:0}}.container[data-v-da0688be]{display:flex;justify-content:space-between;margin:0 auto;max-width:calc(var(--vp-layout-max-width) - 64px);height:var(--vp-nav-height);pointer-events:none}.container>.title[data-v-da0688be],.container>.content[data-v-da0688be]{pointer-events:none}.container[data-v-da0688be] *{pointer-events:auto}@media (min-width: 960px){.VPNavBar.has-sidebar .container[data-v-da0688be]{max-width:100%}}.title[data-v-da0688be]{flex-shrink:0;height:calc(var(--vp-nav-height) - 1px);transition:background-color .5s}@media (min-width: 960px){.VPNavBar.has-sidebar .title[data-v-da0688be]{position:absolute;top:0;left:0;z-index:2;padding:0 32px;width:var(--vp-sidebar-width);height:var(--vp-nav-height);background-color:transparent}}@media (min-width: 1440px){.VPNavBar.has-sidebar .title[data-v-da0688be]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}.content[data-v-da0688be]{flex-grow:1}@media (min-width: 960px){.VPNavBar.has-sidebar .content[data-v-da0688be]{position:relative;z-index:1;padding-right:32px;padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .content[data-v-da0688be]{padding-right:calc((100vw - var(--vp-layout-max-width)) / 2 + 32px);padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.content-body[data-v-da0688be]{display:flex;justify-content:flex-end;align-items:center;height:var(--vp-nav-height);transition:background-color .5s}@media (min-width: 960px){.VPNavBar:not(.home.top) .content-body[data-v-da0688be]{position:relative;background-color:var(--vp-nav-bg-color)}.VPNavBar:not(.has-sidebar):not(.home.top) .content-body[data-v-da0688be]{background-color:transparent}}@media (max-width: 767px){.content-body[data-v-da0688be]{column-gap:.5rem}}.menu+.translations[data-v-da0688be]:before,.menu+.appearance[data-v-da0688be]:before,.menu+.social-links[data-v-da0688be]:before,.translations+.appearance[data-v-da0688be]:before,.appearance+.social-links[data-v-da0688be]:before{margin-right:8px;margin-left:8px;width:1px;height:24px;background-color:var(--vp-c-divider);content:""}.menu+.appearance[data-v-da0688be]:before,.translations+.appearance[data-v-da0688be]:before{margin-right:16px}.appearance+.social-links[data-v-da0688be]:before{margin-left:16px}.social-links[data-v-da0688be]{margin-right:-8px}.divider[data-v-da0688be]{width:100%;height:1px}@media (min-width: 960px){.VPNavBar.has-sidebar .divider[data-v-da0688be]{padding-left:var(--vp-sidebar-width)}}@media (min-width: 1440px){.VPNavBar.has-sidebar .divider[data-v-da0688be]{padding-left:calc((100vw - var(--vp-layout-max-width)) / 2 + var(--vp-sidebar-width))}}.divider-line[data-v-da0688be]{width:100%;height:1px;transition:background-color .5s}.VPNavBar:not(.home) .divider-line[data-v-da0688be]{background-color:var(--vp-c-gutter)}@media (min-width: 960px){.VPNavBar:not(.home.top) .divider-line[data-v-da0688be]{background-color:var(--vp-c-gutter)}.VPNavBar:not(.has-sidebar):not(.home.top) .divider[data-v-da0688be]{background-color:var(--vp-c-gutter)}}.VPNavScreenAppearance[data-v-dfcc1536]{display:flex;justify-content:space-between;align-items:center;border-radius:8px;padding:12px 14px 12px 16px;background-color:var(--vp-c-bg-soft)}.text[data-v-dfcc1536]{line-height:24px;font-size:12px;font-weight:500;color:var(--vp-c-text-2)}.VPNavScreenMenuLink[data-v-8cd41455]{display:block;border-bottom:1px solid var(--vp-c-divider);padding:12px 0 11px;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:border-color .25s,color .25s}.VPNavScreenMenuLink[data-v-8cd41455]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupLink[data-v-b8c7c580]{display:block;margin-left:12px;line-height:32px;font-size:14px;font-weight:400;color:var(--vp-c-text-1);transition:color .25s}.VPNavScreenMenuGroupLink[data-v-b8c7c580]:hover{color:var(--vp-c-brand-1)}.VPNavScreenMenuGroupSection[data-v-a3e7a51c]{display:block}.title[data-v-a3e7a51c]{line-height:32px;font-size:13px;font-weight:700;color:var(--vp-c-text-2);transition:color .25s}.VPNavScreenMenuGroup[data-v-90f695a2]{border-bottom:1px solid var(--vp-c-divider);height:48px;overflow:hidden;transition:border-color .5s}.VPNavScreenMenuGroup .items[data-v-90f695a2]{visibility:hidden}.VPNavScreenMenuGroup.open .items[data-v-90f695a2]{visibility:visible}.VPNavScreenMenuGroup.open[data-v-90f695a2]{padding-bottom:10px;height:auto}.VPNavScreenMenuGroup.open .button[data-v-90f695a2]{padding-bottom:6px;color:var(--vp-c-brand-1)}.VPNavScreenMenuGroup.open .button-icon[data-v-90f695a2]{transform:rotate(45deg)}.button[data-v-90f695a2]{display:flex;justify-content:space-between;align-items:center;padding:12px 4px 11px 0;width:100%;line-height:24px;font-size:14px;font-weight:500;color:var(--vp-c-text-1);transition:color .25s}.button[data-v-90f695a2]:hover{color:var(--vp-c-brand-1)}.button-icon[data-v-90f695a2]{transition:transform .25s}.group[data-v-90f695a2]:first-child{padding-top:0}.group+.group[data-v-90f695a2],.group+.item[data-v-90f695a2]{padding-top:4px}.VPNavScreenTranslations[data-v-95c61444]{height:24px;overflow:hidden}.VPNavScreenTranslations.open[data-v-95c61444]{height:auto}.title[data-v-95c61444]{display:flex;align-items:center;font-size:14px;font-weight:500;color:var(--vp-c-text-1)}.icon[data-v-95c61444]{font-size:16px}.icon.lang[data-v-95c61444]{margin-right:8px}.icon.chevron[data-v-95c61444]{margin-left:4px}.list[data-v-95c61444]{padding:4px 0 0 24px}.link[data-v-95c61444]{line-height:32px;font-size:13px;color:var(--vp-c-text-1)}.VPNavScreen[data-v-c14c1e21]{position:fixed;top:calc(var(--vp-nav-height) + var(--vp-layout-top-height, 0px));right:0;bottom:0;left:0;padding:0 32px;width:100%;background-color:var(--vp-nav-screen-bg-color);overflow-y:auto;transition:background-color .25s;pointer-events:auto}.VPNavScreen.fade-enter-active[data-v-c14c1e21],.VPNavScreen.fade-leave-active[data-v-c14c1e21]{transition:opacity .25s}.VPNavScreen.fade-enter-active .container[data-v-c14c1e21],.VPNavScreen.fade-leave-active .container[data-v-c14c1e21]{transition:transform .25s ease}.VPNavScreen.fade-enter-from[data-v-c14c1e21],.VPNavScreen.fade-leave-to[data-v-c14c1e21]{opacity:0}.VPNavScreen.fade-enter-from .container[data-v-c14c1e21],.VPNavScreen.fade-leave-to .container[data-v-c14c1e21]{transform:translateY(-8px)}@media (min-width: 768px){.VPNavScreen[data-v-c14c1e21]{display:none}}.container[data-v-c14c1e21]{margin:0 auto;padding:24px 0 96px;max-width:288px}.menu+.translations[data-v-c14c1e21],.menu+.appearance[data-v-c14c1e21],.translations+.appearance[data-v-c14c1e21]{margin-top:24px}.menu+.social-links[data-v-c14c1e21]{margin-top:16px}.appearance+.social-links[data-v-c14c1e21]{margin-top:16px}.VPNav[data-v-e823d444]{position:relative;top:var(--vp-layout-top-height, 0px);left:0;z-index:var(--vp-z-index-nav);width:100%;pointer-events:none;transition:background-color .5s}@media (min-width: 960px){.VPNav[data-v-e823d444]{position:fixed}}.VPSidebarItem.level-0[data-v-a9cdba99]{padding-bottom:24px}.VPSidebarItem.collapsed.level-0[data-v-a9cdba99]{padding-bottom:10px}.item[data-v-a9cdba99]{position:relative;display:flex;width:100%}.VPSidebarItem.collapsible>.item[data-v-a9cdba99]{cursor:pointer}.indicator[data-v-a9cdba99]{position:absolute;top:6px;bottom:6px;left:-17px;width:2px;border-radius:2px;transition:background-color .25s}.VPSidebarItem.level-2.is-active>.item>.indicator[data-v-a9cdba99],.VPSidebarItem.level-3.is-active>.item>.indicator[data-v-a9cdba99],.VPSidebarItem.level-4.is-active>.item>.indicator[data-v-a9cdba99],.VPSidebarItem.level-5.is-active>.item>.indicator[data-v-a9cdba99]{background-color:var(--vp-c-brand-1)}.link[data-v-a9cdba99]{display:flex;align-items:center;flex-grow:1}.text[data-v-a9cdba99]{flex-grow:1;padding:4px 0;line-height:24px;font-size:14px;transition:color .25s}.VPSidebarItem.level-0 .text[data-v-a9cdba99]{font-weight:700;color:var(--vp-c-text-1)}.VPSidebarItem.level-1 .text[data-v-a9cdba99],.VPSidebarItem.level-2 .text[data-v-a9cdba99],.VPSidebarItem.level-3 .text[data-v-a9cdba99],.VPSidebarItem.level-4 .text[data-v-a9cdba99],.VPSidebarItem.level-5 .text[data-v-a9cdba99]{font-weight:500;color:var(--vp-c-text-2)}.VPSidebarItem.level-0.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-1.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-2.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-3.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-4.is-link>.item>.link:hover .text[data-v-a9cdba99],.VPSidebarItem.level-5.is-link>.item>.link:hover .text[data-v-a9cdba99]{color:var(--vp-c-brand-1)}.VPSidebarItem.level-0.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-1.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-2.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-3.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-4.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-5.has-active>.item>.text[data-v-a9cdba99],.VPSidebarItem.level-0.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-1.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-2.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-3.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-4.has-active>.item>.link>.text[data-v-a9cdba99],.VPSidebarItem.level-5.has-active>.item>.link>.text[data-v-a9cdba99]{color:var(--vp-c-text-1)}.VPSidebarItem.level-0.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-1.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-2.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-3.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-4.is-active>.item .link>.text[data-v-a9cdba99],.VPSidebarItem.level-5.is-active>.item .link>.text[data-v-a9cdba99]{color:var(--vp-c-brand-1)}.caret[data-v-a9cdba99]{display:flex;justify-content:center;align-items:center;margin-right:-7px;width:32px;height:32px;color:var(--vp-c-text-3);cursor:pointer;transition:color .25s;flex-shrink:0}.item:hover .caret[data-v-a9cdba99]{color:var(--vp-c-text-2)}.item:hover .caret[data-v-a9cdba99]:hover{color:var(--vp-c-text-1)}.caret-icon[data-v-a9cdba99]{font-size:18px;transform:rotate(90deg);transition:transform .25s}.VPSidebarItem.collapsed .caret-icon[data-v-a9cdba99]{transform:rotate(0)}.VPSidebarItem.level-1 .items[data-v-a9cdba99],.VPSidebarItem.level-2 .items[data-v-a9cdba99],.VPSidebarItem.level-3 .items[data-v-a9cdba99],.VPSidebarItem.level-4 .items[data-v-a9cdba99],.VPSidebarItem.level-5 .items[data-v-a9cdba99]{border-left:1px solid var(--vp-c-divider);padding-left:16px}.VPSidebarItem.collapsed .items[data-v-a9cdba99]{display:none}.no-transition[data-v-72c67ed4] .caret-icon{transition:none}.group+.group[data-v-72c67ed4]{border-top:1px solid var(--vp-c-divider);padding-top:10px}@media (min-width: 960px){.group[data-v-72c67ed4]{padding-top:10px;width:calc(var(--vp-sidebar-width) - 64px)}}.VPSidebar[data-v-59ceefa4]{position:fixed;top:var(--vp-layout-top-height, 0px);bottom:0;left:0;z-index:var(--vp-z-index-sidebar);padding:32px 32px 96px;width:calc(100vw - 64px);max-width:320px;background-color:var(--vp-sidebar-bg-color);opacity:0;box-shadow:var(--vp-c-shadow-3);overflow-x:hidden;overflow-y:auto;transform:translate(-100%);transition:opacity .5s,transform .25s ease;overscroll-behavior:contain}.VPSidebar.open[data-v-59ceefa4]{opacity:1;visibility:visible;transform:translate(0);transition:opacity .25s,transform .5s cubic-bezier(.19,1,.22,1)}.dark .VPSidebar[data-v-59ceefa4]{box-shadow:var(--vp-shadow-1)}@media (min-width: 960px){.VPSidebar[data-v-59ceefa4]{padding-top:var(--vp-nav-height);width:var(--vp-sidebar-width);max-width:100%;background-color:var(--vp-sidebar-bg-color);opacity:1;visibility:visible;box-shadow:none;transform:translate(0)}}@media (min-width: 1440px){.VPSidebar[data-v-59ceefa4]{padding-left:max(32px,calc((100% - (var(--vp-layout-max-width) - 64px)) / 2));width:calc((100% - (var(--vp-layout-max-width) - 64px)) / 2 + var(--vp-sidebar-width) - 32px)}}@media (min-width: 960px){.curtain[data-v-59ceefa4]{position:sticky;top:-64px;left:0;z-index:1;margin-top:calc(var(--vp-nav-height) * -1);margin-right:-32px;margin-left:-32px;height:var(--vp-nav-height);background-color:var(--vp-sidebar-bg-color)}}.nav[data-v-59ceefa4]{outline:0}.VPSkipLink[data-v-e813112c]{top:8px;left:8px;padding:8px 16px;z-index:999;border-radius:8px;font-size:12px;font-weight:700;text-decoration:none;color:var(--vp-c-brand-1);box-shadow:var(--vp-shadow-3);background-color:var(--vp-c-bg)}.VPSkipLink[data-v-e813112c]:focus{height:auto;width:auto;clip:auto;clip-path:none}@media (min-width: 1280px){.VPSkipLink[data-v-e813112c]{top:14px;left:16px}}.Layout[data-v-3b4648ff]{display:flex;flex-direction:column;min-height:100vh}.VPHomeSponsors[data-v-e06ca32a]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPHomeSponsors[data-v-e06ca32a]{margin:96px 0}@media (min-width: 768px){.VPHomeSponsors[data-v-e06ca32a]{margin:128px 0}}.VPHomeSponsors[data-v-e06ca32a]{padding:0 24px}@media (min-width: 768px){.VPHomeSponsors[data-v-e06ca32a]{padding:0 48px}}@media (min-width: 960px){.VPHomeSponsors[data-v-e06ca32a]{padding:0 64px}}.container[data-v-e06ca32a]{margin:0 auto;max-width:1152px}.love[data-v-e06ca32a]{margin:0 auto;width:fit-content;font-size:28px;color:var(--vp-c-text-3)}.icon[data-v-e06ca32a]{display:inline-block}.message[data-v-e06ca32a]{margin:0 auto;padding-top:10px;max-width:320px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.sponsors[data-v-e06ca32a]{padding-top:32px}.action[data-v-e06ca32a]{padding-top:40px;text-align:center}.VPTeamPage[data-v-b1db0dbf]{margin:96px 0}@media (min-width: 768px){.VPTeamPage[data-v-b1db0dbf]{margin:128px 0}}.VPHome .VPTeamPageTitle[data-v-b1db0dbf-s]{border-top:1px solid var(--vp-c-gutter);padding-top:88px!important}.VPTeamPageSection+.VPTeamPageSection[data-v-b1db0dbf-s],.VPTeamMembers+.VPTeamPageSection[data-v-b1db0dbf-s]{margin-top:64px}.VPTeamMembers+.VPTeamMembers[data-v-b1db0dbf-s]{margin-top:24px}@media (min-width: 768px){.VPTeamPageTitle+.VPTeamPageSection[data-v-b1db0dbf-s]{margin-top:16px}.VPTeamPageSection+.VPTeamPageSection[data-v-b1db0dbf-s],.VPTeamMembers+.VPTeamPageSection[data-v-b1db0dbf-s]{margin-top:96px}}.VPTeamMembers[data-v-b1db0dbf-s]{padding:0 24px}@media (min-width: 768px){.VPTeamMembers[data-v-b1db0dbf-s]{padding:0 48px}}@media (min-width: 960px){.VPTeamMembers[data-v-b1db0dbf-s]{padding:0 64px}}.VPTeamPageTitle[data-v-67e2507a]{padding:48px 32px;text-align:center}@media (min-width: 768px){.VPTeamPageTitle[data-v-67e2507a]{padding:64px 48px 48px}}@media (min-width: 960px){.VPTeamPageTitle[data-v-67e2507a]{padding:80px 64px 48px}}.title[data-v-67e2507a]{letter-spacing:0;line-height:44px;font-size:36px;font-weight:500}@media (min-width: 768px){.title[data-v-67e2507a]{letter-spacing:-.5px;line-height:56px;font-size:48px}}.lead[data-v-67e2507a]{margin:0 auto;max-width:512px;padding-top:12px;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}@media (min-width: 768px){.lead[data-v-67e2507a]{max-width:592px;letter-spacing:.15px;line-height:28px;font-size:20px}}.VPTeamPageSection[data-v-848babf0]{padding:0 32px}@media (min-width: 768px){.VPTeamPageSection[data-v-848babf0]{padding:0 48px}}@media (min-width: 960px){.VPTeamPageSection[data-v-848babf0]{padding:0 64px}}.title[data-v-848babf0]{position:relative;margin:0 auto;max-width:1152px;text-align:center;color:var(--vp-c-text-2)}.title-line[data-v-848babf0]{position:absolute;top:16px;left:0;width:100%;height:1px;background-color:var(--vp-c-divider)}.title-text[data-v-848babf0]{position:relative;display:inline-block;padding:0 24px;letter-spacing:0;line-height:32px;font-size:20px;font-weight:500;background-color:var(--vp-c-bg)}.lead[data-v-848babf0]{margin:0 auto;max-width:480px;padding-top:12px;text-align:center;line-height:24px;font-size:16px;font-weight:500;color:var(--vp-c-text-2)}.members[data-v-848babf0]{padding-top:40px}.VPTeamMembersItem[data-v-990ef11d]{display:flex;flex-direction:column;gap:2px;border-radius:12px;width:100%;height:100%;overflow:hidden}.VPTeamMembersItem.small .profile[data-v-990ef11d]{padding:32px}.VPTeamMembersItem.small .data[data-v-990ef11d]{padding-top:20px}.VPTeamMembersItem.small .avatar[data-v-990ef11d]{width:64px;height:64px}.VPTeamMembersItem.small .name[data-v-990ef11d]{line-height:24px;font-size:16px}.VPTeamMembersItem.small .affiliation[data-v-990ef11d]{padding-top:4px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .desc[data-v-990ef11d]{padding-top:12px;line-height:20px;font-size:14px}.VPTeamMembersItem.small .links[data-v-990ef11d]{margin:0 -16px -20px;padding:10px 0 0}.VPTeamMembersItem.medium .profile[data-v-990ef11d]{padding:48px 32px}.VPTeamMembersItem.medium .data[data-v-990ef11d]{padding-top:24px;text-align:center}.VPTeamMembersItem.medium .avatar[data-v-990ef11d]{width:96px;height:96px}.VPTeamMembersItem.medium .name[data-v-990ef11d]{letter-spacing:.15px;line-height:28px;font-size:20px}.VPTeamMembersItem.medium .affiliation[data-v-990ef11d]{padding-top:4px;font-size:16px}.VPTeamMembersItem.medium .desc[data-v-990ef11d]{padding-top:16px;max-width:288px;font-size:16px}.VPTeamMembersItem.medium .links[data-v-990ef11d]{margin:0 -16px -12px;padding:16px 12px 0}.profile[data-v-990ef11d]{flex-grow:1;background-color:var(--vp-c-bg-soft)}.data[data-v-990ef11d]{text-align:center}.avatar[data-v-990ef11d]{position:relative;flex-shrink:0;margin:0 auto;border-radius:50%;box-shadow:var(--vp-shadow-3)}.avatar-img[data-v-990ef11d]{position:absolute;top:0;right:0;bottom:0;left:0;border-radius:50%;object-fit:cover}.name[data-v-990ef11d]{margin:0;font-weight:600}.affiliation[data-v-990ef11d]{margin:0;font-weight:500;color:var(--vp-c-text-2)}.org.link[data-v-990ef11d]{color:var(--vp-c-text-2);transition:color .25s}.org.link[data-v-990ef11d]:hover{color:var(--vp-c-brand-1)}.desc[data-v-990ef11d]{margin:0 auto}.desc[data-v-990ef11d] a{font-weight:500;color:var(--vp-c-brand-1);text-decoration-style:dotted;transition:color .25s}.links[data-v-990ef11d]{display:flex;justify-content:center;height:56px}.sp-link[data-v-990ef11d]{display:flex;justify-content:center;align-items:center;text-align:center;padding:16px;font-size:14px;font-weight:500;color:var(--vp-c-sponsor);background-color:var(--vp-c-bg-soft);transition:color .25s,background-color .25s}.sp .sp-link.link[data-v-990ef11d]:hover,.sp .sp-link.link[data-v-990ef11d]:focus{outline:none;color:var(--vp-c-white);background-color:var(--vp-c-sponsor)}.sp-icon[data-v-990ef11d]{margin-right:8px;font-size:16px}.VPTeamMembers.small .container[data-v-387893a3]{grid-template-columns:repeat(auto-fit,minmax(224px,1fr))}.VPTeamMembers.small.count-1 .container[data-v-387893a3]{max-width:276px}.VPTeamMembers.small.count-2 .container[data-v-387893a3]{max-width:576px}.VPTeamMembers.small.count-3 .container[data-v-387893a3]{max-width:876px}.VPTeamMembers.medium .container[data-v-387893a3]{grid-template-columns:repeat(auto-fit,minmax(256px,1fr))}@media (min-width: 375px){.VPTeamMembers.medium .container[data-v-387893a3]{grid-template-columns:repeat(auto-fit,minmax(288px,1fr))}}.VPTeamMembers.medium.count-1 .container[data-v-387893a3]{max-width:368px}.VPTeamMembers.medium.count-2 .container[data-v-387893a3]{max-width:760px}.container[data-v-387893a3]{display:grid;gap:24px;margin:0 auto;max-width:1152px}:root{--vp-font-family-base: "Poppins", "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: "Cousine", monospace}.VPLocalSearchBox[data-v-6120c6bd]{position:fixed;z-index:100;top:0;right:0;bottom:0;left:0;display:flex}.backdrop[data-v-6120c6bd]{position:absolute;top:0;right:0;bottom:0;left:0;background:var(--vp-backdrop-bg-color);transition:opacity .5s}.shell[data-v-6120c6bd]{position:relative;padding:12px;margin:64px auto;display:flex;flex-direction:column;gap:16px;background:var(--vp-local-search-bg);width:min(100vw - 60px,900px);height:min-content;max-height:min(100vh - 128px,900px);border-radius:6px}@media (max-width: 767px){.shell[data-v-6120c6bd]{margin:0;width:100vw;height:100vh;max-height:none;border-radius:0}}.search-bar[data-v-6120c6bd]{border:1px solid var(--vp-c-divider);border-radius:4px;display:flex;align-items:center;padding:0 12px;cursor:text}@media (max-width: 767px){.search-bar[data-v-6120c6bd]{padding:0 8px}}.search-bar[data-v-6120c6bd]:focus-within{border-color:var(--vp-c-brand-1)}.local-search-icon[data-v-6120c6bd]{display:block;font-size:18px}.navigate-icon[data-v-6120c6bd]{display:block;font-size:14px}.search-icon[data-v-6120c6bd]{margin:8px}@media (max-width: 767px){.search-icon[data-v-6120c6bd]{display:none}}.search-input[data-v-6120c6bd]{padding:6px 12px;font-size:inherit;width:100%}@media (max-width: 767px){.search-input[data-v-6120c6bd]{padding:6px 4px}}.search-actions[data-v-6120c6bd]{display:flex;gap:4px}@media (any-pointer: coarse){.search-actions[data-v-6120c6bd]{gap:8px}}@media (min-width: 769px){.search-actions.before[data-v-6120c6bd]{display:none}}.search-actions button[data-v-6120c6bd]{padding:8px}.search-actions button[data-v-6120c6bd]:not([disabled]):hover,.toggle-layout-button.detailed-list[data-v-6120c6bd]{color:var(--vp-c-brand-1)}.search-actions button.clear-button[data-v-6120c6bd]:disabled{opacity:.37}.search-keyboard-shortcuts[data-v-6120c6bd]{font-size:.8rem;opacity:75%;display:flex;flex-wrap:wrap;gap:16px;line-height:14px}.search-keyboard-shortcuts span[data-v-6120c6bd]{display:flex;align-items:center;gap:4px}@media (max-width: 767px){.search-keyboard-shortcuts[data-v-6120c6bd]{display:none}}.search-keyboard-shortcuts kbd[data-v-6120c6bd]{background:#8080801a;border-radius:4px;padding:3px 6px;min-width:24px;display:inline-block;text-align:center;vertical-align:middle;border:1px solid rgba(128,128,128,.15);box-shadow:0 2px 2px #0000001a}.results[data-v-6120c6bd]{display:flex;flex-direction:column;gap:6px;overflow-x:hidden;overflow-y:auto;overscroll-behavior:contain}.result[data-v-6120c6bd]{display:flex;align-items:center;gap:8px;border-radius:4px;transition:none;line-height:1rem;border:solid 2px var(--vp-local-search-result-border);outline:none}.result>div[data-v-6120c6bd]{margin:12px;width:100%;overflow:hidden}@media (max-width: 767px){.result>div[data-v-6120c6bd]{margin:8px}}.titles[data-v-6120c6bd]{display:flex;flex-wrap:wrap;gap:4px;position:relative;z-index:1001;padding:2px 0}.title[data-v-6120c6bd]{display:flex;align-items:center;gap:4px}.title.main[data-v-6120c6bd]{font-weight:500}.title-icon[data-v-6120c6bd]{opacity:.5;font-weight:500;color:var(--vp-c-brand-1)}.title svg[data-v-6120c6bd]{opacity:.5}.result.selected[data-v-6120c6bd]{--vp-local-search-result-bg: var(--vp-local-search-result-selected-bg);border-color:var(--vp-local-search-result-selected-border)}.excerpt-wrapper[data-v-6120c6bd]{position:relative}.excerpt[data-v-6120c6bd]{opacity:50%;pointer-events:none;max-height:140px;overflow:hidden;position:relative;margin-top:4px}.result.selected .excerpt[data-v-6120c6bd]{opacity:1}.excerpt[data-v-6120c6bd] *{font-size:.8rem!important;line-height:130%!important}.titles[data-v-6120c6bd] mark,.excerpt[data-v-6120c6bd] mark{background-color:var(--vp-local-search-highlight-bg);color:var(--vp-local-search-highlight-text);border-radius:2px;padding:0 2px}.excerpt[data-v-6120c6bd] .vp-code-group .tabs{display:none}.excerpt[data-v-6120c6bd] .vp-code-group div[class*=language-]{border-radius:8px!important}.excerpt-gradient-bottom[data-v-6120c6bd]{position:absolute;bottom:-1px;left:0;width:100%;height:8px;background:linear-gradient(transparent,var(--vp-local-search-result-bg));z-index:1000}.excerpt-gradient-top[data-v-6120c6bd]{position:absolute;top:-1px;left:0;width:100%;height:8px;background:linear-gradient(var(--vp-local-search-result-bg),transparent);z-index:1000}.result.selected .titles[data-v-6120c6bd],.result.selected .title-icon[data-v-6120c6bd]{color:var(--vp-c-brand-1)!important}.no-results[data-v-6120c6bd]{font-size:.9rem;text-align:center;padding:12px}svg[data-v-6120c6bd]{flex:none}
diff --git a/assets/zht_api_mp_math_line.md.DopGqzVZ.js b/assets/zht_api_mp_math_line.md.BmXiOeCt.js
similarity index 96%
rename from assets/zht_api_mp_math_line.md.DopGqzVZ.js
rename to assets/zht_api_mp_math_line.md.BmXiOeCt.js
index f52d208..34c19fd 100644
--- a/assets/zht_api_mp_math_line.md.DopGqzVZ.js
+++ b/assets/zht_api_mp_math_line.md.BmXiOeCt.js
@@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

説明: 工厂函数 由两点构造直线。

變數説明:

返回: Line3: 直线

源碼 或 於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

變數説明:

返回: Line3 | Point3 | None: 交集

源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

變數説明:

返回: Line3 | Point3 | None: 交集

源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
diff --git a/assets/zht_api_mp_math_line.md.DopGqzVZ.lean.js b/assets/zht_api_mp_math_line.md.BmXiOeCt.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_line.md.DopGqzVZ.lean.js
rename to assets/zht_api_mp_math_line.md.BmXiOeCt.lean.js
diff --git a/assets/zht_api_mp_math_plane.md.OnI32y0z.js b/assets/zht_api_mp_math_plane.md.DYh81-YI.js
similarity index 97%
rename from assets/zht_api_mp_math_plane.md.OnI32y0z.js
rename to assets/zht_api_mp_math_plane.md.DYh81-YI.js
index d113dd4..2c38b78 100644
--- a/assets/zht_api_mp_math_plane.md.OnI32y0z.js
+++ b/assets/zht_api_mp_math_plane.md.DYh81-YI.js
@@ -1,4 +1,4 @@
-import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=t(`
模組 mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),n={name:"zht/api/mp_math/plane.md"},h=t(`
模組 mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     self.a = a
     self.b = b
     self.c = c
@@ -13,7 +13,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t('',1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[z],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t(`
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t('',1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t('',1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t('',1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[z],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t(`
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     if isinstance(other, Line3):
         return self.normal.cal_angle(other.direction).complementary
     elif isinstance(other, Plane3):
@@ -25,7 +25,7 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t('',1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
變數説明:
  • other (Plane3): 另一个平面
返回: Line3: 交线
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t('',1),es=[ts],ls=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t('',1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t('',1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t('',1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
變數説明:
  • other (Plane3): 另一个平面
返回: Line3: 交线
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -68,11 +68,11 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         v2 = l2.get_point(1) - l1.point
     return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method self & other: Line3 => Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self & other: Plane3 => Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
返回: Line3 | Point3 | None: 交集
抛出:
源碼 或 於GitHub上查看
python
def __and__(self, other):
+    ...
method self & other ​
説明: 取两平面的交集（人话：交线）
變數説明:
返回: Line3 | Point3 | None: 交集
抛出:
源碼 或 於GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -84,4 +84,4 @@ import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1Zp
     else:
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default};
+    return self.cal_intersection_point3(other)
`,81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default};
diff --git a/assets/zht_api_mp_math_plane.md.OnI32y0z.lean.js b/assets/zht_api_mp_math_plane.md.DYh81-YI.lean.js
similarity index 95%
rename from assets/zht_api_mp_math_plane.md.OnI32y0z.lean.js
rename to assets/zht_api_mp_math_plane.md.DYh81-YI.lean.js
index d9975a5..9a93590 100644
--- a/assets/zht_api_mp_math_plane.md.OnI32y0z.lean.js
+++ b/assets/zht_api_mp_math_plane.md.DYh81-YI.lean.js
@@ -1 +1 @@
-import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},_=t("",1),b=[_],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[z],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t("",16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ns=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t("",1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,b)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ns]),e(", "),s("mjx-container",ls,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",_s,Cs)),xs])]),ws])}const Ps=n(l,[["render",Hs]]);export{Zs as __pageData,Ps as default};
+import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),n={name:"zht/api/mp_math/plane.md"},h=t("",16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t("",1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},E=t("",1),y=[E],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"1")])],-1),F={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 -666 1100 677","aria-hidden":"true"},b=t("",1),_=[b],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n"),s("mn",null,"2")])],-1),x={class:"tip custom-block"},w=s("p",{class:"custom-block-title"},"TIP",-1),H=s("p",null,"平面与直线夹角计算公式:",-1),L={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},D={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"19.568ex",height:"5.269ex",role:"img",focusable:"false",viewBox:"0 -1370 8649 2329","aria-hidden":"true"},A=t("",1),v=[A],B=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mo",null,"⋅"),s("mi",null,"d")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"d"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),M={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.357ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 600 453","aria-hidden":"true"},Z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D45B",d:"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),P=[Z],q=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"n")])],-1),S={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.023ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.176ex",height:"1.593ex",role:"img",focusable:"false",viewBox:"0 -694 520 704","aria-hidden":"true"},z=s("g",{stroke:"currentColor",fill:"currentColor","stroke-width":"0",transform:"scale(1,-1)"},[s("g",{"data-mml-node":"math"},[s("g",{"data-mml-node":"mi"},[s("path",{"data-c":"1D451",d:"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z",style:{"stroke-width":"3"}})])])],-1),N=[z],G=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),I=t("",16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t("",1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"d"),s("mo",null,"="),s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"n"),s("mn",null,"2")])],-1),ss={start:"2"},as={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},is={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.442ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2405.6 748","aria-hidden":"true"},ts=t("",1),es=[ts],ls=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ns={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t("",1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"y"),s("mo",null,"="),s("mn",null,"0")])],-1),ks={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},ds={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.2ex",height:"1.692ex",role:"img",focusable:"false",viewBox:"0 -666 2298.6 748","aria-hidden":"true"},Qs=t("",1),Ts=[Qs],gs=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"z"),s("mo",null,"="),s("mn",null,"0")])],-1),ms={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},cs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.281ex"},xmlns:"http://www.w3.org/2000/svg",width:"13.363ex",height:"7.692ex",role:"img",focusable:"false",viewBox:"0 -1950 5906.6 3400","aria-hidden":"true"},Es=t("",1),ys=[Es],us=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"{"),s("mtable",{columnalign:"left left",columnspacing:"1em",rowspacing:".2em"},[s("mtr",null,[s("mtd",null,[s("mi",null,"x"),s("mo",null,"="),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"y"),s("mo",null,"="),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"z"),s("mo",null,"="),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",null,"+"),s("mi",null,"d"),s("mi",null,"t")])])]),s("mo",{"data-mjx-texclass":"CLOSE",fence:"true",stretchy:"true",symmetric:"true"})])])],-1),Fs=s("p",null,"或",-1),fs={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},bs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},_s=t("",1),Cs=[_s],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t("",81);function Hs(Ls,Ds,As,vs,Bs,Ms){return i(),a("div",null,[h,s("div",p,[r,o,s("mjx-container",k,[(i(),a("svg",d,T)),g]),s("p",null,[e("其中 "),s("mjx-container",m,[(i(),a("svg",c,y)),u]),e(" 和 "),s("mjx-container",F,[(i(),a("svg",f,_)),C]),e(" 分别为两个平面的法向量")])]),s("div",x,[w,H,s("mjx-container",L,[(i(),a("svg",D,v)),B]),s("p",null,[e("其中 "),s("mjx-container",M,[(i(),a("svg",V,P)),q]),e(" 为平面的法向量，"),s("mjx-container",S,[(i(),a("svg",j,N)),G]),e(" 为直线的方向向量")])]),I,s("div",R,[J,O,$,s("mjx-container",U,[(i(),a("svg",K,X)),Y]),s("ol",ss,[s("li",null,[e("寻找直线上的一点，依次假设"),s("mjx-container",as,[(i(),a("svg",is,es)),ls]),e(", "),s("mjx-container",ns,[(i(),a("svg",hs,rs)),os]),e(", "),s("mjx-container",ks,[(i(),a("svg",ds,Ts)),gs]),e("，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示")])]),s("mjx-container",ms,[(i(),a("svg",cs,ys)),us]),Fs,s("mjx-container",fs,[(i(),a("svg",bs,Cs)),xs])]),ws])}const Ps=l(n,[["render",Hs]]);export{Zs as __pageData,Ps as default};
diff --git a/demo/best-practice.html b/demo/best-practice.html
index e8a675a..bc45bc3 100644
--- a/demo/best-practice.html
+++ b/demo/best-practice.html
@@ -6,10 +6,10 @@
     最佳实践 | MBCP 文档
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/demo/index.html b/demo/index.html
index c323ea1..03a5533 100644
--- a/demo/index.html
+++ b/demo/index.html
@@ -6,10 +6,10 @@
     demo | MBCP 文档
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
demo ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/index.html b/en/api/index.html
index f62b6eb..febde94 100644
--- a/en/api/index.html
+++ b/en/api/index.html
@@ -6,10 +6,10 @@
     mbcp | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
Module mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index b8a677f..807563a 100644
--- a/en/api/mp_math/angle.html
+++ b/en/api/mp_math/angle.html
@@ -6,10 +6,10 @@
     mbcp.mp_math.angle | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -56,7 +56,7 @@
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
- + \ No newline at end of file diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html index e87e739..934e2ac 100644 --- a/en/api/mp_math/const.html +++ b/en/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Module mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • Description: 常量 π

  • Default: math.pi

var E ​

  • Description: 自然对数的底 exp(1)

  • Default: math.e

var GOLDEN_RATIO ​

  • Description: 黄金分割比

  • Default: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • Description: 欧拉常数

  • Default: 0.5772156649015329

var EPSILON ​

  • Description: 精度误差

  • Default: 0.0001

var APPROX ​

  • Description: 约等于判定误差

  • Default: 0.001

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html index 9bd0f4a..3c96094 100644 --- a/en/api/mp_math/equation.html +++ b/en/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP docs - + - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type') - + \ No newline at end of file diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html index cf6df05..9cdc2d3 100644 --- a/en/api/mp_math/function.html +++ b/en/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP docs - + - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func - + \ No newline at end of file diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html index acd0664..e8c4fbc 100644 --- a/en/api/mp_math/index.html +++ b/en/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Module mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html index 1eb64e2..315958d 100644 --- a/en/api/mp_math/line.html +++ b/en/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP docs - + - - + + - + @@ -58,7 +58,7 @@ self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

Description: 工厂函数 由两点构造直线。

Arguments:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

Arguments:

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

Arguments:

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
@@ -66,7 +66,7 @@
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
- + \ No newline at end of file diff --git a/en/api/mp_math/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html index 3652b19..bf44538 100644 --- a/en/api/mp_math/mp_math_typing.html +++ b/en/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Module mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • Description: 实数

  • Type: TypeAlias

  • Default: int | float

var Number ​

  • Description: 数

  • Type: TypeAlias

  • Default: RealNumber | complex

var SingleVar ​

  • Description: 单变量

  • Default: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • Description: 数组变量

  • Default: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • Description: 变量

  • Type: TypeAlias

  • Default: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • Description: 一元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • Description: 一元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • Description: 一元函数

  • Type: TypeAlias

  • Default: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • Description: 二元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • Description: 二元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • Description: 二元函数

  • Type: TypeAlias

  • Default: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • Description: 三元单变量函数

  • Type: TypeAlias

  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • Description: 三元数组函数

  • Type: TypeAlias

  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • Description: 三元函数

  • Type: TypeAlias

  • Default: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • Description: 多元单变量函数

  • Type: TypeAlias

  • Default: Callable[..., SingleVar]

var MultiArraysFunc ​

  • Description: 多元数组函数

  • Type: TypeAlias

  • Default: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • Description: 多元函数

  • Type: TypeAlias

  • Default: MultiSingleVarsFunc | MultiArraysFunc

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html index b245a1d..cbf6b0b 100644 --- a/en/api/mp_math/plane.html +++ b/en/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP docs - + - - + + - + @@ -88,11 +88,11 @@ v2 = l2.get_point(1) - l1.point return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method __and__(self, other: Line3) -> Point3 | None ​

Source code or View on GitHub
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None ​

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method __and__(self, other: Plane3) -> Line3 | None ​

Source code or View on GitHub
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None ​

Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method __and__(self, other) ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
+    ...

method self & other ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -105,7 +105,7 @@
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

Description: 判断两个平面是否等价。

Arguments:

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method __rand__(self, other: Line3) -> Point3 ​

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html index 7324d34..1253bbd 100644 --- a/en/api/mp_math/point.html +++ b/en/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP docs - + - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

Description: P - P -> V

P - V -> P 已在 Vector3 中实现

Arguments:

Return: Vector3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
- + \ No newline at end of file diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html index 03a5d14..d04c929 100644 --- a/en/api/mp_math/segment.html +++ b/en/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP docs - + - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2) - + \ No newline at end of file diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html index ba3c5f6..03fc4e1 100644 --- a/en/api/mp_math/utils.html +++ b/en/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP docs - + - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return '' - + \ No newline at end of file diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html index a61136e..22cb777 100644 --- a/en/api/mp_math/vector.html +++ b/en/api/mp_math/vector.html @@ -6,10 +6,10 @@ mbcp.mp_math.vector | MBCP docs - + - - + + @@ -78,7 +78,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

Description: 取负。

Return: Vector3: 负向量

Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

- + \ No newline at end of file diff --git a/en/api/particle/index.html b/en/api/particle/index.html index 66f46d8..f0ff38f 100644 --- a/en/api/particle/index.html +++ b/en/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Module mbcp.particle ​

本模块定义了粒子生成相关的工具

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/presets/index.html b/en/api/presets/index.html index 7f1ca14..3061881 100644 --- a/en/api/presets/index.html +++ b/en/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Module mbcp.presets ​

本模块塞了一些预设

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html index adc9d63..7416d40 100644 --- a/en/api/presets/model/index.html +++ b/en/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP docs - + - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)] - + \ No newline at end of file diff --git a/en/demo/best-practice.html b/en/demo/best-practice.html index b992f29..5507dbf 100644 --- a/en/demo/best-practice.html +++ b/en/demo/best-practice.html @@ -6,10 +6,10 @@ Best Practice | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/guide/index.html b/en/guide/index.html index 6db94d4..965fdc6 100644 --- a/en/guide/index.html +++ b/en/guide/index.html @@ -6,10 +6,10 @@ 开始不了一点 | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

开始不了一点 ​

∫12x111

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/index.html b/en/index.html index 3380009..b0bf16b 100644 --- a/en/index.html +++ b/en/index.html @@ -6,10 +6,10 @@ MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

MBCP

More basic change particle

A Library for Python to create Minecraft particle effects and geometric figures

Get Started
API Reference
Best Practice
MBCP logo
🛠️

Easy to use

Through a simple interface, most of the geometric operations and particle production requirements have been achieved

📦

Integrated

Encapsulated and integratednumpy, scipy and sympy, making script writing as simple as using Geogebra

🧊

Rich presets

Rich presets and examples, you can use it directly, and you can also customize the parameters to create your own effects

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/en/refer/index.html b/en/refer/index.html index f5fe29b..ee2c5cd 100644 --- a/en/refer/index.html +++ b/en/refer/index.html @@ -6,10 +6,10 @@ Reference | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

简体中文
日本語
繁體中文

Appearance

Reference ​

help us to improve the documentation

Documentation built with VitePress | API references generated by litedoc

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/guide/index.html b/guide/index.html index ea7f049..1b1fab1 100644 --- a/guide/index.html +++ b/guide/index.html @@ -6,10 +6,10 @@ 快速开始 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

快速开始 ​

TIP

建议：把你项目所使用的Python换成PyPy，这样可以提高性能(兼容性优先)

安装 ​

shell
pip install mbcp

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/hashmap.json b/hashmap.json index 1d07044..d506585 100644 --- a/hashmap.json +++ b/hashmap.json @@ -1 +1 @@ -{"api_index.md":"BO3OGCZm","api_mp_math_angle.md":"DRCLNUJL","api_mp_math_const.md":"B_APaY-d","api_mp_math_equation.md":"Q6tfqPV1","api_mp_math_function.md":"CDW7K4aO","api_mp_math_index.md":"BfSAi6YB","api_mp_math_line.md":"Ld9EytA4","api_mp_math_mp_math_typing.md":"D0jHaHho","api_mp_math_plane.md":"DRZNcHy5","api_mp_math_point.md":"C4s5FhwG","api_mp_math_segment.md":"JYVgLepk","api_mp_math_utils.md":"DuXZd_EC","api_mp_math_vector.md":"FC-qe2-I","api_particle_index.md":"BnaJlvrB","api_presets_index.md":"Cn3tbiU4","api_presets_model_index.md":"DTQNHoYw","demo_best-practice.md":"CmYjfrxd","demo_index.md":"CVAdlaFI","en_api_index.md":"C0-LRrMB","en_api_mp_math_angle.md":"Bd_SmddI","en_api_mp_math_const.md":"f-2wQHW5","en_api_mp_math_equation.md":"B0ThTNcD","en_api_mp_math_function.md":"l19FY4Hu","en_api_mp_math_index.md":"BiDCWhuz","en_api_mp_math_line.md":"Bd5Z3iC3","en_api_mp_math_mp_math_typing.md":"A2oAWINP","en_api_mp_math_plane.md":"D91Vt6aU","en_api_mp_math_point.md":"Dr2bDE6-","en_api_mp_math_segment.md":"D0wpX8Us","en_api_mp_math_utils.md":"n9Hkxc_q","en_api_mp_math_vector.md":"ARDQGWRk","en_api_particle_index.md":"j3_p5KtY","en_api_presets_index.md":"Bj8HQN_s","en_api_presets_model_index.md":"CF6gWxhr","en_demo_best-practice.md":"CmtY105n","en_guide_index.md":"C3kI8f8A","en_index.md":"Cc-Nt9Ot","en_refer_index.md":"Cq6GWi0V","guide_index.md":"CJOqvlSE","index.md":"WVpbC1C1","ja_api_index.md":"CGngNEPX","ja_api_mp_math_angle.md":"DurFoqAy","ja_api_mp_math_const.md":"kKAd6ihV","ja_api_mp_math_equation.md":"ClACMtEE","ja_api_mp_math_function.md":"pJM1NJ2m","ja_api_mp_math_index.md":"BCReRKfD","ja_api_mp_math_line.md":"BbbGydDH","ja_api_mp_math_mp_math_typing.md":"CzEPV5Ep","ja_api_mp_math_plane.md":"BvT51o_C","ja_api_mp_math_point.md":"CevhXWsh","ja_api_mp_math_segment.md":"DZAkmIjJ","ja_api_mp_math_utils.md":"Bk8MHgOd","ja_api_mp_math_vector.md":"c1mtKaM8","ja_api_particle_index.md":"CW1rqarC","ja_api_presets_index.md":"BFc_PfJb","ja_api_presets_model_index.md":"wZZUhvvV","ja_demo_best-practice.md":"CBHiF6ec","ja_guide_index.md":"w1Tf2Adm","ja_index.md":"BvjV8RIJ","ja_refer_index.md":"DamUscs8","refer_7-differential-euqtion_index.md":"Dd2-7I9S","refer_function_curry.md":"D_oqRDd3","refer_function_function.md":"Bi_82lIJ","refer_index.md":"yFZW0kI4","zht_api_index.md":"Bh7ICG6U","zht_api_mp_math_angle.md":"CBKEZciJ","zht_api_mp_math_const.md":"D9eBwcNw","zht_api_mp_math_equation.md":"DckV9F7F","zht_api_mp_math_function.md":"3Rru8vfk","zht_api_mp_math_index.md":"DVqLRZhm","zht_api_mp_math_line.md":"DopGqzVZ","zht_api_mp_math_mp_math_typing.md":"DWzRfFJe","zht_api_mp_math_plane.md":"OnI32y0z","zht_api_mp_math_point.md":"DoQ35q26","zht_api_mp_math_segment.md":"CqQitARa","zht_api_mp_math_utils.md":"itNFG1x8","zht_api_mp_math_vector.md":"Dug1hqAu","zht_api_particle_index.md":"bdouG1sk","zht_api_presets_index.md":"9wdPAkKN","zht_api_presets_model_index.md":"BfmFWGa-","zht_demo_best-practice.md":"CPNbD_Lg","zht_guide_index.md":"BNnMViC8","zht_index.md":"fkOYkZZe","zht_refer_index.md":"B7CQS2UW"} +{"api_index.md":"BO3OGCZm","api_mp_math_angle.md":"DRCLNUJL","api_mp_math_const.md":"B_APaY-d","api_mp_math_equation.md":"Q6tfqPV1","api_mp_math_function.md":"CDW7K4aO","api_mp_math_index.md":"BfSAi6YB","api_mp_math_line.md":"lCQRkZtk","api_mp_math_mp_math_typing.md":"D0jHaHho","api_mp_math_plane.md":"2ZclJA1V","api_mp_math_point.md":"C4s5FhwG","api_mp_math_segment.md":"JYVgLepk","api_mp_math_utils.md":"DuXZd_EC","api_mp_math_vector.md":"FC-qe2-I","api_particle_index.md":"BnaJlvrB","api_presets_index.md":"Cn3tbiU4","api_presets_model_index.md":"DTQNHoYw","demo_best-practice.md":"CmYjfrxd","demo_index.md":"CVAdlaFI","en_api_index.md":"C0-LRrMB","en_api_mp_math_angle.md":"Bd_SmddI","en_api_mp_math_const.md":"f-2wQHW5","en_api_mp_math_equation.md":"B0ThTNcD","en_api_mp_math_function.md":"l19FY4Hu","en_api_mp_math_index.md":"BiDCWhuz","en_api_mp_math_line.md":"DFwE8llX","en_api_mp_math_mp_math_typing.md":"A2oAWINP","en_api_mp_math_plane.md":"CBNCeDF4","en_api_mp_math_point.md":"Dr2bDE6-","en_api_mp_math_segment.md":"D0wpX8Us","en_api_mp_math_utils.md":"n9Hkxc_q","en_api_mp_math_vector.md":"ARDQGWRk","en_api_particle_index.md":"j3_p5KtY","en_api_presets_index.md":"Bj8HQN_s","en_api_presets_model_index.md":"CF6gWxhr","en_demo_best-practice.md":"CmtY105n","en_guide_index.md":"C3kI8f8A","en_index.md":"Cc-Nt9Ot","en_refer_index.md":"Cq6GWi0V","guide_index.md":"CJOqvlSE","index.md":"WVpbC1C1","ja_api_index.md":"CGngNEPX","ja_api_mp_math_angle.md":"DurFoqAy","ja_api_mp_math_const.md":"kKAd6ihV","ja_api_mp_math_equation.md":"ClACMtEE","ja_api_mp_math_function.md":"pJM1NJ2m","ja_api_mp_math_index.md":"BCReRKfD","ja_api_mp_math_line.md":"CMckwGpV","ja_api_mp_math_mp_math_typing.md":"CzEPV5Ep","ja_api_mp_math_plane.md":"D549kBN0","ja_api_mp_math_point.md":"CevhXWsh","ja_api_mp_math_segment.md":"DZAkmIjJ","ja_api_mp_math_utils.md":"Bk8MHgOd","ja_api_mp_math_vector.md":"c1mtKaM8","ja_api_particle_index.md":"CW1rqarC","ja_api_presets_index.md":"BFc_PfJb","ja_api_presets_model_index.md":"wZZUhvvV","ja_demo_best-practice.md":"CBHiF6ec","ja_guide_index.md":"w1Tf2Adm","ja_index.md":"BvjV8RIJ","ja_refer_index.md":"DamUscs8","refer_7-differential-euqtion_index.md":"Dd2-7I9S","refer_function_curry.md":"D_oqRDd3","refer_function_function.md":"Bi_82lIJ","refer_index.md":"yFZW0kI4","zht_api_index.md":"Bh7ICG6U","zht_api_mp_math_angle.md":"CBKEZciJ","zht_api_mp_math_const.md":"D9eBwcNw","zht_api_mp_math_equation.md":"DckV9F7F","zht_api_mp_math_function.md":"3Rru8vfk","zht_api_mp_math_index.md":"DVqLRZhm","zht_api_mp_math_line.md":"BmXiOeCt","zht_api_mp_math_mp_math_typing.md":"DWzRfFJe","zht_api_mp_math_plane.md":"DYh81-YI","zht_api_mp_math_point.md":"DoQ35q26","zht_api_mp_math_segment.md":"CqQitARa","zht_api_mp_math_utils.md":"itNFG1x8","zht_api_mp_math_vector.md":"Dug1hqAu","zht_api_particle_index.md":"bdouG1sk","zht_api_presets_index.md":"9wdPAkKN","zht_api_presets_model_index.md":"BfmFWGa-","zht_demo_best-practice.md":"CPNbD_Lg","zht_guide_index.md":"BNnMViC8","zht_index.md":"fkOYkZZe","zht_refer_index.md":"B7CQS2UW"} diff --git a/index.html b/index.html index 07fe391..aa5ce41 100644 --- a/index.html +++ b/index.html @@ -6,10 +6,10 @@ MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

MBCP

更多基础变换粒子

用于几何运算和Minecraft粒子制作的库

快速开始
API文档
最佳实践
MBCP logo
🛠️

高可用性

通过简单的接口，实现了大部分几何运算和粒子制作的需求

📦

高集成度

对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单

🧊

内置预设

提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/index.html b/ja/api/index.html index d988d8a..431b6bd 100644 --- a/ja/api/index.html +++ b/ja/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html index 76c5140..e5c8818 100644 --- a/ja/api/mp_math/angle.html +++ b/ja/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP ドキュメント - + - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True) - + \ No newline at end of file diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html index be9bc04..dec3aa0 100644 --- a/ja/api/mp_math/const.html +++ b/ja/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 説明: 常量 π

  • デフォルト: math.pi

var E ​

  • 説明: 自然对数的底 exp(1)

  • デフォルト: math.e

var GOLDEN_RATIO ​

  • 説明: 黄金分割比

  • デフォルト: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 説明: 欧拉常数

  • デフォルト: 0.5772156649015329

var EPSILON ​

  • 説明: 精度误差

  • デフォルト: 0.0001

var APPROX ​

  • 説明: 约等于判定误差

  • デフォルト: 0.001

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html index 248d038..063ca77 100644 --- a/ja/api/mp_math/equation.html +++ b/ja/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP ドキュメント - + - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type') - + \ No newline at end of file diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html index f63ad62..a78efe5 100644 --- a/ja/api/mp_math/function.html +++ b/ja/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP ドキュメント - + - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func - + \ No newline at end of file diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html index 49dc79a..19a699e 100644 --- a/ja/api/mp_math/index.html +++ b/ja/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html index aef19d6..c537568 100644 --- a/ja/api/mp_math/line.html +++ b/ja/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP ドキュメント - + - - + + - + @@ -58,7 +58,7 @@ self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

説明: 工厂函数 由两点构造直线。

引数:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

引数:

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

引数:

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
@@ -66,7 +66,7 @@
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
- + \ No newline at end of file diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html index 871504f..f6484e2 100644 --- a/ja/api/mp_math/mp_math_typing.html +++ b/ja/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 説明: 实数

  • タイプ: TypeAlias

  • デフォルト: int | float

var Number ​

  • 説明: 数

  • タイプ: TypeAlias

  • デフォルト: RealNumber | complex

var SingleVar ​

  • 説明: 单变量

  • デフォルト: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • 説明: 数组变量

  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • 説明: 变量

  • タイプ: TypeAlias

  • デフォルト: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 説明: 一元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • 説明: 一元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • 説明: 一元函数

  • タイプ: TypeAlias

  • デフォルト: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 説明: 二元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • 説明: 二元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • 説明: 二元函数

  • タイプ: TypeAlias

  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 説明: 三元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • 説明: 三元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • 説明: 三元函数

  • タイプ: TypeAlias

  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 説明: 多元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 説明: 多元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 説明: 多元函数

  • タイプ: TypeAlias

  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html index d2e6d94..509fecf 100644 --- a/ja/api/mp_math/plane.html +++ b/ja/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP ドキュメント - + - - + + - + @@ -88,11 +88,11 @@ v2 = l2.get_point(1) - l1.point return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method __and__(self, other: Line3) -> Point3 | None ​

ソースコード または GitHubで表示
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None ​

ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method __and__(self, other: Plane3) -> Line3 | None ​

ソースコード または GitHubで表示
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None ​

ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
+    ...

method self & other ​

説明: 取两平面的交集（人话：交线）

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -105,7 +105,7 @@
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

引数:

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method __rand__(self, other: Line3) -> Point3 ​

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html index d16ca2a..4ccd2ed 100644 --- a/ja/api/mp_math/point.html +++ b/ja/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP ドキュメント - + - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

引数:

戻り値: Vector3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
- + \ No newline at end of file diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html index 1db5d68..4898de0 100644 --- a/ja/api/mp_math/segment.html +++ b/ja/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP ドキュメント - + - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2) - + \ No newline at end of file diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html index fe95f1a..a4209f7 100644 --- a/ja/api/mp_math/utils.html +++ b/ja/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP ドキュメント - + - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return '' - + \ No newline at end of file diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html index 89dc6a9..763f5ff 100644 --- a/ja/api/mp_math/vector.html +++ b/ja/api/mp_math/vector.html @@ -6,10 +6,10 @@ mbcp.mp_math.vector | MBCP ドキュメント - + - - + + @@ -78,7 +78,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

説明: 取负。

戻り値: Vector3: 负向量

ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

- + \ No newline at end of file diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html index 8cb950d..46fc84c 100644 --- a/ja/api/particle/index.html +++ b/ja/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.particle ​

本模块定义了粒子生成相关的工具

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html index aaa70af..2452e25 100644 --- a/ja/api/presets/index.html +++ b/ja/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.presets ​

本模块塞了一些预设

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html index 7814bde..a9c3b02 100644 --- a/ja/api/presets/model/index.html +++ b/ja/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP ドキュメント - + - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)] - + \ No newline at end of file diff --git a/ja/demo/best-practice.html b/ja/demo/best-practice.html index 8f51e36..fbdd1d7 100644 --- a/ja/demo/best-practice.html +++ b/ja/demo/best-practice.html @@ -6,10 +6,10 @@ ベストプラクティス | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/guide/index.html b/ja/guide/index.html index 0878f75..6cdaa3f 100644 --- a/ja/guide/index.html +++ b/ja/guide/index.html @@ -6,10 +6,10 @@ 开始不了一点 | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

开始不了一点 ​

∫12x111

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/index.html b/ja/index.html index 59068f5..8dd66eb 100644 --- a/ja/index.html +++ b/ja/index.html @@ -6,10 +6,10 @@ MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

MBCP

More basic change particle

ジオメトリ演算とパーティクル作成のためのライブラリ

はじめる
API リファレンス
ベストプラクティス
MBCP logo
🛠️

高可用性

シンプルなインターフェースを通じて、ほとんどのジオメトリ演算とパーティクル作成のニーズを実現しました

📦

高集積度

numpy、scipy、およびsympyをラップして統合し、Geogebraを使用するように簡単にスクリプトを作成できます

🧊

組み込みプリセット

多くのプリセットを提供しており、一般的なジオメトリ図形やパーティクル効果など、迅速に作成できます

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/ja/refer/index.html b/ja/refer/index.html index 6d18a83..0b6b549 100644 --- a/ja/refer/index.html +++ b/ja/refer/index.html @@ -6,10 +6,10 @@ Reference | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

Reference ​

Help us to improve the documentation

VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/refer/7-differential-euqtion/index.html b/refer/7-differential-euqtion/index.html index cc7a005..03d2ddc 100644 --- a/refer/7-differential-euqtion/index.html +++ b/refer/7-differential-euqtion/index.html @@ -6,10 +6,10 @@ 微分方程 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

微分方程 ​

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/refer/function/curry.html b/refer/function/curry.html index 58cfad4..e5180c4 100644 --- a/refer/function/curry.html +++ b/refer/function/curry.html @@ -6,10 +6,10 @@ 柯里化 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/refer/function/function.html b/refer/function/function.html index 66ac971..9e62fed 100644 --- a/refer/function/function.html +++ b/refer/function/function.html @@ -6,10 +6,10 @@ 函数 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/refer/index.html b/refer/index.html index 289a425..57cd5f3 100644 --- a/refer/index.html +++ b/refer/index.html @@ -6,10 +6,10 @@ 参考 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

Reference ​

Help us to improve the documentation

文档由 VitePress 构建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/index.html b/zht/api/index.html index a3ea43d..4c83afc 100644 --- a/zht/api/index.html +++ b/zht/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

模組 mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html index a5d60e7..8dd2cb9 100644 --- a/zht/api/mp_math/angle.html +++ b/zht/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP 文檔 - + - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True) - + \ No newline at end of file diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html index 2a48918..418ca46 100644 --- a/zht/api/mp_math/const.html +++ b/zht/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

模組 mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 説明: 常量 π

  • 默認值: math.pi

var E ​

  • 説明: 自然对数的底 exp(1)

  • 默認值: math.e

var GOLDEN_RATIO ​

  • 説明: 黄金分割比

  • 默認值: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 説明: 欧拉常数

  • 默認值: 0.5772156649015329

var EPSILON ​

  • 説明: 精度误差

  • 默認值: 0.0001

var APPROX ​

  • 説明: 约等于判定误差

  • 默認值: 0.001

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html index 1ff298d..ad76677 100644 --- a/zht/api/mp_math/equation.html +++ b/zht/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP 文檔 - + - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type') - + \ No newline at end of file diff --git a/zht/api/mp_math/function.html b/zht/api/mp_math/function.html index 80e665d..20c297d 100644 --- a/zht/api/mp_math/function.html +++ b/zht/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP 文檔 - + - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func - + \ No newline at end of file diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html index 7eb9dc0..67e84ef 100644 --- a/zht/api/mp_math/index.html +++ b/zht/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

模組 mbcp.mp_math ​

本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html index fa4b3e1..2964201 100644 --- a/zht/api/mp_math/line.html +++ b/zht/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP 文檔 - + - - + + - + @@ -58,7 +58,7 @@ self.point.z = 0

@classmethod

method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​

説明: 工厂函数 由两点构造直线。

變數説明:

返回: Line3: 直线

源碼 或 於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     direction = p2 - p1
-    return cls(p1, direction)

method __and__(self, other: Line3) -> Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

變數説明:

返回: Line3 | Point3 | None: 交集

源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)

method self & other: Line3 => Line3 | Point3 | None ​

説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。

變數説明:

返回: Line3 | Point3 | None: 交集

源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
@@ -66,7 +66,7 @@
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
- + \ No newline at end of file diff --git a/zht/api/mp_math/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html index ce1a5c7..5b69dba 100644 --- a/zht/api/mp_math/mp_math_typing.html +++ b/zht/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

模組 mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 説明: 实数

  • 類型: TypeAlias

  • 默認值: int | float

var Number ​

  • 説明: 数

  • 類型: TypeAlias

  • 默認值: RealNumber | complex

var SingleVar ​

  • 説明: 单变量

  • 默認值: TypeVar('SingleVar', bound=Number)

var ArrayVar ​

  • 説明: 数组变量

  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])

var Var ​

  • 説明: 变量

  • 類型: TypeAlias

  • 默認值: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 説明: 一元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar], SingleVar]

var OneArrayFunc ​

  • 説明: 一元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar], ArrayVar]

var OneVarFunc ​

  • 説明: 一元函数

  • 類型: TypeAlias

  • 默認值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 説明: 二元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]

var TwoArraysFunc ​

  • 説明: 二元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]

var TwoVarsFunc ​

  • 説明: 二元函数

  • 類型: TypeAlias

  • 默認值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 説明: 三元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]

var ThreeArraysFunc ​

  • 説明: 三元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]

var ThreeVarsFunc ​

  • 説明: 三元函数

  • 類型: TypeAlias

  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 説明: 多元单变量函数

  • 類型: TypeAlias

  • 默認值: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 説明: 多元数组函数

  • 類型: TypeAlias

  • 默認值: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 説明: 多元函数

  • 類型: TypeAlias

  • 默認值: MultiSingleVarsFunc | MultiArraysFunc

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html index 3fae06a..2bc5e8b 100644 --- a/zht/api/mp_math/plane.html +++ b/zht/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP 文檔 - + - - + + - + @@ -88,11 +88,11 @@ v2 = l2.get_point(1) - l1.point return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    return cls.from_point_and_normal(point, line.direction)

@overload

method __and__(self, other: Line3) -> Point3 | None ​

源碼 或 於GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)

@overload

method self & other: Line3 => Point3 | None ​

源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...

@overload

method __and__(self, other: Plane3) -> Line3 | None ​

源碼 或 於GitHub上查看
python
@overload
+    ...

@overload

method self & other: Plane3 => Line3 | None ​

源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼 或 於GitHub上查看
python
def __and__(self, other):
+    ...

method self & other ​

説明: 取两平面的交集（人话：交线）

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼 或 於GitHub上查看
python
def __and__(self, other):
     if isinstance(other, Plane3):
         if self.normal.is_parallel(other.normal):
             return None
@@ -105,7 +105,7 @@
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

變數説明:

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     return self.approx(other)

method __rand__(self, other: Line3) -> Point3 ​

源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html index d9e16f9..dfafed4 100644 --- a/zht/api/mp_math/point.html +++ b/zht/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP 文檔 - + - - + + @@ -31,7 +31,7 @@ return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self - other: Point3 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

變數説明:

返回: Vector3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
- + \ No newline at end of file diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html index 8f6425b..28c8c40 100644 --- a/zht/api/mp_math/segment.html +++ b/zht/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP 文檔 - + - - + + @@ -27,7 +27,7 @@ self.length = self.direction.length '中心点' self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2) - + \ No newline at end of file diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html index 016a8bf..334ac3e 100644 --- a/zht/api/mp_math/utils.html +++ b/zht/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP 文檔 - + - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return '' - + \ No newline at end of file diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html index 96c3bf2..c3d7d2c 100644 --- a/zht/api/mp_math/vector.html +++ b/zht/api/mp_math/vector.html @@ -6,10 +6,10 @@ mbcp.mp_math.vector | MBCP 文檔 - + - - + + @@ -78,7 +78,7 @@ return self.x * other.x + self.y * other.y + self.z * other.z

method self / other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
     return Vector3(self.x / other, self.y / other, self.z / other)

method - self => Vector3 ​

説明: 取负。

返回: Vector3: 负向量

源碼 或 於GitHub上查看
python
def __neg__(self) -> 'Vector3':
     return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

- + \ No newline at end of file diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html index a69cd42..fb36a75 100644 --- a/zht/api/particle/index.html +++ b/zht/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

模組 mbcp.particle ​

本模块定义了粒子生成相关的工具

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html index 13beff4..3730a4a 100644 --- a/zht/api/presets/index.html +++ b/zht/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

模組 mbcp.presets ​

本模块塞了一些预设

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html index f7b52d6..630515d 100644 --- a/zht/api/presets/model/index.html +++ b/zht/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP 文檔 - + - - + + @@ -28,7 +28,7 @@ y_array = radius * np.sin(phi_list) * np.sin(theta_list) z_array = radius * np.cos(phi_list) return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)] - + \ No newline at end of file diff --git a/zht/demo/best-practice.html b/zht/demo/best-practice.html index 653951a..b3cbc89 100644 --- a/zht/demo/best-practice.html +++ b/zht/demo/best-practice.html @@ -6,10 +6,10 @@ 最佳實踐 | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/guide/index.html b/zht/guide/index.html index 1dc6287..64c95ee 100644 --- a/zht/guide/index.html +++ b/zht/guide/index.html @@ -6,10 +6,10 @@ 开始不了一点 | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

开始不了一点 ​

∫12x111

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/index.html b/zht/index.html index e5af54e..9d947ad 100644 --- a/zht/index.html +++ b/zht/index.html @@ -6,10 +6,10 @@ MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

MBCP

更多基礎變化粒子

用於幾何運算和 當個創世神 粒子製作的軟體庫

跟隨引導
API文檔
最佳實踐
MBCP logo
🛠️

高度易用

通過簡單的接口，實現了大部分幾何運算及粒子製作的需求

📦

高度集成

對numpy、scipy及sympy進行了封裝和集成，使腳本編寫像使用Geogebra一樣easy

🧊

內置預設

提供了大量的預設，包括常見的幾何圖形、粒子效果等，便於快速生產

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file diff --git a/zht/refer/index.html b/zht/refer/index.html index 4545f78..3df5481 100644 --- a/zht/refer/index.html +++ b/zht/refer/index.html @@ -6,10 +6,10 @@ Reference | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

繁體中文

简体中文
English
日本語

繁體中文

简体中文
English
日本語

Appearance

Reference ​

Help us to improve the documentation

文檔由 VitePress 構建 | API引用由 litedoc 生成

Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

- + \ No newline at end of file