diff --git a/404.html b/404.html index 8897036..f74c953 100644 --- a/404.html +++ b/404.html @@ -8,7 +8,7 @@ - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index 2798acb..29814d2 100644 --- a/api/index.html +++ b/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 b54109e..718c146 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -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 0ec878d..c935d10 100644 --- a/api/mp_math/const.html +++ b/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -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 1b4aa82..dc81e33 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -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 705d46d..596e7da 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -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 d95ba2b..8c670ab 100644 --- a/api/mp_math/index.html +++ b/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 05faf10..c59e573 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method 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 36abb28..f30888b 100644 --- a/api/mp_math/mp_math_typing.html +++ b/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -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 a92671d..570b862 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method 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 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 ca70d89..ded9cec 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -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 a54fbfc..d9a1703 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -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 cf3b73c..9f423e1 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -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 ec9761e..72b6f6e 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

method project(self, other: Vector3) -> Vector3 ​

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

说明: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源代码 或 在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

源代码 或 在GitHub上查看
python
@property
@@ -79,7 +79,7 @@
     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 4198f16..42c6ccc 100644 --- a/api/particle/index.html +++ b/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 41c28a4..a9ec96d 100644 --- a/api/presets/index.html +++ b/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 abe8d26..0ea47e7 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -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_vector.md.Bmtslkkm.js b/assets/api_mp_math_vector.md.Bmtslkkm.js new file mode 100644 index 0000000..ae1eb1d --- /dev/null +++ b/assets/api_mp_math_vector.md.Bmtslkkm.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t('

模块 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

说明: 3维向量

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

说明: 判断两个向量是否近似相等。

参数:

返回: bool: 是否近似相等

源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

说明: 计算两个向量之间的夹角。

',16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t('',1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t('

参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

说明: 向量积 叉乘：v1 x v2 -> v3

',6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t('',1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t('',1),V=[H],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t('

参数:

返回: Vector3: 叉乘结果

源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

说明: 判断两个向量是否近似平行。

参数:

返回: bool: 是否近似平行

源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

说明: 判断两个向量是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

说明: 将向量归一化。

自体归一化，不返回值。

源代码 或 在GitHub上查看
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

说明: 计算自向量在另一个向量上的投影向量。

',22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t('',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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t('',1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t('

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源代码 或 在GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

源代码 或 在GitHub上查看
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

说明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源代码 或 在GitHub上查看
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

源代码 或 在GitHub上查看
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

说明: V + P -> P

V + V -> V

参数:

返回: Vector3 | Point3: 新的向量或点

源代码 或 在GitHub上查看
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

说明: 判断两个向量是否相等。

参数:

返回: bool: 是否相等

源代码 或 在GitHub上查看
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

说明: P + V -> P

别去点那边实现了。

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

说明: V - P -> P

V - V -> V

参数:

返回: Vector3 | Point3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

说明: P - V -> P

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

参数:

返回: Vector3: 数组运算结果

源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

说明: 点乘。

参数:

返回: float: 点乘结果

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

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

',99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/api_mp_math_vector.md.Bmtslkkm.lean.js b/assets/api_mp_math_vector.md.Bmtslkkm.lean.js new file mode 100644 index 0000000..d90298b --- /dev/null +++ b/assets/api_mp_math_vector.md.Bmtslkkm.lean.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t("",16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t("",1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t("",6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t("",1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t("",1),V=[H],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t("",22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t("",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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t("",1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t("",99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/api_mp_math_vector.md.DjjcwrqW.js b/assets/api_mp_math_vector.md.DjjcwrqW.js deleted file mode 100644 index a5c670c..0000000 --- a/assets/api_mp_math_vector.md.DjjcwrqW.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),l={name:"api/mp_math/vector.md"},h=a('

模块 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

说明: 3维向量

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

说明: 判断两个向量是否近似相等。

参数:

返回: bool: 是否近似相等

源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

说明: 计算两个向量之间的夹角。

',16),n={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),o={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a('',1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a('

参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

说明: 向量积 叉乘：v1 x v2 -> v3

',6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a('',1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},V=a('',1),H=[V],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a('

参数:

返回: Vector3: 叉乘结果

源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

说明: 判断两个向量是否近似平行。

参数:

返回: bool: 是否近似平行

源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

说明: 判断两个向量是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

说明: 将向量归一化。

自体归一化，不返回值。

源代码 或 在GitHub上查看
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

参数:

返回: Vector3: 投影向量

源代码 或 在GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源代码 或 在GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

源代码 或 在GitHub上查看
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

说明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源代码 或 在GitHub上查看
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

源代码 或 在GitHub上查看
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

说明: V + P -> P

V + V -> V

参数:

返回: Vector3 | Point3: 新的向量或点

源代码 或 在GitHub上查看
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

说明: 判断两个向量是否相等。

参数:

返回: bool: 是否相等

源代码 或 在GitHub上查看
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

说明: P + V -> P

别去点那边实现了。

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

说明: V - P -> P

V - V -> V

参数:

返回: Vector3 | Point3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

说明: P - V -> P

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

参数:

返回: Vector3: 数组运算结果

源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

说明: 点乘。

参数:

返回: float: 点乘结果

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

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

',120);function B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",_,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/assets/api_mp_math_vector.md.DjjcwrqW.lean.js b/assets/api_mp_math_vector.md.DjjcwrqW.lean.js deleted file mode 100644 index 2cb1acc..0000000 --- a/assets/api_mp_math_vector.md.DjjcwrqW.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),l={name:"api/mp_math/vector.md"},h=a("",16),n={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),o={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a("",1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a("",6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a("",1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},V=a("",1),H=[V],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a("",120);function B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",_,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/assets/app.ooCHBEUz.js b/assets/app.BSLaYTq9.js similarity index 95% rename from assets/app.ooCHBEUz.js rename to assets/app.BSLaYTq9.js index 815449b..ba97c66 100644 --- a/assets/app.ooCHBEUz.js +++ b/assets/app.BSLaYTq9.js @@ -1 +1 @@ -import{t as p}from"./chunks/theme.DVJrRbLX.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$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&x().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{x as createApp}; +import{t as p}from"./chunks/theme.5eFoszBF.js";import{U as o,a5 as u,a6 as c,a7 as l,a8 as f,a9 as d,aa as m,ab as h,ac as g,ad as A,ae as y,d as P,u as v,y as C,x as b,af as w,ag as E,ah as R,ai as S}from"./chunks/framework.DpC1ZpOZ.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return C(()=>{b(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&w(),E(),R(),s.setup&&s.setup(),()=>S(s.Layout)}});async function x(){globalThis.__VITEPRESS__=!0;const e=_(),a=D();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$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.CXLYQH14.js b/assets/chunks/@localSearchIndexen.CXLYQH14.js deleted file mode 100644 index 1657ec0..0000000 --- a/assets/chunks/@localSearchIndexen.CXLYQH14.js +++ /dev/null @@ -1 +0,0 @@ -const t='{"documentCount":161,"nextId":161,"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-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-1","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-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-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-self-other-bool","95":"/en/api/mp_math/plane.html#method-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-self-other-1","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-self-other","113":"/en/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/en/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/en/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/en/api/mp_math/vector.html#method-length-self-float","130":"/en/api/mp_math/vector.html#method-unit-self-vector3","131":"/en/api/mp_math/vector.html#method-abs-self","132":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/en/api/mp_math/vector.html#method-self-other-point3-point3","134":"/en/api/mp_math/vector.html#method-self-other","135":"/en/api/mp_math/vector.html#method-self-other-1","136":"/en/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/en/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/en/api/mp_math/vector.html#method-self-other-2","140":"/en/api/mp_math/vector.html#method-self-other-point3","141":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/en/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/en/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/en/api/mp_math/vector.html#method-self-vector3","148":"/en/api/mp_math/vector.html#var-zero-vector3","149":"/en/api/mp_math/vector.html#var-x-axis","150":"/en/api/mp_math/vector.html#var-y-axis","151":"/en/api/mp_math/vector.html#var-z-axis","152":"/en/api/particle/#module-mbcp-particle","153":"/en/api/presets/#module-mbcp-presets","154":"/en/api/presets/model/#module-mbcp-presets-model","155":"/en/api/presets/model/#class-geometricmodels","156":"/en/api/presets/model/#method-sphere-radius-float-density-float","157":"/en/demo/best-practice.html#best-practice","158":"/en/demo/best-practice.html#works","159":"/en/guide/#开始不了一点","160":"/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":[4,9,14],"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":[7,7,31],"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":[7,7,22],"95":[8,7,18],"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":[4,7,25],"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":[4,7,34],"113":[7,7,18],"114":[4,7,14],"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":[4,7,19],"127":[6,7,21],"128":[6,7,21],"129":[5,7,26],"130":[5,7,20],"131":[4,7,13],"132":[7,7,15],"133":[7,7,15],"134":[4,7,40],"135":[4,7,25],"136":[7,7,28],"137":[6,7,15],"138":[6,7,15],"139":[3,7,39],"140":[4,7,38],"141":[6,7,15],"142":[7,7,16],"143":[9,7,42],"144":[7,7,16],"145":[7,7,26],"146":[7,7,18],"147":[5,7,20],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,49],"157":[2,1,1],"158":[1,2,25],"159":[1,1,2],"160":[1,1,7]},"averageFieldLength":[5.751552795031055,5.937888198757761,19.801242236024844],"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 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 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 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 self == other => bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method 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 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 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 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 project(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["Module mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["Module mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["Module mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["Module mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["Module mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["Module mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["Module mbcp.mp_math.vector"]},"152":{"title":"Module mbcp.particle","titles":[]},"153":{"title":"Module mbcp.presets","titles":[]},"154":{"title":"Module mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["Module mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["Module mbcp.presets.model","class GeometricModels"]},"157":{"title":"Best Practice","titles":[]},"158":{"title":"Works","titles":["Best Practice"]},"159":{"title":"开始不了一点","titles":[]},"160":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"159":1}}],["开始不了一点",{"0":{"159":1}}],["红石音乐",{"2":{"158":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["works",{"0":{"158":1}}],["warning",{"2":{"34":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":1}}],["投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"160":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"160":1}}],["heart",{"2":{"158":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":{"143":1}}],["数组运算",{"2":{"143":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":{"135":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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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,"135":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":{"153":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":{"152":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":{"158":1}}],["best",{"0":{"157":1},"1":{"158":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,"135":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":{"160":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":{"156":1},"2":{"156":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,"148":1,"149":1,"150":1,"151":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":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,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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,"143":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,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"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,"115":3,"120":4,"121":2,"123":4,"126":1,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"148":3,"149":2,"150":2,"151":2,"156":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":{"160":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"160":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,"134":1,"139":1,"140":1,"143":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,"134":2,"139":2,"140":2,"143":2,"148":1,"149":1,"150":1,"151":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,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["ep",{"2":{"158":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,"134":1,"139":1,"143":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,"134":1,"139":1,"140":1,"143":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",{"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"132":1,"133":1,"134":1,"136":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,"129":2,"134":9,"136":4,"145":2,"156":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,"149":1,"150":1,"151":1,"156":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":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"129":3,"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"160":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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":2,"131":1,"134":3,"135":2,"136":2,"139":3,"140":2,"143":3,"144":1,"145":2,"146":1,"147":2,"156":2}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":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,"134":1,"139":1,"140":1,"143":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":{"155":1},"1":{"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"147":1,"156":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"90":1,"91":2,"92":1,"99":1,"100":2,"101":1,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"127":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":{"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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["one",{"2":{"158":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,"147":1,"156":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,"147":1,"156":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,"151":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,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":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,"134":4,"136":1,"139":4,"140":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,"148":1,"149":1,"150":1,"151":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,"147":1,"156":1}}],["can",{"2":{"158":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",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":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,"155":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,"147":1,"156":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,"156":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,"147":1,"156":1}}],["sphere",{"0":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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,"147":1,"156":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"147":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["默认为否",{"2":{"4":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1,"95":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":1}}],["abs",{"0":{"131":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":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,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":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,"134":1,"135":2,"139":1,"140":1,"143":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,"134":1,"139":1,"140":1,"143":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,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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,"129":1,"143":1,"156":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,"129":2,"143":3,"145":1,"156":2}}],["==",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"135":1},"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,"33":1,"34":1,"36":1,"42":1,"49":1,"56":1,"57":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"156":7}}],["improve",{"2":{"160":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":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,"143":1},"2":{"34":3,"37":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":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,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":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":{"156":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":{"152":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,"134":2,"136":2,"139":2,"140":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,"133":2,"136":2,"138":2,"140":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["practice",{"0":{"157":1},"1":{"158":1}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":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":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":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,"151":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,"129":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,"147":1,"156":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,"151":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1},"2":{"0":3}}]],"serializationVersion":2}';export{t as default}; diff --git a/assets/chunks/@localSearchIndexen.ke4OFQjO.js b/assets/chunks/@localSearchIndexen.ke4OFQjO.js new file mode 100644 index 0000000..3204728 --- /dev/null +++ b/assets/chunks/@localSearchIndexen.ke4OFQjO.js @@ -0,0 +1 @@ +const t='{"documentCount":161,"nextId":161,"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-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-1","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-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/#module-mbcp-mp-math","36":"/en/api/mp_math/function.html#module-mbcp-mp-math-function","37":"/en/api/mp_math/function.html#func-cal-gradient-3vf-func-threesinglevarsfunc-p-point3-epsilon-float-epsilon-vector3","38":"/en/api/mp_math/function.html#func-curry-func-multivarsfunc-args-var-onevarfunc","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-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/point.html#module-mbcp-mp-math-point","77":"/en/api/mp_math/point.html#class-point3","78":"/en/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","79":"/en/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","80":"/en/api/mp_math/point.html#method-self-other-vector3-point3","81":"/en/api/mp_math/point.html#method-self-other-point3-point3","82":"/en/api/mp_math/point.html#method-self-other","83":"/en/api/mp_math/point.html#method-self-other-1","84":"/en/api/mp_math/point.html#method-self-other-point3-vector3","85":"/en/api/mp_math/plane.html#module-mbcp-mp-math-plane","86":"/en/api/mp_math/plane.html#class-plane3","87":"/en/api/mp_math/plane.html#method-init-self-a-float-b-float-c-float-d-float","88":"/en/api/mp_math/plane.html#method-approx-self-other-plane3-bool","89":"/en/api/mp_math/plane.html#method-cal-angle-self-other-line3-plane3-anyangle","90":"/en/api/mp_math/plane.html#method-cal-distance-self-other-plane3-point3-float","91":"/en/api/mp_math/plane.html#method-cal-intersection-line3-self-other-plane3-line3","92":"/en/api/mp_math/plane.html#method-cal-intersection-point3-self-other-line3-point3","93":"/en/api/mp_math/plane.html#method-cal-parallel-plane3-self-point-point3-plane3","94":"/en/api/mp_math/plane.html#method-is-parallel-self-other-plane3-bool","95":"/en/api/mp_math/plane.html#method-normal-self-vector3","96":"/en/api/mp_math/plane.html#method-from-point-and-normal-cls-point-point3-normal-vector3-plane3","97":"/en/api/mp_math/plane.html#method-from-three-points-cls-p1-point3-p2-point3-p3-point3-plane3","98":"/en/api/mp_math/plane.html#method-from-two-lines-cls-l1-line3-l2-line3-plane3","99":"/en/api/mp_math/plane.html#method-from-point-and-line-cls-point-point3-line-line3-plane3","100":"/en/api/mp_math/plane.html#method-self-other-line3-point3-none","101":"/en/api/mp_math/plane.html#method-self-other-plane3-line3-none","102":"/en/api/mp_math/plane.html#method-self-other","103":"/en/api/mp_math/plane.html#method-self-other-bool","104":"/en/api/mp_math/plane.html#method-self-other-line3-point3","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-self-other","113":"/en/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/en/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/en/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/en/api/mp_math/vector.html#method-length-self-float","130":"/en/api/mp_math/vector.html#method-unit-self-vector3","131":"/en/api/mp_math/vector.html#method-abs-self","132":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/en/api/mp_math/vector.html#method-self-other-point3-point3","134":"/en/api/mp_math/vector.html#method-self-other","135":"/en/api/mp_math/vector.html#method-self-other-1","136":"/en/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/en/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/en/api/mp_math/vector.html#method-self-other-2","140":"/en/api/mp_math/vector.html#method-self-other-point3","141":"/en/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/en/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/en/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/en/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/en/api/mp_math/vector.html#method-self-vector3","148":"/en/api/mp_math/vector.html#var-zero-vector3","149":"/en/api/mp_math/vector.html#var-x-axis","150":"/en/api/mp_math/vector.html#var-y-axis","151":"/en/api/mp_math/vector.html#var-z-axis","152":"/en/api/particle/#module-mbcp-particle","153":"/en/api/presets/#module-mbcp-presets","154":"/en/api/presets/model/#module-mbcp-presets-model","155":"/en/api/presets/model/#class-geometricmodels","156":"/en/api/presets/model/#method-sphere-radius-float-density-float","157":"/en/demo/best-practice.html#best-practice","158":"/en/demo/best-practice.html#works","159":"/en/guide/#开始不了一点","160":"/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":[4,9,14],"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":[4,1,20],"36":[5,1,2],"37":[13,5,48],"38":[7,5,43],"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":[7,7,31],"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":[8,7,19],"79":[11,7,32],"80":[8,7,16],"81":[7,7,15],"82":[4,7,27],"83":[4,7,25],"84":[7,7,31],"85":[5,1,2],"86":[2,5,1],"87":[9,7,28],"88":[7,7,33],"89":[10,7,58],"90":[10,7,47],"91":[9,7,67],"92":[9,7,54],"93":[9,7,26],"94":[8,7,24],"95":[5,7,23],"96":[10,7,37],"97":[11,7,37],"98":[10,7,41],"99":[10,7,31],"100":[10,7,18],"101":[10,7,18],"102":[4,7,50],"103":[7,7,22],"104":[8,7,18],"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":[4,7,34],"113":[7,7,18],"114":[4,7,14],"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":[4,7,19],"127":[6,7,29],"128":[6,7,21],"129":[5,7,26],"130":[5,7,20],"131":[4,7,13],"132":[7,7,15],"133":[7,7,15],"134":[4,7,40],"135":[4,7,25],"136":[7,7,28],"137":[6,7,15],"138":[6,7,15],"139":[3,7,39],"140":[4,7,38],"141":[6,7,15],"142":[7,7,16],"143":[9,7,42],"144":[7,7,16],"145":[7,7,26],"146":[7,7,18],"147":[5,7,20],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,49],"157":[2,1,1],"158":[1,2,25],"159":[1,1,2],"160":[1,1,7]},"averageFieldLength":[5.751552795031055,5.937888198757761,19.85093167701862],"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 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 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","titles":[]},"36":{"title":"Module mbcp.mp_math.function","titles":[]},"37":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["Module mbcp.mp_math.function"]},"38":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["Module mbcp.mp_math.function"]},"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 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.point","titles":[]},"77":{"title":"class Point3","titles":["Module mbcp.mp_math.point"]},"78":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.point","class Point3"]},"79":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.point","class Point3"]},"80":{"title":"method self + other: Vector3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"81":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"82":{"title":"method self + other","titles":["Module mbcp.mp_math.point","class Point3"]},"83":{"title":"method self == other","titles":["Module mbcp.mp_math.point","class Point3"]},"84":{"title":"method self - other: Point3 => Vector3","titles":["Module mbcp.mp_math.point","class Point3"]},"85":{"title":"Module mbcp.mp_math.plane","titles":[]},"86":{"title":"class Plane3","titles":["Module mbcp.mp_math.plane"]},"87":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["Module mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method approx(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["Module mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["Module mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method normal(self) -> Vector3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"96":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"97":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"98":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"99":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"100":{"title":"method self & other: Line3 => Point3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"101":{"title":"method self & other: Plane3 => Line3 | None","titles":["Module mbcp.mp_math.plane","class Plane3"]},"102":{"title":"method self & other","titles":["Module mbcp.mp_math.plane","class Plane3"]},"103":{"title":"method self == other => bool","titles":["Module mbcp.mp_math.plane","class Plane3"]},"104":{"title":"method self & other: Line3 => Point3","titles":["Module mbcp.mp_math.plane","class Plane3"]},"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 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 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 project(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["Module mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["Module mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["Module mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["Module mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["Module mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["Module mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["Module mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["Module mbcp.mp_math.vector"]},"152":{"title":"Module mbcp.particle","titles":[]},"153":{"title":"Module mbcp.presets","titles":[]},"154":{"title":"Module mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["Module mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["Module mbcp.presets.model","class GeometricModels"]},"157":{"title":"Best Practice","titles":[]},"158":{"title":"Works","titles":["Best Practice"]},"159":{"title":"开始不了一点","titles":[]},"160":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"159":1}}],["开始不了一点",{"0":{"159":1}}],["红石音乐",{"2":{"158":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"38":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["works",{"0":{"158":1}}],["warning",{"2":{"34":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"102":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":1}}],["投影向量",{"2":{"127":1}}],["投影向量计算公式",{"2":{"127":1}}],["表示向量u在向量v上的投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"160":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"89":1,"90":1,"102":1,"113":1,"134":1,"139":1,"140":1,"143":1}}],["u",{"2":{"127":2}}],["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":{"160":1}}],["heart",{"2":{"158":1}}],["have",{"2":{"91":1}}],["high",{"2":{"34":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":{"54":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":{"34":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":{"56":1}}],["新的向量或点",{"2":{"134":1}}],["新的向量",{"2":{"84":1,"139":1}}],["新的点",{"2":{"82":1,"136":1,"140":1}}],["已在",{"2":{"84":1}}],["已知一个函数f",{"2":{"37":1}}],["坐标",{"2":{"78":3}}],["笛卡尔坐标系中的点",{"2":{"78":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":{"143":1}}],["数组运算",{"2":{"143":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":{"91":1,"102":1}}],["交线返回交点",{"2":{"56":1}}],["交集",{"2":{"56":1,"102":1}}],["交点",{"2":{"45":1,"92":1}}],["重合线返回自身",{"2":{"56":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":{"55":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":{"41":1}}],["工厂函数",{"2":{"55":1,"96":1,"97":1,"98":1,"99":1}}],["处理",{"2":{"54":1}}],["处的梯度向量为",{"2":{"37":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,"89":1,"90":1,"102":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":{"135":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":{"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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":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,"136":1,"140":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":{"37":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,"93":1}}],["直线最终可用参数方程或点向式表示",{"2":{"91":1}}],["直线",{"2":{"55":1,"92":1,"98":2,"99":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,"90":1}}],["夹角",{"2":{"43":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,"135":1}}],["是否等价",{"2":{"57":1,"103":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,"94":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,"88":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"42":1,"49":1,"79":1,"115":1,"121":1,"124":1}}],["方向向量",{"2":{"41":1,"107":1}}],["6",{"2":{"38":1}}],["3维向量",{"2":{"120":1}}],["3",{"2":{"38":1}}],["3vf",{"0":{"37":1},"2":{"37":1}}],["breaking",{"2":{"158":1}}],["best",{"0":{"157":1},"1":{"158":1}}],["by",{"2":{"87":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,"88":1,"94":1,"103":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,"83":1,"88":2,"94":2,"103":2,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"135":1}}],["b",{"0":{"87":1},"2":{"38":2,"87":4,"88":7,"90":2,"91":12,"92":2,"95":1,"96":3}}],["柯里化后的函数",{"2":{"38":1}}],["柯理化",{"2":{"38":1}}],["函数",{"2":{"38":1}}],["对多参数函数进行柯里化",{"2":{"38":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":{"160":1}}],["do",{"2":{"45":2}}],["distance",{"0":{"44":1,"90":1},"2":{"44":1,"90":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,"89":1,"91":2,"92":4,"98":1,"99":1,"102":1,"107":2}}],["dz",{"2":{"37":2}}],["dy",{"2":{"37":2}}],["dx",{"2":{"37":2}}],["density",{"0":{"156":1},"2":{"156":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,"148":1,"149":1,"150":1,"151":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,"38":1,"55":1,"80":1,"81":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"37":1,"38":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,"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,"127":1,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["梯度",{"2":{"37":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":1}}],["点3",{"2":{"97":1}}],["点法式构造",{"2":{"96":1}}],["点2",{"2":{"55":1,"97":1}}],["点1",{"2":{"55":1,"97":1}}],["点",{"2":{"37":1,"47":1,"52":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":{"37":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":{"35":1}}],["三维线段",{"2":{"35":1}}],["三维点",{"2":{"35":1}}],["三维平面",{"2":{"35":1}}],["三维直线",{"2":{"35":1}}],["∂f∂z",{"2":{"37":1}}],["∂f∂y",{"2":{"37":1}}],["∂f∂x",{"2":{"37":1}}],["∇f",{"2":{"37":1}}],["计算自向量在另一个向量上的投影向量",{"2":{"127":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":{"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":{"37":1}}],["计算曲线上的点",{"2":{"33":1}}],["导入的类有",{"2":{"35":1}}],["本包定义了一些常用的导入",{"2":{"35":1}}],["本模块塞了一些预设",{"2":{"153":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":{"152":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":{"39":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":{"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}}],["l2",{"0":{"98":1},"2":{"98":4}}],["l1",{"0":{"98":1},"2":{"98":6}}],["lambda",{"2":{"48":3}}],["linalg",{"2":{"91":3}}],["lines",{"0":{"98":1},"2":{"45":2,"98":1}}],["line",{"0":{"39":1,"99":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":{"92":1,"99":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,"89":1,"91":2,"92":1,"98":2,"99":1,"100":1,"101":1,"104":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":{"35":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,"89":3,"91":4,"92":2,"98":4,"99":2,"100":1,"101":1,"102":4,"104":1,"112":1}}],["list",{"2":{"34":8,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"89":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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,"37":1}}],["高阶偏导",{"2":{"34":1}}],["可愛くてごめん",{"2":{"158":1}}],["可参考函数式编程",{"2":{"38":1}}],["可直接从mbcp",{"2":{"35":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"91":9,"128":4,"156":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":{"54":1,"126":1}}],["none",{"0":{"56":1,"100":1,"101":1},"2":{"56":3,"100":1,"101":1,"102":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,"38":1}}],["|",{"0":{"33":1,"34":1,"44":1,"56":2,"89":1,"90":1,"100":1,"101":1,"143":2},"2":{"33":1,"34":1,"44":2,"56":4,"59":1,"60":1,"63":1,"66":1,"69":1,"72":1,"75":1,"82":1,"89":2,"90":2,"100":1,"101":1,"102":3,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"35":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":1},"2":{"98":1,"125":1}}],["z=0",{"2":{"91":1}}],["z系数",{"2":{"87":1}}],["z0",{"2":{"37":2}}],["zip",{"2":{"33":1}}],["z函数",{"2":{"32":1}}],["z",{"0":{"32":1,"78":1,"120":1,"151":1},"2":{"32":4,"33":4,"37":7,"48":2,"54":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":1}}],["y轴分量",{"2":{"120":1}}],["y=0",{"2":{"91":1}}],["y系数",{"2":{"87":1}}],["y0",{"2":{"37":2}}],["y函数",{"2":{"32":1}}],["y",{"0":{"32":1,"78":1,"115":1,"120":1,"150":1},"2":{"32":4,"33":4,"37":7,"48":2,"54":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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}}],["x0",{"2":{"37":2}}],["x函数",{"2":{"32":1}}],["x",{"0":{"32":1,"78":1,"109":1,"115":1,"116":1,"117":1,"120":1,"149":1},"2":{"32":4,"33":4,"37":7,"48":2,"54":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"87":1,"88":3,"90":2,"91":9,"92":1,"102":1,"115":1,"116":2,"117":3,"148":3,"149":2,"150":2,"151":2,"156":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}}],["π",{"2":{"24":1}}],["to",{"2":{"160":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"92":2,"160":1}}],["three",{"0":{"97":1},"2":{"97":1}}],["threevarsfunc",{"0":{"72":1}}],["threearraysfunc",{"0":{"71":1},"2":{"72":1}}],["threesinglevarsfunc",{"0":{"37":1,"70":1},"2":{"37":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,"89":2,"90":2,"102":2,"113":1,"134":1,"139":1,"140":1,"143":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,"89":2,"90":2,"102":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":2,"148":1,"149":1,"150":1,"151":1}}],["twovarsfunc",{"0":{"69":1}}],["twoarraysfunc",{"0":{"68":1},"2":{"69":1}}],["twosinglevarsfunc",{"0":{"67":1},"2":{"69":1}}],["two",{"0":{"55":1,"98":1},"2":{"55":1,"98":1}}],["tip",{"2":{"37":1,"38":1,"89":2,"91":1,"122":1,"123":1,"127":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,"92":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["ep",{"2":{"158":1}}],["epsilon",{"0":{"28":1,"34":2,"37":2,"42":1,"49":1,"79":1,"115":1,"121":1,"124":1},"2":{"34":6,"37":11,"42":4,"49":3,"79":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["examples",{"2":{"38":1}}],["exp",{"2":{"25":1}}],["elif",{"2":{"34":1,"44":3,"56":1,"88":2,"89":1,"90":1,"91":2,"102":1,"112":1,"116":1,"117":1,"134":1,"139":1,"143":1}}],["else",{"2":{"4":1,"33":1,"34":1,"44":2,"56":1,"88":1,"89":1,"90":1,"102":1,"112":2,"116":2,"117":2,"134":1,"139":1,"140":1,"143":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"48":1},"2":{"48":1,"92":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"2":{"17":1,"57":1,"83":1,"103":1,"112":1,"114":1,"135":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"80":1,"81":1,"82":1,"132":1,"133":1,"134":1,"136":1},"2":{"16":1,"26":1,"37":3,"38":2,"45":1,"47":1,"48":3,"82":5,"87":3,"90":5,"92":5,"107":3,"116":2,"117":2,"129":2,"134":9,"136":4,"145":2,"156":1}}],["1e",{"0":{"49":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"38":1,"98":1,"117":3,"149":1,"150":1,"151":1,"156":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":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"37":3,"38":1,"45":1,"90":3,"107":3,"129":3,"156":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,"37":1,"38":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,"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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"160":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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,"37":2,"38":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":2,"82":2,"83":2,"84":2,"88":5,"89":3,"90":3,"91":2,"92":2,"93":2,"94":2,"95":2,"96":2,"97":2,"98":2,"99":2,"102":5,"103":2,"104":1,"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":2,"131":1,"134":3,"135":2,"136":2,"139":3,"140":2,"143":3,"144":1,"145":2,"146":1,"147":2,"156":2}}],["range",{"2":{"156":2}}],["rand",{"2":{"104":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":1}}],["raise",{"0":{"113":1},"2":{"34":1,"44":1,"45":2,"89":1,"90":1,"91":1,"92":1,"102":1,"112":2,"113":2,"134":1,"139":1,"140":1,"143":1}}],["raises",{"2":{"34":1,"44":1,"45":1,"89":1,"90":1,"91":1,"92":1,"102":1}}],["ratio",{"0":{"26":1}}],["geometricmodels",{"0":{"155":1},"1":{"156":1}}],["get",{"0":{"34":1,"47":1,"48":1},"2":{"34":2,"47":1,"48":1,"92":1,"98":1}}],["gradient",{"0":{"37":1},"2":{"37":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,"37":1,"38":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,"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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"82":2,"84":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"37":1,"38":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,"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,"147":1,"156":1}}],["operand",{"2":{"102":1,"134":1,"139":1,"140":1,"143":1}}],["overload",{"2":{"19":1,"20":2,"21":1,"79":1,"80":2,"81":1,"99":1,"100":2,"101":1,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"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,"127":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":{"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":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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["one",{"2":{"158":1}}],["onearrayfunc",{"0":{"65":1},"2":{"66":1}}],["onesinglevarfunc",{"0":{"48":3,"64":1},"2":{"48":6,"66":1}}],["onevarfunc",{"0":{"32":3,"38":1,"66":1},"2":{"32":6,"38":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,"37":1,"38":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,"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,"147":1,"156":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,"37":1,"38":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":1,"84":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":2,"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,"147":1,"156":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,"151":1},"2":{"84":1}}],["vector3",{"0":{"37":1,"41":1,"80":1,"84":1,"95":1,"96":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":1},"2":{"35":1,"37":2,"41":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":2}}],["v2",{"2":{"57":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":{"57":2,"97":2,"98":2,"123":1}}],["v",{"2":{"34":2,"82":1,"84":2,"134":4,"136":1,"139":4,"140":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":1,"38":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,"148":1,"149":1,"150":1,"151":1},"2":{"33":1,"34":12,"38":4}}],["valueerror",{"2":{"34":2,"45":4,"91":2,"92":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,"37":1,"38":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,"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,"147":1,"156":1}}],["can",{"2":{"158":1}}],["cal",{"0":{"37":1,"43":1,"44":1,"45":1,"46":1,"89":1,"90":1,"91":1,"92":1,"93":1,"122":1},"2":{"37":1,"43":2,"44":1,"45":1,"46":1,"56":1,"89":2,"90":1,"91":1,"92":1,"93":1,"102":2,"104":1,"122":1}}],["callable",{"2":{"64":1,"65":1,"67":1,"68":1,"70":1,"71":1,"73":1,"74":1}}],["call",{"2":{"33":1}}],["cz",{"2":{"87":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":1}}],["classmethod",{"2":{"54":1,"55":1,"95":1,"96":2,"97":2,"98":2,"99":1}}],["class",{"0":{"2":1,"3":1,"31":1,"40":1,"77":1,"86":1,"106":1,"110":1,"119":1,"155":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,"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,"147":1,"156":1}}],["cls",{"0":{"55":1,"96":1,"97":1,"98":1,"99":1},"2":{"55":2,"96":2,"97":2,"98":2,"99":2}}],["cross",{"0":{"123":1},"2":{"44":4,"45":3,"46":1,"53":1,"91":1,"97":1,"98":1,"123":1,"124":1,"125":1}}],["c",{"0":{"87":1},"2":{"38":2,"87":4,"88":7,"90":2,"91":6,"92":2,"95":1,"96":3}}],["curried",{"2":{"38":4}}],["currying",{"2":{"38":1}}],["curry",{"0":{"38":1},"2":{"38":2}}],["curveequation",{"0":{"31":1},"1":{"32":1,"33":1},"2":{"35":1}}],["csc",{"0":{"15":1},"2":{"15":1}}],["coincident",{"2":{"92":1}}],["complex",{"2":{"60":1}}],["complementary",{"0":{"5":1},"2":{"5":1,"89":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,"156":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,"37":1,"38":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,"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,"147":1,"156":1}}],["sphere",{"0":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"102":1,"134":1,"139":1,"140":1,"143":1}}],["solve",{"2":{"91":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,"37":1,"38":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,"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,"147":1,"156":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"84":1,"137":1,"138":1,"139":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":{"35":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,"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,"147":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":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["默认为否",{"2":{"4":1}}],["acos",{"2":{"89":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"87":1}}],["all",{"2":{"79":1,"112":1,"121":1}}],["amp",{"0":{"56":1,"100":1,"101":1,"102":1,"104":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"91":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":2}}],["are",{"2":{"45":2,"91":1,"92":1}}],["args2",{"2":{"38":2}}],["args",{"0":{"38":1},"2":{"34":11,"38":3}}],["arguments",{"2":{"4":1,"32":1,"33":1,"34":1,"37":1,"38":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,"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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":1}}],["abs",{"0":{"131":1},"2":{"44":1,"79":3,"90":1,"112":1,"115":1,"117":1,"121":3,"131":1}}],["a",{"0":{"87":1},"2":{"38":2,"87":4,"88":7,"90":2,"91":12,"92":2,"95":1,"96":3}}],["aaa",{"2":{"36":1}}],["approx",{"0":{"29":1,"42":2,"49":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,"42":3,"49":2,"79":1,"83":3,"88":10,"103":1,"112":4,"115":1,"121":1,"124":1,"125":1,"135":3}}],["add",{"2":{"16":1,"38":4,"80":1,"81":1,"82":1,"132":1,"133":1,"134":1}}],["and",{"0":{"96":1,"99":1},"2":{"42":1,"45":2,"51":1,"56":1,"57":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,"134":1,"135":2,"139":1,"140":1,"143":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,"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,"35":1,"43":2,"89":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"43":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":{"43":2,"89":2,"122":1}}],["任意角度",{"2":{"4":1,"35":1}}],["f",{"2":{"89":1,"90":1,"102":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":1}}],["from",{"0":{"55":1,"96":1,"97":1,"98":1,"99":1},"2":{"55":1,"84":1,"93":1,"96":1,"97":2,"98":2,"99":2,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"102":1,"134":1,"139":1,"140":1,"143":1,"156":2}}],["function",{"0":{"36":1},"1":{"37":1,"38":1}}],["func",{"0":{"32":3,"34":3,"37":2,"38":2,"109":1,"115":1,"116":1,"117":1},"2":{"32":12,"33":6,"34":15,"37":8,"38":5}}],["false",{"0":{"4":1,"116":1,"117":1},"2":{"88":1}}],["float=0",{"2":{"115":1}}],["float=1e",{"2":{"49":1}}],["float=approx",{"2":{"42":1,"79":1,"115":1,"121":1,"124":1}}],["float=epsilon",{"2":{"37":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,"37":1,"42":1,"44":1,"49":1,"78":3,"79":1,"87":4,"90":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"129":1,"143":1,"156":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":6,"79":1,"87":8,"90":2,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"129":2,"143":3,"145":1,"156":2}}],["=u⋅v|v|2⋅v",{"2":{"127":1}}],["==",{"0":{"17":1,"57":1,"83":1,"103":1,"112":1,"135":1},"2":{"33":1,"44":1,"53":1,"54":3,"92":1,"98":1,"102":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"37":1,"42":1,"49":1,"56":1,"57":1,"79":1,"80":1,"81":1,"84":1,"100":1,"101":1,"103":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"4":2,"32":3,"34":5,"37":4,"38":1,"41":2,"54":3,"55":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,"156":7}}],["improve",{"2":{"160":1}}],["import",{"2":{"84":1}}],["i",{"2":{"156":4,"158":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"45":2}}],["intersection",{"0":{"45":1,"91":1,"92":1},"2":{"45":1,"56":1,"91":2,"92":1,"102":2,"104":1}}],["int",{"0":{"34":2,"143":1},"2":{"34":3,"38":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":2}}],["init",{"0":{"4":1,"32":1,"41":1,"78":1,"87":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"41":1,"78":1,"87":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,"88":1,"89":1,"90":1,"91":2,"92":1,"98":1,"102":3,"112":3,"116":2,"117":2,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"89":2,"90":2,"102":2,"112":4,"134":2,"139":2,"140":1,"143":2}}],["is",{"0":{"4":1,"49":1,"50":1,"51":1,"52":1,"53":1,"94":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,"89":1,"91":1,"94":2,"102":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"156":5}}],["p3",{"0":{"97":1},"2":{"97":3}}],["p2",{"0":{"55":1,"97":1,"107":1},"2":{"55":3,"57":1,"97":3,"107":8}}],["p1",{"0":{"55":1,"97":1,"107":1},"2":{"55":4,"57":1,"97":5,"107":8}}],["perpendicular",{"0":{"46":1},"2":{"46":1}}],["parametric",{"0":{"48":1},"2":{"48":1,"92":1}}],["parallel",{"0":{"49":1,"50":1,"93":1,"94":1,"124":1,"125":1},"2":{"42":2,"44":1,"45":2,"49":2,"50":2,"51":2,"52":1,"56":1,"57":2,"91":2,"92":1,"93":1,"94":2,"102":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"152":1},"2":{"0":1}}],["p",{"0":{"37":1},"2":{"37":20,"82":5,"84":4,"134":2,"136":2,"139":2,"140":2}}],["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":{"35":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":{"34":3}}],["points",{"0":{"55":1,"97":1},"2":{"55":1,"97":1}}],["point",{"0":{"41":1,"46":1,"47":1,"52":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":{"41":4,"42":2,"44":5,"45":3,"46":5,"47":2,"48":3,"51":2,"52":5,"53":2,"54":3,"57":2,"92":3,"93":4,"96":6,"97":1,"98":6,"99":5}}],["point3",{"0":{"33":2,"37":1,"41":1,"44":1,"45":1,"46":1,"47":1,"52":1,"55":2,"56":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,"133":2,"136":2,"138":2,"140":1},"1":{"78":1,"79":1,"80":1,"81":1,"82":1,"83":1,"84":1},"2":{"33":4,"35":1,"37":2,"41":2,"44":3,"45":2,"46":2,"47":2,"52":2,"55":4,"56":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"80":1,"81":1,"95":1,"96":1,"97":1,"98":1,"99":1,"100":1,"101":1,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["pythondef",{"2":{"4":1,"16":1,"17":1,"18":1,"19":1,"22":1,"32":1,"33":1,"34":1,"37":1,"38":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,"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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["practice",{"0":{"157":1},"1":{"158":1}}],["projv",{"2":{"127":2}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":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":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["module",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"36":1,"39":1,"58":1,"76":1,"85":1,"105":1,"108":1,"118":1,"152":1,"153":1,"154":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,"37":1,"38":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,"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,"151":1,"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"38":1,"75":1},"2":{"34":3,"38":2}}],["mul",{"2":{"19":1,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":1}}],["math导入使用",{"2":{"35":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"36":1,"39":1,"58":2,"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,"33":1,"34":1,"37":1,"38":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,"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,"151":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,"129":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,"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,"147":1,"156":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"36":1,"39":1,"58":2,"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,"33":1,"34":1,"37":1,"38":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,"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,"151":1},"2":{"0":1,"35":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"36":1,"39":1,"58":1,"76":1,"85":1,"105":1,"108":1,"118":1,"152":1,"153":1,"154":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,"37":1,"38":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,"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,"151":1,"155":1,"156":1},"2":{"0":3}}]],"serializationVersion":2}';export{t as default}; diff --git a/assets/chunks/@localSearchIndexja.BCRaXGU0.js b/assets/chunks/@localSearchIndexja.BCRaXGU0.js deleted file mode 100644 index 43999ca..0000000 --- a/assets/chunks/@localSearchIndexja.BCRaXGU0.js +++ /dev/null @@ -1 +0,0 @@ -const t='{"documentCount":161,"nextId":161,"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-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-1","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-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-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-self-other-bool","95":"/ja/api/mp_math/plane.html#method-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-self-other-1","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-self-other","113":"/ja/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/ja/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/ja/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/ja/api/mp_math/vector.html#method-length-self-float","130":"/ja/api/mp_math/vector.html#method-unit-self-vector3","131":"/ja/api/mp_math/vector.html#method-abs-self","132":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/ja/api/mp_math/vector.html#method-self-other-point3-point3","134":"/ja/api/mp_math/vector.html#method-self-other","135":"/ja/api/mp_math/vector.html#method-self-other-1","136":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/ja/api/mp_math/vector.html#method-self-other-2","140":"/ja/api/mp_math/vector.html#method-self-other-point3","141":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/ja/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/ja/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/ja/api/mp_math/vector.html#method-self-vector3","148":"/ja/api/mp_math/vector.html#var-zero-vector3","149":"/ja/api/mp_math/vector.html#var-x-axis","150":"/ja/api/mp_math/vector.html#var-y-axis","151":"/ja/api/mp_math/vector.html#var-z-axis","152":"/ja/api/particle/#モジュール-mbcp-particle","153":"/ja/api/presets/#モジュール-mbcp-presets","154":"/ja/api/presets/model/#モジュール-mbcp-presets-model","155":"/ja/api/presets/model/#class-geometricmodels","156":"/ja/api/presets/model/#method-sphere-radius-float-density-float","157":"/ja/demo/best-practice.html#ベストプラクティス","158":"/ja/demo/best-practice.html#作品","159":"/ja/guide/#开始不了一点","160":"/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":[4,9,11],"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":[7,7,28],"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":[7,7,19],"95":[8,7,15],"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":[4,7,22],"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":[4,7,31],"113":[7,7,15],"114":[4,7,11],"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":[4,7,16],"127":[6,7,18],"128":[6,7,18],"129":[5,7,23],"130":[5,7,17],"131":[4,7,10],"132":[7,7,12],"133":[7,7,12],"134":[4,7,37],"135":[4,7,22],"136":[7,7,25],"137":[6,7,12],"138":[6,7,12],"139":[3,7,36],"140":[4,7,35],"141":[6,7,12],"142":[7,7,13],"143":[9,7,39],"144":[7,7,13],"145":[7,7,23],"146":[7,7,15],"147":[5,7,17],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,46],"157":[1,1,1],"158":[1,1,25],"159":[1,1,2],"160":[1,1,7]},"averageFieldLength":[5.745341614906832,5.931677018633538,17.881987577639762],"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 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 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 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 self == other => bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method 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 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 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 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 project(self, other: Vector3) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["モジュール mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["モジュール mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["モジュール mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["モジュール mbcp.mp_math.vector"]},"152":{"title":"モジュール mbcp.particle","titles":[]},"153":{"title":"モジュール mbcp.presets","titles":[]},"154":{"title":"モジュール mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["モジュール mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["モジュール mbcp.presets.model","class GeometricModels"]},"157":{"title":"ベストプラクティス","titles":[]},"158":{"title":"作品","titles":["ベストプラクティス"]},"159":{"title":"开始不了一点","titles":[]},"160":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"159":1}}],["开始不了一点",{"0":{"159":1}}],["红石音乐",{"2":{"158":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["作品",{"0":{"158":1}}],["ベストプラクティス",{"0":{"157":1},"1":{"158":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":1}}],["投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"160":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"160":1}}],["heart",{"2":{"158":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":{"143":1}}],["数组运算",{"2":{"143":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,"148":1,"149":1,"150":1,"151":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":{"135":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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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,"135":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":{"153":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":{"152":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":{"158":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,"135":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":{"160":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":{"156":1},"2":{"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":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,"151":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,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":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,"134":4,"136":1,"139":4,"140":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,"148":1,"149":1,"150":1,"151":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,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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,"143":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,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"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,"115":3,"120":4,"121":2,"123":4,"126":1,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"148":3,"149":2,"150":2,"151":2,"156":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,"148":1,"149":1,"150":1,"151":1}}],["π",{"2":{"24":1}}],["to",{"2":{"160":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"160":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,"134":1,"139":1,"140":1,"143":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":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,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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":{"158":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,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"127":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":{"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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["ep",{"2":{"158":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,"134":1,"139":1,"143":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,"134":1,"139":1,"140":1,"143":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",{"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1,"95":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"131":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":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,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":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,"134":1,"135":2,"139":1,"140":1,"143":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,"132":1,"133":1,"134":1,"136":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,"129":2,"134":9,"136":4,"145":2,"156":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,"149":1,"150":1,"151":1,"156":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":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"147":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["255万个粒子",{"2":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"129":3,"156":2}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"160":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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,"131":1,"134":2,"135":1,"136":1,"139":2,"140":1,"143":2,"144":1,"145":1,"146":1,"147":1,"156":1}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":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,"134":1,"139":1,"140":1,"143":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"156":1}}],["geometricmodels",{"0":{"155":1},"1":{"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"147":1,"156":1}}],["can",{"2":{"158":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",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":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,"155":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,"147":1,"156":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,"156":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,"147":1,"156":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,"147":1,"156":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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":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,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":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,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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,"129":1,"143":1,"156":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,"129":2,"143":3,"145":1,"156":2}}],["==",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"135":1},"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,"33":1,"34":1,"36":1,"42":1,"49":1,"56":1,"57":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"156":7}}],["improve",{"2":{"160":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":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,"143":1},"2":{"34":3,"37":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":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,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":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":{"156":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":{"152":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,"134":2,"136":2,"139":2,"140":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,"133":2,"136":2,"138":2,"140":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":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,"151":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,"129":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,"147":1,"156":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,"151":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1}}]],"serializationVersion":2}';export{t as default}; diff --git a/assets/chunks/@localSearchIndexja.COlRHLLs.js b/assets/chunks/@localSearchIndexja.COlRHLLs.js new file mode 100644 index 0000000..b8bb0ce --- /dev/null +++ b/assets/chunks/@localSearchIndexja.COlRHLLs.js @@ -0,0 +1 @@ +const t='{"documentCount":161,"nextId":161,"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-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-1","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-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-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-self-other-bool","95":"/ja/api/mp_math/plane.html#method-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-self-other-1","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-self-other","113":"/ja/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/ja/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/ja/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/ja/api/mp_math/vector.html#method-length-self-float","130":"/ja/api/mp_math/vector.html#method-unit-self-vector3","131":"/ja/api/mp_math/vector.html#method-abs-self","132":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/ja/api/mp_math/vector.html#method-self-other-point3-point3","134":"/ja/api/mp_math/vector.html#method-self-other","135":"/ja/api/mp_math/vector.html#method-self-other-1","136":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/ja/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/ja/api/mp_math/vector.html#method-self-other-2","140":"/ja/api/mp_math/vector.html#method-self-other-point3","141":"/ja/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/ja/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/ja/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/ja/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/ja/api/mp_math/vector.html#method-self-vector3","148":"/ja/api/mp_math/vector.html#var-zero-vector3","149":"/ja/api/mp_math/vector.html#var-x-axis","150":"/ja/api/mp_math/vector.html#var-y-axis","151":"/ja/api/mp_math/vector.html#var-z-axis","152":"/ja/api/particle/#モジュール-mbcp-particle","153":"/ja/api/presets/#モジュール-mbcp-presets","154":"/ja/api/presets/model/#モジュール-mbcp-presets-model","155":"/ja/api/presets/model/#class-geometricmodels","156":"/ja/api/presets/model/#method-sphere-radius-float-density-float","157":"/ja/demo/best-practice.html#ベストプラクティス","158":"/ja/demo/best-practice.html#作品","159":"/ja/guide/#开始不了一点","160":"/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":[4,9,11],"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":[7,7,28],"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":[7,7,19],"95":[8,7,15],"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":[4,7,22],"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":[4,7,31],"113":[7,7,15],"114":[4,7,11],"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":[4,7,16],"127":[6,7,26],"128":[6,7,18],"129":[5,7,23],"130":[5,7,17],"131":[4,7,10],"132":[7,7,12],"133":[7,7,12],"134":[4,7,37],"135":[4,7,22],"136":[7,7,25],"137":[6,7,12],"138":[6,7,12],"139":[3,7,36],"140":[4,7,35],"141":[6,7,12],"142":[7,7,13],"143":[9,7,39],"144":[7,7,13],"145":[7,7,23],"146":[7,7,15],"147":[5,7,17],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,46],"157":[1,1,1],"158":[1,1,25],"159":[1,1,2],"160":[1,1,7]},"averageFieldLength":[5.745341614906832,5.931677018633538,17.93167701863355],"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 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 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 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 self == other => bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method 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 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 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 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 project(self, other: Vector3) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["モジュール mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["モジュール mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["モジュール mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["モジュール mbcp.mp_math.vector"]},"152":{"title":"モジュール mbcp.particle","titles":[]},"153":{"title":"モジュール mbcp.presets","titles":[]},"154":{"title":"モジュール mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["モジュール mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["モジュール mbcp.presets.model","class GeometricModels"]},"157":{"title":"ベストプラクティス","titles":[]},"158":{"title":"作品","titles":["ベストプラクティス"]},"159":{"title":"开始不了一点","titles":[]},"160":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"159":1}}],["开始不了一点",{"0":{"159":1}}],["红石音乐",{"2":{"158":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["作品",{"0":{"158":1}}],["ベストプラクティス",{"0":{"157":1},"1":{"158":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":1}}],["投影向量",{"2":{"127":1}}],["投影向量计算公式",{"2":{"127":1}}],["表示向量u在向量v上的投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"160":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":1}}],["u",{"2":{"127":2}}],["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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"160":1}}],["heart",{"2":{"158":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":{"143":1}}],["数组运算",{"2":{"143":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,"148":1,"149":1,"150":1,"151":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":{"135":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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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,"135":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":{"153":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":{"152":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":{"158":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,"135":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":{"160":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":{"156":1},"2":{"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":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}}],["计算自向量在另一个向量上的投影向量",{"2":{"127":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,"151":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,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":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,"134":4,"136":1,"139":4,"140":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,"148":1,"149":1,"150":1,"151":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,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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,"143":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,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"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,"115":3,"120":4,"121":2,"123":4,"126":1,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"148":3,"149":2,"150":2,"151":2,"156":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,"148":1,"149":1,"150":1,"151":1}}],["π",{"2":{"24":1}}],["to",{"2":{"160":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"160":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,"134":1,"139":1,"140":1,"143":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":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,"127":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,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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":{"158":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,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"127":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":{"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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["ep",{"2":{"158":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,"134":1,"139":1,"143":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,"134":1,"139":1,"140":1,"143":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",{"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1,"95":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"131":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":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,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":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,"134":1,"135":2,"139":1,"140":1,"143":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,"132":1,"133":1,"134":1,"136":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,"129":2,"134":9,"136":4,"145":2,"156":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,"149":1,"150":1,"151":1,"156":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":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"147":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["255万个粒子",{"2":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"129":3,"156":2}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"160":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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,"131":1,"134":2,"135":1,"136":1,"139":2,"140":1,"143":2,"144":1,"145":1,"146":1,"147":1,"156":1}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":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,"134":1,"139":1,"140":1,"143":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"156":1}}],["geometricmodels",{"0":{"155":1},"1":{"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"147":1,"156":1}}],["can",{"2":{"158":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",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":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,"155":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,"147":1,"156":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,"156":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,"147":1,"156":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,"147":1,"156":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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":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,"127":1,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":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,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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,"129":1,"143":1,"156":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,"129":2,"143":3,"145":1,"156":2}}],["=u⋅v|v|2⋅v",{"2":{"127":1}}],["==",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"135":1},"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,"33":1,"34":1,"36":1,"42":1,"49":1,"56":1,"57":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"156":7}}],["improve",{"2":{"160":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":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,"143":1},"2":{"34":3,"37":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":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,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":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":{"156":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":{"152":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,"134":2,"136":2,"139":2,"140":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,"133":2,"136":2,"138":2,"140":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["projv",{"2":{"127":2}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":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,"151":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,"129":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,"147":1,"156":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,"151":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1}}]],"serializationVersion":2}';export{t as default}; diff --git a/assets/chunks/@localSearchIndexroot.CVf1h8jm.js b/assets/chunks/@localSearchIndexroot.CVf1h8jm.js deleted file mode 100644 index 06c3955..0000000 --- a/assets/chunks/@localSearchIndexroot.CVf1h8jm.js +++ /dev/null @@ -1 +0,0 @@ -const t='{"documentCount":164,"nextId":164,"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-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-1","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-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-self-other-line3-line3-point3-none","57":"/api/mp_math/line.html#method-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-self-other-bool","95":"/api/mp_math/plane.html#method-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-self-other-1","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-self-other","113":"/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/api/mp_math/vector.html#method-length-self-float","130":"/api/mp_math/vector.html#method-unit-self-vector3","131":"/api/mp_math/vector.html#method-abs-self","132":"/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/api/mp_math/vector.html#method-self-other-point3-point3","134":"/api/mp_math/vector.html#method-self-other","135":"/api/mp_math/vector.html#method-self-other-1","136":"/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/api/mp_math/vector.html#method-self-other-2","140":"/api/mp_math/vector.html#method-self-other-point3","141":"/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/api/mp_math/vector.html#method-self-vector3","148":"/api/mp_math/vector.html#var-zero-vector3","149":"/api/mp_math/vector.html#var-x-axis","150":"/api/mp_math/vector.html#var-y-axis","151":"/api/mp_math/vector.html#var-z-axis","152":"/api/particle/#模块-mbcp-particle","153":"/api/presets/#模块-mbcp-presets","154":"/api/presets/model/#模块-mbcp-presets-model","155":"/api/presets/model/#class-geometricmodels","156":"/api/presets/model/#method-sphere-radius-float-density-float","157":"/demo/best-practice.html#最佳实践","158":"/demo/best-practice.html#作品","159":"/demo/#demo","160":"/guide/#快速开始","161":"/guide/#安装","162":"/refer/7-differential-euqtion/#微分方程","163":"/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":[4,9,11],"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":[10,7,34],"57":[7,7,28],"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":[7,7,19],"95":[8,7,15],"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":[4,7,22],"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":[4,7,31],"113":[7,7,15],"114":[4,7,11],"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":[4,7,16],"127":[6,7,18],"128":[6,7,18],"129":[5,7,23],"130":[5,7,17],"131":[4,7,10],"132":[7,7,12],"133":[7,7,12],"134":[4,7,37],"135":[4,7,22],"136":[7,7,25],"137":[6,7,12],"138":[6,7,12],"139":[3,7,36],"140":[4,7,35],"141":[6,7,12],"142":[7,7,13],"143":[9,7,39],"144":[7,7,13],"145":[7,7,23],"146":[7,7,15],"147":[5,7,17],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,46],"157":[1,1,1],"158":[1,1,25],"159":[1,1,1],"160":[1,1,6],"161":[1,1,4],"162":[1,1,1],"163":[1,1,7]},"averageFieldLength":[5.658536585365853,5.841463414634144,17.603658536585368],"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 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 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 self & other: Line3 => Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"57":{"title":"method 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 self == other => bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method 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 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 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 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 project(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["模块 mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["模块 mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["模块 mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["模块 mbcp.mp_math.vector"]},"152":{"title":"模块 mbcp.particle","titles":[]},"153":{"title":"模块 mbcp.presets","titles":[]},"154":{"title":"模块 mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["模块 mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["模块 mbcp.presets.model","class GeometricModels"]},"157":{"title":"最佳实践","titles":[]},"158":{"title":"作品","titles":["最佳实践"]},"159":{"title":"demo","titles":[]},"160":{"title":"快速开始","titles":[]},"161":{"title":"安装","titles":["快速开始"]},"162":{"title":"微分方程","titles":[]},"163":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["微分方程",{"0":{"162":1}}],["安装",{"0":{"161":1}}],["兼容性优先",{"2":{"160":1}}],["把你项目所使用的python换成pypy",{"2":{"160":1}}],["建议",{"2":{"160":1}}],["快速开始",{"0":{"160":1},"1":{"161":1}}],["红石音乐",{"2":{"158":1}}],["这样可以提高性能",{"2":{"160":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["作品",{"0":{"158":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1}}],["投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"163":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"163":1}}],["heart",{"2":{"158":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":{"143":1}}],["数组运算",{"2":{"143":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,"148":1,"149":1,"150":1,"151":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":{"135":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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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,"135":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":{"153":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":{"152":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":{"158":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,"135":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":{"163":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":{"159":1}}],["density",{"0":{"156":1},"2":{"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":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,"151":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,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":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,"134":4,"136":1,"139":4,"140":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,"148":1,"149":1,"150":1,"151":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,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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,"143":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,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"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,"115":3,"120":4,"121":2,"123":4,"126":1,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"148":3,"149":2,"150":2,"151":2,"156":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":{"155":1},"1":{"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"148":1,"149":1,"150":1,"151":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"163":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"163":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,"134":1,"139":1,"140":1,"143":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":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,"160":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,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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":{"158":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,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"127":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":{"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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["ep",{"2":{"158":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,"134":1,"139":1,"143":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,"134":1,"139":1,"140":1,"143":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",{"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1,"95":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"131":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":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,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":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,"134":1,"135":2,"139":1,"140":1,"143":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,"132":1,"133":1,"134":1,"136":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,"129":2,"134":9,"136":4,"145":2,"156":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,"149":1,"150":1,"151":1,"156":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":{"157":1},"1":{"158":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":{"161":1}}],["sphere",{"0":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"147":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["255万个粒子",{"2":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"129":3,"156":2}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"163":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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,"131":1,"134":2,"135":1,"136":1,"139":2,"140":1,"143":2,"144":1,"145":1,"146":1,"147":1,"156":1}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":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,"134":1,"139":1,"140":1,"143":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"156":1}}],["can",{"2":{"158":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",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":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,"155":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,"147":1,"156":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,"156":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,"147":1,"156":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,"147":1,"156":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,"147":1,"156":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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":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,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":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,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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,"129":1,"143":1,"156":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,"129":2,"143":3,"145":1,"156":2}}],["==",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"135":1},"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,"33":1,"34":1,"36":1,"42":1,"49":1,"56":1,"57":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"156":7}}],["improve",{"2":{"163":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":1}}],["install",{"2":{"161":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,"143":1},"2":{"34":3,"37":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":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,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":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":{"156":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":{"152":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,"134":2,"136":2,"139":2,"140":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,"133":2,"136":2,"138":2,"140":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":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,"151":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,"129":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,"147":1,"156":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,"151":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1},"2":{"0":3,"161":1}}],["提供了一些工具",{"2":{"0":1}}]],"serializationVersion":2}';export{t as default}; diff --git a/assets/chunks/@localSearchIndexroot.xPvxH6jA.js b/assets/chunks/@localSearchIndexroot.xPvxH6jA.js new file mode 100644 index 0000000..3c03936 --- /dev/null +++ b/assets/chunks/@localSearchIndexroot.xPvxH6jA.js @@ -0,0 +1 @@ +const t='{"documentCount":164,"nextId":164,"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-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-1","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-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/mp_math_typing.html#模块-mbcp-mp-math-mp-math-typing","40":"/api/mp_math/mp_math_typing.html#var-realnumber","41":"/api/mp_math/mp_math_typing.html#var-number","42":"/api/mp_math/mp_math_typing.html#var-singlevar","43":"/api/mp_math/mp_math_typing.html#var-arrayvar","44":"/api/mp_math/mp_math_typing.html#var-var","45":"/api/mp_math/mp_math_typing.html#var-onesinglevarfunc","46":"/api/mp_math/mp_math_typing.html#var-onearrayfunc","47":"/api/mp_math/mp_math_typing.html#var-onevarfunc","48":"/api/mp_math/mp_math_typing.html#var-twosinglevarsfunc","49":"/api/mp_math/mp_math_typing.html#var-twoarraysfunc","50":"/api/mp_math/mp_math_typing.html#var-twovarsfunc","51":"/api/mp_math/mp_math_typing.html#var-threesinglevarsfunc","52":"/api/mp_math/mp_math_typing.html#var-threearraysfunc","53":"/api/mp_math/mp_math_typing.html#var-threevarsfunc","54":"/api/mp_math/mp_math_typing.html#var-multisinglevarsfunc","55":"/api/mp_math/mp_math_typing.html#var-multiarraysfunc","56":"/api/mp_math/mp_math_typing.html#var-multivarsfunc","57":"/api/mp_math/line.html#模块-mbcp-mp-math-line","58":"/api/mp_math/line.html#class-line3","59":"/api/mp_math/line.html#method-init-self-point-point3-direction-vector3","60":"/api/mp_math/line.html#method-approx-self-other-line3-epsilon-float-approx-bool","61":"/api/mp_math/line.html#method-cal-angle-self-other-line3-anyangle","62":"/api/mp_math/line.html#method-cal-distance-self-other-line3-point3-float","63":"/api/mp_math/line.html#method-cal-intersection-self-other-line3-point3","64":"/api/mp_math/line.html#method-cal-perpendicular-self-point-point3-line3","65":"/api/mp_math/line.html#method-get-point-self-t-realnumber-point3","66":"/api/mp_math/line.html#method-get-parametric-equations-self-tuple-onesinglevarfunc-onesinglevarfunc-onesinglevarfunc","67":"/api/mp_math/line.html#method-is-approx-parallel-self-other-line3-epsilon-float-1e-06-bool","68":"/api/mp_math/line.html#method-is-parallel-self-other-line3-bool","69":"/api/mp_math/line.html#method-is-collinear-self-other-line3-bool","70":"/api/mp_math/line.html#method-is-point-on-self-point-point3-bool","71":"/api/mp_math/line.html#method-is-coplanar-self-other-line3-bool","72":"/api/mp_math/line.html#method-simplify-self","73":"/api/mp_math/line.html#method-from-two-points-cls-p1-point3-p2-point3-line3","74":"/api/mp_math/line.html#method-self-other-line3-line3-point3-none","75":"/api/mp_math/line.html#method-self-other-bool","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-self-other-bool","95":"/api/mp_math/plane.html#method-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-self-other-1","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-self-other","113":"/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/api/mp_math/vector.html#method-length-self-float","130":"/api/mp_math/vector.html#method-unit-self-vector3","131":"/api/mp_math/vector.html#method-abs-self","132":"/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/api/mp_math/vector.html#method-self-other-point3-point3","134":"/api/mp_math/vector.html#method-self-other","135":"/api/mp_math/vector.html#method-self-other-1","136":"/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/api/mp_math/vector.html#method-self-other-2","140":"/api/mp_math/vector.html#method-self-other-point3","141":"/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/api/mp_math/vector.html#method-self-vector3","148":"/api/mp_math/vector.html#var-zero-vector3","149":"/api/mp_math/vector.html#var-x-axis","150":"/api/mp_math/vector.html#var-y-axis","151":"/api/mp_math/vector.html#var-z-axis","152":"/api/particle/#模块-mbcp-particle","153":"/api/presets/#模块-mbcp-presets","154":"/api/presets/model/#模块-mbcp-presets-model","155":"/api/presets/model/#class-geometricmodels","156":"/api/presets/model/#method-sphere-radius-float-density-float","157":"/demo/best-practice.html#最佳实践","158":"/demo/best-practice.html#作品","159":"/demo/#demo","160":"/guide/#快速开始","161":"/guide/#安装","162":"/refer/7-differential-euqtion/#微分方程","163":"/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":[4,9,11],"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":[2,5,9],"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":[10,7,34],"75":[7,7,28],"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":[7,7,19],"95":[8,7,15],"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":[4,7,22],"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":[4,7,31],"113":[7,7,15],"114":[4,7,11],"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":[4,7,16],"127":[6,7,26],"128":[6,7,18],"129":[5,7,23],"130":[5,7,17],"131":[4,7,10],"132":[7,7,12],"133":[7,7,12],"134":[4,7,37],"135":[4,7,22],"136":[7,7,25],"137":[6,7,12],"138":[6,7,12],"139":[3,7,36],"140":[4,7,35],"141":[6,7,12],"142":[7,7,13],"143":[9,7,39],"144":[7,7,13],"145":[7,7,23],"146":[7,7,15],"147":[5,7,17],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,46],"157":[1,1,1],"158":[1,1,25],"159":[1,1,1],"160":[1,1,6],"161":[1,1,4],"162":[1,1,1],"163":[1,1,7]},"averageFieldLength":[5.658536585365853,5.841463414634144,17.652439024390254],"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 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 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.mp_math_typing","titles":[]},"40":{"title":"var RealNumber","titles":["模块 mbcp.mp_math.mp_math_typing"]},"41":{"title":"var Number","titles":["模块 mbcp.mp_math.mp_math_typing"]},"42":{"title":"var SingleVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"43":{"title":"var ArrayVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"44":{"title":"var Var","titles":["模块 mbcp.mp_math.mp_math_typing"]},"45":{"title":"var OneSingleVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"46":{"title":"var OneArrayFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"47":{"title":"var OneVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"48":{"title":"var TwoSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"49":{"title":"var TwoArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"50":{"title":"var TwoVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"51":{"title":"var ThreeSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"52":{"title":"var ThreeArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"53":{"title":"var ThreeVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"54":{"title":"var MultiSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"55":{"title":"var MultiArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"56":{"title":"var MultiVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"57":{"title":"模块 mbcp.mp_math.line","titles":[]},"58":{"title":"class Line3","titles":["模块 mbcp.mp_math.line"]},"59":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模块 mbcp.mp_math.line","class Line3"]},"60":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"61":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模块 mbcp.mp_math.line","class Line3"]},"62":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模块 mbcp.mp_math.line","class Line3"]},"63":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"64":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"65":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"66":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模块 mbcp.mp_math.line","class Line3"]},"67":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"68":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"69":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"70":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"71":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"72":{"title":"method simplify(self)","titles":["模块 mbcp.mp_math.line","class Line3"]},"73":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"74":{"title":"method self & other: Line3 => Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"75":{"title":"method self == other => bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"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 self == other => bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method 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 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 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 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 project(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["模块 mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["模块 mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["模块 mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["模块 mbcp.mp_math.vector"]},"152":{"title":"模块 mbcp.particle","titles":[]},"153":{"title":"模块 mbcp.presets","titles":[]},"154":{"title":"模块 mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["模块 mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["模块 mbcp.presets.model","class GeometricModels"]},"157":{"title":"最佳实践","titles":[]},"158":{"title":"作品","titles":["最佳实践"]},"159":{"title":"demo","titles":[]},"160":{"title":"快速开始","titles":[]},"161":{"title":"安装","titles":["快速开始"]},"162":{"title":"微分方程","titles":[]},"163":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["微分方程",{"0":{"162":1}}],["安装",{"0":{"161":1}}],["兼容性优先",{"2":{"160":1}}],["把你项目所使用的python换成pypy",{"2":{"160":1}}],["建议",{"2":{"160":1}}],["快速开始",{"0":{"160":1},"1":{"161":1}}],["红石音乐",{"2":{"158":1}}],["这样可以提高性能",{"2":{"160":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["作品",{"0":{"158":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"42":1}}],["模",{"2":{"129":1}}],["模块",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"57":1,"76":1,"96":1,"105":1,"108":1,"118":1,"152":1,"153":1,"154":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,"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,"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,"151":1,"155":1,"156":1}}],["投影向量",{"2":{"127":1}}],["投影向量计算公式",{"2":{"127":1}}],["表示向量u在向量v上的投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"163":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"62":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":1}}],["u",{"2":{"127":2}}],["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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"163":1}}],["heart",{"2":{"158":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":{"72":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":{"74":1}}],["∧",{"2":{"75":1}}],["交线",{"2":{"82":1,"93":1}}],["交线返回交点",{"2":{"74":1}}],["交集",{"2":{"74":1,"93":1}}],["交点",{"2":{"63":1,"83":1}}],["重合线返回自身",{"2":{"74":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":{"73":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":{"59":1}}],["工厂函数",{"2":{"73":1,"87":1,"88":1,"89":1,"90":1}}],["处理",{"2":{"72":1}}],["处的梯度向量为",{"2":{"36":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,"80":1,"81":1,"93":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":{"135":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":{"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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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":{"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":{"36":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,"84":1}}],["直线最终可用参数方程或点向式表示",{"2":{"82":1}}],["直线",{"2":{"73":1,"83":1,"89":2,"90":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,"81":1}}],["夹角",{"2":{"61":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,"135":1}}],["是否等价",{"2":{"75":1,"94":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,"85":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,"99":1,"115":1,"121":1}}],["是否为弧度",{"2":{"4":1}}],["误差",{"2":{"60":1,"67":1,"99":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":{"34":1}}],["变量",{"2":{"44":1}}],["变量位置",{"2":{"34":1}}],["数组运算结果",{"2":{"143":1}}],["数组运算",{"2":{"143":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}}],["类型",{"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,"148":1,"149":1,"150":1,"151":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":{"36":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":{"153":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":{"152":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":{"57":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":{"158":1}}],["by",{"2":{"78":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,"85":1,"94":1,"99":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,"85":2,"94":2,"99":2,"103":1,"115":2,"116":1,"117":1,"121":2,"124":2,"125":2,"135":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":{"163":1}}],["do",{"2":{"63":2}}],["distance",{"0":{"62":1,"81":1},"2":{"62":1,"81":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,"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":{"159":1}}],["density",{"0":{"156":1},"2":{"156":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,"73":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":1}}],["点3",{"2":{"88":1}}],["点法式构造",{"2":{"87":1}}],["点2",{"2":{"73":1,"88":1}}],["点1",{"2":{"73":1,"88":1}}],["点",{"2":{"36":1,"65":1,"70":1}}],["∂f∂z",{"2":{"36":1}}],["∂f∂y",{"2":{"36":1}}],["∂f∂x",{"2":{"36":1}}],["∇f",{"2":{"36":1}}],["计算自向量在另一个向量上的投影向量",{"2":{"127":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":{"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,"151":1},"2":{"104":1}}],["vector3",{"0":{"36":1,"59":1,"86":1,"87":1,"100":1,"104":1,"119":1,"121":1,"122":1,"123":2,"124":1,"125":1,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":1},"2":{"36":2,"38":1,"59":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":2}}],["v2",{"2":{"75":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":{"75":2,"88":2,"89":2,"123":1}}],["v",{"2":{"34":2,"102":1,"104":2,"134":4,"136":1,"139":4,"140":1}}],["var",{"0":{"24":1,"25":1,"26":1,"27":1,"28":1,"29":1,"33":1,"34":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,"148":1,"149":1,"150":1,"151":1},"2":{"33":1,"34":12,"37":4}}],["valueerror",{"2":{"34":2,"63":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":{"66":3}}],["linalg",{"2":{"82":3}}],["lines",{"0":{"89":1},"2":{"63":2,"89":1}}],["line",{"0":{"57":1,"90":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":{"83":1,"90":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,"80":1,"82":2,"83":1,"89":2,"90":1,"91":1,"92":1,"95":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,"80":3,"82":4,"83":2,"89":4,"90":2,"91":1,"92":1,"93":4,"95":1,"112":1}}],["list",{"2":{"34":8,"156":9}}],["length",{"0":{"129":1},"2":{"62":5,"63":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":1}}],["len",{"2":{"33":1}}],["无效变量类型",{"2":{"34":1}}],["引发",{"2":{"34":1,"62":1,"63":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"41":1},"2":{"43":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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":{"72":1,"126":1}}],["none",{"0":{"74":1,"91":1,"92":1},"2":{"74":3,"91":1,"92":1,"93":3}}],["not",{"2":{"62":1,"63":4,"74":1,"114":1,"116":1,"117":1}}],["n元函数",{"2":{"34":1}}],["|",{"0":{"33":1,"34":1,"62":1,"74":2,"80":1,"81":1,"91":1,"92":1,"143":2},"2":{"33":1,"34":1,"40":1,"41":1,"44":1,"47":1,"50":1,"53":1,"56":1,"62":2,"74":4,"80":2,"81":2,"91":1,"92":1,"93":3,"102":1,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":1},"2":{"32":4,"33":4,"36":7,"66":2,"72":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"150":1},"2":{"32":4,"33":4,"36":7,"66":2,"72":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":1},"2":{"32":4,"33":4,"36":7,"66":2,"72":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["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,"33":3,"62":2,"71":1,"72":7,"78":1,"79":3,"81":2,"82":9,"83":1,"93":1,"115":1,"116":2,"117":3,"148":3,"149":2,"150":2,"151":2,"156":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":{"155":1},"1":{"156":1}}],["get",{"0":{"34":1,"65":1,"66":1},"2":{"34":2,"65":1,"66":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,"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,"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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":1}}],["默认值",{"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,"148":1,"149":1,"150":1,"151":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"163":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"163":1}}],["three",{"0":{"88":1},"2":{"88":1}}],["threevarsfunc",{"0":{"53":1}}],["threearraysfunc",{"0":{"52":1},"2":{"53":1}}],["threesinglevarsfunc",{"0":{"36":1,"51":1},"2":{"36":2,"53":1}}],["two",{"0":{"73":1,"89":1},"2":{"73":1,"89":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,"80":2,"81":2,"93":2,"113":1,"134":1,"139":1,"140":1,"143":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":{"34":1,"62":1,"80":2,"81":2,"93":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":2}}],["tip",{"2":{"36":1,"37":1,"80":2,"82":1,"122":1,"123":1,"127":1,"160":1}}],["tuple",{"0":{"33":1,"34":1,"66":1},"2":{"33":2,"34":2,"66":2}}],["t",{"0":{"33":1,"65":1},"2":{"33":9,"65":3,"66":6,"83":4}}],["truediv",{"2":{"20":1,"21":1,"22":1,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":1}}],["or",{"2":{"74":1,"83":1}}],["order",{"2":{"34":2}}],["only",{"0":{"116":1,"117":1},"2":{"116":3,"117":3}}],["on",{"0":{"70":1},"2":{"70":1}}],["one",{"2":{"158":1}}],["onearrayfunc",{"0":{"46":1},"2":{"47":1}}],["onesinglevarfunc",{"0":{"45":1,"66":3},"2":{"47":1,"66":6}}],["onevarfunc",{"0":{"32":3,"37":1,"47":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,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"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,"127":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":{"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":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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["ep",{"2":{"158":1}}],["epsilon",{"0":{"28":1,"34":2,"36":2,"60":1,"67":1,"99":1,"115":1,"121":1,"124":1},"2":{"34":6,"36":11,"60":4,"67":3,"99":5,"115":3,"121":5,"124":3}}],["error",{"0":{"113":1},"2":{"112":2,"113":1}}],["elif",{"2":{"34":1,"62":3,"74":1,"79":2,"80":1,"81":1,"82":2,"93":1,"112":1,"116":1,"117":1,"134":1,"139":1,"143":1}}],["else",{"2":{"4":1,"33":1,"34":1,"62":2,"74":1,"79":1,"80":1,"81":1,"93":1,"112":2,"116":2,"117":2,"134":1,"139":1,"140":1,"143":1}}],["exp",{"2":{"25":1}}],["e",{"0":{"25":1},"2":{"25":1}}],["equations",{"0":{"66":1},"2":{"66":1,"83":1}}],["equation",{"0":{"30":1},"1":{"31":1,"32":1,"33":1,"34":1}}],["eq",{"2":{"17":1,"75":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"74":1,"91":1,"92":1,"93":1,"95":1}}],["abs",{"0":{"131":1},"2":{"62":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"43":1},"2":{"43":1,"44":1,"46":2,"49":3,"52":4,"55":1}}],["area",{"2":{"156":2}}],["are",{"2":{"63":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["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,"60":2,"67":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,"60":3,"67":2,"79":10,"94":1,"99":1,"103":3,"112":4,"115":1,"121":1,"124":1,"125":1,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":1}}],["and",{"0":{"87":1,"90":1},"2":{"60":1,"63":2,"69":1,"74":1,"75":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,"134":1,"135":2,"139":1,"140":1,"143":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,"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,"61":2,"80":3,"122":3}}],["angle",{"0":{"1":1,"2":1,"3":1,"61":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":{"61":2,"80":2,"122":1}}],["+1",{"2":{"117":1}}],["+=",{"2":{"34":1}}],["+",{"0":{"16":1,"100":1,"101":1,"102":1,"132":1,"133":1,"134":1,"136":1},"2":{"16":1,"26":1,"36":3,"37":2,"63":1,"65":1,"66":3,"78":3,"81":5,"83":5,"102":5,"107":3,"116":2,"117":2,"129":2,"134":9,"136":4,"145":2,"156":1}}],["1e",{"0":{"67":1}}],["1",{"2":{"13":1,"14":1,"15":1,"25":1,"26":1,"33":1,"37":1,"89":1,"117":3,"149":1,"150":1,"151":1,"156":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":{"157":1},"1":{"158":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":{"161":1}}],["sphere",{"0":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":1}}],["solve",{"2":{"82":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"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,"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,"147":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,"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":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["255万个粒子",{"2":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"63":1,"81":3,"107":3,"129":3,"156":2}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"163":1}}],["realnumber",{"0":{"40":1,"65":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"41":1,"65":2,"111":2,"142":1,"144":1,"145":1,"146":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,"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":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,"131":1,"134":2,"135":1,"136":1,"139":2,"140":1,"143":2,"144":1,"145":1,"146":1,"147":1,"156":1}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":1}}],["raise",{"0":{"113":1},"2":{"34":1,"62":1,"63":2,"80":1,"81":1,"82":1,"83":1,"93":1,"112":2,"113":2,"134":1,"139":1,"140":1,"143":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,"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,"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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"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,"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,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"156":1}}],["can",{"2":{"158":1}}],["cal",{"0":{"36":1,"61":1,"62":1,"63":1,"64":1,"80":1,"81":1,"82":1,"83":1,"84":1,"122":1},"2":{"36":1,"61":2,"62":1,"63":1,"64":1,"74":1,"80":2,"81":1,"82":1,"83":1,"84":1,"93":2,"95":1,"122":1}}],["callable",{"2":{"45":1,"46":1,"48":1,"49":1,"51":1,"52":1,"54":1,"55":1}}],["call",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":1}}],["classmethod",{"2":{"72":1,"73":1,"86":1,"87":2,"88":2,"89":2,"90":1}}],["class",{"0":{"2":1,"3":1,"31":1,"58":1,"77":1,"97":1,"106":1,"110":1,"119":1,"155":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,"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,"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,"147":1,"156":1}}],["cls",{"0":{"73":1,"87":1,"88":1,"89":1,"90":1},"2":{"73":2,"87":2,"88":2,"89":2,"90":2}}],["cross",{"0":{"123":1},"2":{"62":4,"63":3,"64":1,"71":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}}],["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,"80":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,"156":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,"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,"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,"147":1,"156":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,"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,"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,"147":1,"156":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,"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,"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,"147":1,"156":1}}],["参数方程",{"2":{"66":1}}],["参数t",{"2":{"65":1}}],["参数",{"2":{"4":1,"32":1,"33":2,"34":1,"36":1,"37":2,"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,"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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":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,"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,"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,"127":1,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":1}}],["from",{"0":{"73":1,"87":1,"88":1,"89":1,"90":1},"2":{"73":1,"84":1,"87":1,"88":2,"89":2,"90":2,"104":1,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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":{"67":1}}],["float=approx",{"2":{"60":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,"60":1,"62":1,"67":1,"78":4,"81":1,"98":3,"99":1,"109":4,"115":3,"116":1,"117":1,"120":3,"121":1,"124":1,"129":1,"143":1,"156":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":8,"81":2,"98":6,"99":1,"109":8,"112":2,"115":4,"116":2,"117":2,"120":6,"121":1,"124":1,"129":2,"143":3,"145":1,"156":2}}],["=u⋅v|v|2⋅v",{"2":{"127":1}}],["==",{"0":{"17":1,"75":1,"94":1,"103":1,"112":1,"135":1},"2":{"33":1,"62":1,"71":1,"72":3,"83":1,"89":1,"93":1}}],["=",{"0":{"4":1,"16":1,"18":1,"19":1,"20":1,"21":1,"33":1,"34":1,"36":1,"60":1,"67":1,"74":1,"75":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"4":2,"32":3,"34":5,"36":4,"37":1,"59":2,"72":3,"73":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,"156":7}}],["improve",{"2":{"163":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":1}}],["install",{"2":{"161":1}}],["invalid",{"2":{"34":1}}],["intersect",{"2":{"63":2}}],["intersection",{"0":{"63":1,"82":1,"83":1},"2":{"63":1,"74":1,"82":2,"83":1,"93":2,"95":1}}],["int",{"0":{"34":2,"143":1},"2":{"34":3,"37":4,"40":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":2}}],["init",{"0":{"4":1,"32":1,"59":1,"78":1,"98":1,"107":1,"111":1,"120":1},"2":{"4":1,"32":1,"59":1,"78":1,"98":1,"107":1,"111":1,"120":1}}],["if",{"2":{"4":1,"22":1,"33":1,"34":1,"62":2,"63":2,"72":3,"74":1,"79":1,"80":1,"81":1,"82":2,"83":1,"89":1,"93":3,"112":3,"116":2,"117":2,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"62":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":2}}],["is",{"0":{"4":1,"67":1,"68":1,"69":1,"70":1,"71":1,"85":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,"80":1,"82":1,"85":2,"93":1,"122":1,"124":1,"125":1}}],["预设",{"2":{"0":1}}],["phi",{"2":{"156":5}}],["p3",{"0":{"88":1},"2":{"88":3}}],["p2",{"0":{"73":1,"88":1,"107":1},"2":{"73":3,"75":1,"88":3,"107":8}}],["p1",{"0":{"73":1,"88":1,"107":1},"2":{"73":4,"75":1,"88":5,"107":8}}],["perpendicular",{"0":{"64":1},"2":{"64":1}}],["parametric",{"0":{"66":1},"2":{"66":1,"83":1}}],["parallel",{"0":{"67":1,"68":1,"84":1,"85":1,"124":1,"125":1},"2":{"60":2,"62":1,"63":2,"67":2,"68":2,"69":2,"70":1,"74":1,"75":2,"82":2,"83":1,"84":1,"85":2,"93":1,"124":1,"125":1}}],["partial",{"0":{"34":1},"2":{"34":6}}],["particle",{"0":{"152":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,"134":2,"136":2,"139":2,"140":2}}],["points",{"0":{"73":1,"88":1},"2":{"73":1,"88":1}}],["point",{"0":{"59":1,"64":1,"65":1,"70":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":{"59":4,"60":2,"62":5,"63":3,"64":5,"65":2,"66":3,"69":2,"70":5,"71":2,"72":3,"75":2,"83":3,"84":4,"87":6,"88":1,"89":6,"90":5}}],["point3",{"0":{"33":2,"36":1,"59":1,"62":1,"63":1,"64":1,"65":1,"70":1,"73":2,"74":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,"133":2,"136":2,"138":2,"140":1},"1":{"98":1,"99":1,"100":1,"101":1,"102":1,"103":1,"104":1},"2":{"33":4,"36":2,"38":1,"59":2,"62":3,"63":2,"64":2,"65":2,"70":2,"73":4,"74":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"73":1,"86":1,"87":1,"88":1,"89":1,"90":1,"91":1,"92":1,"100":1,"101":1,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"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,"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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["projv",{"2":{"127":2}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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":{"55":1},"2":{"56":1}}],["multisinglevarsfunc",{"0":{"54":1},"2":{"56":1}}],["multivarsfunc",{"0":{"34":2,"37":1,"56":1},"2":{"34":3,"37":2}}],["mul",{"2":{"19":1,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":1}}],["math导入使用",{"2":{"38":1}}],["math",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":2,"57":1,"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":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,"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,"151":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,"129":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,"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,"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,"147":1,"156":1}}],["mp",{"0":{"1":1,"23":1,"30":1,"35":1,"38":1,"39":2,"57":1,"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":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,"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,"151":1},"2":{"0":1,"38":1}}],["mbcp",{"0":{"0":1,"1":1,"23":1,"30":1,"35":1,"38":1,"39":1,"57":1,"76":1,"96":1,"105":1,"108":1,"118":1,"152":1,"153":1,"154":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,"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,"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,"151":1,"155":1,"156":1},"2":{"0":3,"161":1}}],["提供了一些工具",{"2":{"0":1}}]],"serializationVersion":2}';export{t as default}; diff --git a/assets/chunks/@localSearchIndexzht.Buw3O8cF.js b/assets/chunks/@localSearchIndexzht.Buw3O8cF.js new file mode 100644 index 0000000..c17d07a --- /dev/null +++ b/assets/chunks/@localSearchIndexzht.Buw3O8cF.js @@ -0,0 +1 @@ +const t='{"documentCount":161,"nextId":161,"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-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-1","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-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-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-self-other-bool","95":"/zht/api/mp_math/plane.html#method-self-other-line3-point3","96":"/zht/api/mp_math/point.html#模組-mbcp-mp-math-point","97":"/zht/api/mp_math/point.html#class-point3","98":"/zht/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/zht/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/zht/api/mp_math/point.html#method-self-other-vector3-point3","101":"/zht/api/mp_math/point.html#method-self-other-point3-point3","102":"/zht/api/mp_math/point.html#method-self-other","103":"/zht/api/mp_math/point.html#method-self-other-1","104":"/zht/api/mp_math/point.html#method-self-other-point3-vector3","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-self-other","113":"/zht/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/zht/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/zht/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/zht/api/mp_math/vector.html#method-length-self-float","130":"/zht/api/mp_math/vector.html#method-unit-self-vector3","131":"/zht/api/mp_math/vector.html#method-abs-self","132":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/zht/api/mp_math/vector.html#method-self-other-point3-point3","134":"/zht/api/mp_math/vector.html#method-self-other","135":"/zht/api/mp_math/vector.html#method-self-other-1","136":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/zht/api/mp_math/vector.html#method-self-other-2","140":"/zht/api/mp_math/vector.html#method-self-other-point3","141":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/zht/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/zht/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/zht/api/mp_math/vector.html#method-self-vector3","148":"/zht/api/mp_math/vector.html#var-zero-vector3","149":"/zht/api/mp_math/vector.html#var-x-axis","150":"/zht/api/mp_math/vector.html#var-y-axis","151":"/zht/api/mp_math/vector.html#var-z-axis","152":"/zht/api/particle/#模組-mbcp-particle","153":"/zht/api/presets/#模組-mbcp-presets","154":"/zht/api/presets/model/#模組-mbcp-presets-model","155":"/zht/api/presets/model/#class-geometricmodels","156":"/zht/api/presets/model/#method-sphere-radius-float-density-float","157":"/zht/demo/best-practice.html#最佳實踐","158":"/zht/demo/best-practice.html#作品","159":"/zht/guide/#开始不了一点","160":"/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":[4,9,11],"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":[7,7,28],"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":[7,7,19],"95":[8,7,15],"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":[4,7,22],"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":[4,7,31],"113":[7,7,15],"114":[4,7,11],"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":[4,7,16],"127":[6,7,26],"128":[6,7,18],"129":[5,7,23],"130":[5,7,17],"131":[4,7,10],"132":[7,7,12],"133":[7,7,12],"134":[4,7,37],"135":[4,7,22],"136":[7,7,25],"137":[6,7,12],"138":[6,7,12],"139":[3,7,36],"140":[4,7,35],"141":[6,7,12],"142":[7,7,13],"143":[9,7,39],"144":[7,7,13],"145":[7,7,23],"146":[7,7,15],"147":[5,7,17],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,46],"157":[1,1,1],"158":[1,1,25],"159":[1,1,2],"160":[1,1,7]},"averageFieldLength":[5.745341614906832,5.931677018633538,17.93167701863355],"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 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 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 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 self == other => bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模組 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模組 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模組 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["模組 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模組 mbcp.mp_math.point","class Point3"]},"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 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 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 project(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["模組 mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["模組 mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["模組 mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["模組 mbcp.mp_math.vector"]},"152":{"title":"模組 mbcp.particle","titles":[]},"153":{"title":"模組 mbcp.presets","titles":[]},"154":{"title":"模組 mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["模組 mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["模組 mbcp.presets.model","class GeometricModels"]},"157":{"title":"最佳實踐","titles":[]},"158":{"title":"作品","titles":["最佳實踐"]},"159":{"title":"开始不了一点","titles":[]},"160":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"159":1}}],["开始不了一点",{"0":{"159":1}}],["红石音乐",{"2":{"158":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["作品",{"0":{"158":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":1}}],["模組",{"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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1}}],["投影向量",{"2":{"127":1}}],["投影向量计算公式",{"2":{"127":1}}],["表示向量u在向量v上的投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"160":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":1}}],["u",{"2":{"127":2}}],["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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"160":1}}],["heart",{"2":{"158":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":{"143":1}}],["数组运算",{"2":{"143":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,"148":1,"149":1,"150":1,"151":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":{"135":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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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,"135":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":{"153":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":{"152":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":{"158":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,"135":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":{"160":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":{"156":1},"2":{"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":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}}],["计算自向量在另一个向量上的投影向量",{"2":{"127":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,"151":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,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":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,"134":4,"136":1,"139":4,"140":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,"148":1,"149":1,"150":1,"151":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,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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,"143":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,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"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,"115":3,"120":4,"121":2,"123":4,"126":1,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"148":3,"149":2,"150":2,"151":2,"156":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":{"155":1},"1":{"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"148":1,"149":1,"150":1,"151":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"160":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"160":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,"134":1,"139":1,"140":1,"143":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":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,"127":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,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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":{"158":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,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"127":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":{"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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["ep",{"2":{"158":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,"134":1,"139":1,"143":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,"134":1,"139":1,"140":1,"143":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",{"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1,"95":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"131":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":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,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":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,"134":1,"135":2,"139":1,"140":1,"143":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,"132":1,"133":1,"134":1,"136":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,"129":2,"134":9,"136":4,"145":2,"156":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,"149":1,"150":1,"151":1,"156":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":{"157":1},"1":{"158":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":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"147":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["255万个粒子",{"2":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"129":3,"156":2}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"160":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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,"131":1,"134":2,"135":1,"136":1,"139":2,"140":1,"143":2,"144":1,"145":1,"146":1,"147":1,"156":1}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":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,"134":1,"139":1,"140":1,"143":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"156":1}}],["can",{"2":{"158":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",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":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,"155":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,"147":1,"156":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,"156":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,"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,"147":1,"156":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,"147":1,"156":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,"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,"147":1,"156":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,"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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":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,"127":1,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":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,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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,"129":1,"143":1,"156":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,"129":2,"143":3,"145":1,"156":2}}],["=u⋅v|v|2⋅v",{"2":{"127":1}}],["==",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"135":1},"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,"33":1,"34":1,"36":1,"42":1,"49":1,"56":1,"57":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"156":7}}],["improve",{"2":{"160":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":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,"143":1},"2":{"34":3,"37":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":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,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":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":{"156":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":{"152":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,"134":2,"136":2,"139":2,"140":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,"133":2,"136":2,"138":2,"140":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["projv",{"2":{"127":2}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"153":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":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,"151":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,"129":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,"147":1,"156":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,"151":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":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.o8aepsrg.js b/assets/chunks/@localSearchIndexzht.o8aepsrg.js deleted file mode 100644 index 8a5e009..0000000 --- a/assets/chunks/@localSearchIndexzht.o8aepsrg.js +++ /dev/null @@ -1 +0,0 @@ -const t='{"documentCount":161,"nextId":161,"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-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-1","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-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-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-self-other-bool","95":"/zht/api/mp_math/plane.html#method-self-other-line3-point3","96":"/zht/api/mp_math/point.html#模組-mbcp-mp-math-point","97":"/zht/api/mp_math/point.html#class-point3","98":"/zht/api/mp_math/point.html#method-init-self-x-float-y-float-z-float","99":"/zht/api/mp_math/point.html#method-approx-self-other-point3-epsilon-float-approx-bool","100":"/zht/api/mp_math/point.html#method-self-other-vector3-point3","101":"/zht/api/mp_math/point.html#method-self-other-point3-point3","102":"/zht/api/mp_math/point.html#method-self-other","103":"/zht/api/mp_math/point.html#method-self-other-1","104":"/zht/api/mp_math/point.html#method-self-other-point3-vector3","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-self-other","113":"/zht/api/mp_math/utils.html#method-raise-type-error-self-other","114":"/zht/api/mp_math/utils.html#method-self-other-1","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-project-self-other-vector3-vector3","128":"/zht/api/mp_math/vector.html#method-np-array-self-np-ndarray","129":"/zht/api/mp_math/vector.html#method-length-self-float","130":"/zht/api/mp_math/vector.html#method-unit-self-vector3","131":"/zht/api/mp_math/vector.html#method-abs-self","132":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3","133":"/zht/api/mp_math/vector.html#method-self-other-point3-point3","134":"/zht/api/mp_math/vector.html#method-self-other","135":"/zht/api/mp_math/vector.html#method-self-other-1","136":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-1","137":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-1","138":"/zht/api/mp_math/vector.html#method-self-other-point3-point3-2","139":"/zht/api/mp_math/vector.html#method-self-other-2","140":"/zht/api/mp_math/vector.html#method-self-other-point3","141":"/zht/api/mp_math/vector.html#method-self-other-vector3-vector3-2","142":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3","143":"/zht/api/mp_math/vector.html#method-self-other-int-float-vector3-vector3","144":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-1","145":"/zht/api/mp_math/vector.html#method-self-other-vector3-realnumber","146":"/zht/api/mp_math/vector.html#method-self-other-realnumber-vector3-2","147":"/zht/api/mp_math/vector.html#method-self-vector3","148":"/zht/api/mp_math/vector.html#var-zero-vector3","149":"/zht/api/mp_math/vector.html#var-x-axis","150":"/zht/api/mp_math/vector.html#var-y-axis","151":"/zht/api/mp_math/vector.html#var-z-axis","152":"/zht/api/presets/#模組-mbcp-presets","153":"/zht/api/particle/#模組-mbcp-particle","154":"/zht/api/presets/model/#模組-mbcp-presets-model","155":"/zht/api/presets/model/#class-geometricmodels","156":"/zht/api/presets/model/#method-sphere-radius-float-density-float","157":"/zht/demo/best-practice.html#最佳實踐","158":"/zht/demo/best-practice.html#作品","159":"/zht/guide/#开始不了一点","160":"/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":[4,9,11],"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":[7,7,28],"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":[7,7,19],"95":[8,7,15],"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":[4,7,22],"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":[4,7,31],"113":[7,7,15],"114":[4,7,11],"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":[4,7,16],"127":[6,7,18],"128":[6,7,18],"129":[5,7,23],"130":[5,7,17],"131":[4,7,10],"132":[7,7,12],"133":[7,7,12],"134":[4,7,37],"135":[4,7,22],"136":[7,7,25],"137":[6,7,12],"138":[6,7,12],"139":[3,7,36],"140":[4,7,35],"141":[6,7,12],"142":[7,7,13],"143":[9,7,39],"144":[7,7,13],"145":[7,7,23],"146":[7,7,15],"147":[5,7,17],"148":[3,5,7],"149":[3,5,8],"150":[3,5,8],"151":[3,5,8],"152":[3,1,2],"153":[3,1,2],"154":[4,1,2],"155":[2,4,2],"156":[6,6,46],"157":[1,1,1],"158":[1,1,25],"159":[1,1,2],"160":[1,1,7]},"averageFieldLength":[5.745341614906832,5.931677018633538,17.881987577639762],"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 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 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 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 self == other => bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method self & other: Line3 => Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模組 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模組 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模組 mbcp.mp_math.point","class Point3"]},"103":{"title":"method self == other","titles":["模組 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模組 mbcp.mp_math.point","class Point3"]},"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 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 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 project(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self == other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"139":{"title":"method self - other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"140":{"title":"method self - other: Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"141":{"title":"method self * other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"142":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"143":{"title":"method self * other: int | float | Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"144":{"title":"method self * other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"145":{"title":"method self @ other: Vector3 => RealNumber","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"146":{"title":"method self / other: RealNumber => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"147":{"title":"method - self => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"148":{"title":"var zero_vector3","titles":["模組 mbcp.mp_math.vector"]},"149":{"title":"var x_axis","titles":["模組 mbcp.mp_math.vector"]},"150":{"title":"var y_axis","titles":["模組 mbcp.mp_math.vector"]},"151":{"title":"var z_axis","titles":["模組 mbcp.mp_math.vector"]},"152":{"title":"模組 mbcp.presets","titles":[]},"153":{"title":"模組 mbcp.particle","titles":[]},"154":{"title":"模組 mbcp.presets.model","titles":[]},"155":{"title":"class GeometricModels","titles":["模組 mbcp.presets.model"]},"156":{"title":"method sphere(radius: float, density: float)","titles":["模組 mbcp.presets.model","class GeometricModels"]},"157":{"title":"最佳實踐","titles":[]},"158":{"title":"作品","titles":["最佳實踐"]},"159":{"title":"开始不了一点","titles":[]},"160":{"title":"Reference","titles":[]}},"dirtCount":0,"index":[["∫12x111",{"2":{"159":1}}],["开始不了一点",{"0":{"159":1}}],["红石音乐",{"2":{"158":1}}],["这么可爱真是抱歉",{"2":{"158":1}}],["这玩意不太稳定",{"2":{"34":1}}],["轻涟",{"2":{"158":1}}],["芙宁娜pv曲",{"2":{"158":1}}],["有点甜~",{"2":{"158":1}}],["有关函数柯里化",{"2":{"37":1}}],["星穹铁道",{"2":{"158":1}}],["崩坏",{"2":{"158":1}}],["使一颗心免于哀伤",{"2":{"158":1}}],["总有一条蜿蜒在童话镇里",{"2":{"158":1}}],["童话镇~",{"2":{"158":1}}],["特效红石音乐",{"2":{"158":2}}],["作品",{"0":{"158":1}}],["4",{"2":{"156":1}}],["球体上的点集",{"2":{"156":1}}],["生成球体上的点集",{"2":{"156":1}}],["几何模型点集",{"2":{"154":1}}],["零向量",{"2":{"148":1}}],["负向量",{"2":{"147":1}}],["取负",{"2":{"147":1}}],["取两平面的交集",{"2":{"93":1}}],["非点乘",{"2":{"143":1}}],["别去点那边实现了",{"2":{"136":1}}],["单位向量",{"2":{"130":1}}],["单变量",{"2":{"61":1}}],["模",{"2":{"129":1}}],["模組",{"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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":1}}],["投影向量",{"2":{"127":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":{"143":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":{"129":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":{"130":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":{"160":1}}],["unit",{"0":{"130":1},"2":{"127":1,"130":1}}],["unsupported",{"2":{"44":1,"80":1,"81":1,"93":1,"113":1,"134":1,"139":1,"140":1,"143":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":{"134":1}}],["新的向量",{"2":{"104":1,"139":1}}],["新的点",{"2":{"102":1,"136":1,"140":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":{"160":1}}],["heart",{"2":{"158":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":{"143":1}}],["数组运算",{"2":{"143":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,"148":1,"149":1,"150":1,"151":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":{"135":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":{"143":1}}],["另一个向量或点",{"2":{"134":1,"139":1}}],["另一个向量",{"2":{"121":1,"122":1,"123":1,"124":1,"125":1,"127":1,"135":1,"145":1}}],["另一个点或向量",{"2":{"102":1}}],["另一个点",{"2":{"99":1,"103":1,"104":1,"136":1,"140":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,"135":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":{"153":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":{"158":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,"135":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":{"160":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":{"156":1},"2":{"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":1}}],["梯度",{"2":{"36":1}}],["点乘结果",{"2":{"145":1}}],["点乘",{"2":{"145":1}}],["点乘使用",{"2":{"143":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,"151":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,"127":2,"130":1,"132":2,"137":2,"141":2,"142":1,"143":2,"144":1,"145":1,"146":1,"147":1,"148":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,"147":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,"127":4,"130":2,"132":2,"134":5,"135":1,"137":2,"139":5,"140":1,"141":2,"142":1,"143":8,"144":1,"145":2,"146":2,"147":3,"148":2,"149":2,"150":2,"151":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,"134":4,"136":1,"139":4,"140":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,"148":1,"149":1,"150":1,"151":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,"156":9}}],["length",{"0":{"129":1},"2":{"44":5,"45":1,"80":2,"107":2,"122":2,"124":1,"126":5,"127":1,"129":1,"130":1,"131":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":{"158":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":{"156":5}}],["numpy数组",{"2":{"128":1}}],["number=epsilon",{"2":{"34":1}}],["number",{"0":{"34":1,"60":1},"2":{"62":1}}],["ndarray",{"0":{"128":1},"2":{"128":2}}],["neg",{"0":{"116":1,"117":1},"2":{"116":3,"117":3,"147":1}}],["negative",{"0":{"9":1},"2":{"9":1}}],["ne",{"2":{"114":1}}],["np",{"0":{"128":2},"2":{"82":9,"128":4,"156":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,"143":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,"134":2,"139":2,"143":3}}],["曲线方程",{"2":{"32":1,"38":1}}],["z轴单位向量",{"2":{"151":1}}],["z轴分量",{"2":{"120":1}}],["zero",{"0":{"148":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,"151":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["y轴单位向量",{"2":{"150":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,"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,"115":3,"120":4,"121":2,"123":4,"126":1,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":2}}],["x轴单位向量",{"2":{"149":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,"149":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,"128":1,"129":1,"134":4,"135":2,"136":2,"139":4,"140":2,"143":3,"145":2,"146":1,"147":1,"156":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,"148":3,"149":2,"150":2,"151":2,"156":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":{"155":1},"1":{"156":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":1},"2":{"102":2,"104":2,"117":3,"123":1,"134":2,"136":1,"139":2,"140":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,"148":1,"149":1,"150":1,"151":1}}],["默认为否",{"2":{"4":1}}],["π",{"2":{"24":1}}],["to",{"2":{"160":1}}],["theta",{"2":{"156":3}}],["the",{"2":{"83":2,"160":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,"134":1,"139":1,"140":1,"143":1}}],["type",{"0":{"113":1},"2":{"34":1,"44":1,"80":2,"81":2,"93":2,"112":2,"113":4,"134":2,"139":2,"140":2,"143":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,"146":1}}],["tan",{"0":{"12":1},"2":{"12":2,"13":1}}],["operand",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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":{"158":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,"131":1,"132":2,"133":1,"136":1,"137":2,"138":1,"140":1,"141":2,"142":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,"127":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":{"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,"127":5,"132":1,"133":1,"134":11,"135":5,"136":5,"137":1,"138":1,"139":11,"140":7,"141":1,"142":1,"143":11,"144":2,"145":5,"146":4}}],["ep",{"2":{"158":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,"134":1,"139":1,"143":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,"134":1,"139":1,"140":1,"143":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",{"2":{"17":1,"57":1,"94":1,"103":1,"112":1,"114":1,"135":1}}],["all",{"2":{"99":1,"112":1,"121":1}}],["acos",{"2":{"80":1,"122":1}}],["axis",{"0":{"149":1,"150":1,"151":1}}],["ax",{"2":{"78":1}}],["amp",{"0":{"56":1,"91":1,"92":1,"93":1,"95":1}}],["arccos",{"2":{"156":1}}],["array",{"0":{"128":1},"2":{"82":6,"128":2,"156":6}}],["arrayvar",{"0":{"62":1},"2":{"62":1,"63":1,"65":2,"68":3,"71":4,"74":1}}],["area",{"2":{"156":2}}],["are",{"2":{"45":2,"82":1,"83":1}}],["args2",{"2":{"37":2}}],["args",{"0":{"37":1},"2":{"34":11,"37":3}}],["abs",{"0":{"131":1},"2":{"44":1,"81":1,"99":3,"112":1,"115":1,"117":1,"121":3,"131":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,"135":3}}],["add",{"2":{"16":1,"37":4,"100":1,"101":1,"102":1,"132":1,"133":1,"134":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,"134":1,"135":2,"139":1,"140":1,"143":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,"132":1,"133":1,"134":1,"136":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,"129":2,"134":9,"136":4,"145":2,"156":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,"149":1,"150":1,"151":1,"156":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":{"157":1},"1":{"158":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":{"156":1},"2":{"156":1}}],["stop",{"2":{"158":1}}],["staticmethod",{"2":{"155":1,"156":1}}],["str",{"0":{"116":1,"117":1},"2":{"116":2,"117":2}}],["s",{"2":{"93":1,"134":1,"139":1,"140":1,"143":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,"156":3}}],["sqrt",{"2":{"26":1,"129":1,"156":1}}],["sub",{"2":{"18":1,"104":1,"137":1,"138":1,"139":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,"147":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":2,"128":4,"129":4,"130":3,"131":2,"132":1,"133":1,"134":7,"135":4,"136":4,"137":1,"138":1,"139":7,"140":4,"141":1,"142":1,"143":7,"144":2,"145":4,"146":4,"147":4}}],["255万个粒子",{"2":{"158":1}}],["2",{"2":{"5":1,"8":1,"9":1,"26":1,"34":1,"36":3,"37":1,"45":1,"81":3,"107":3,"129":3,"156":2}}],["rmul",{"2":{"144":1}}],["rsub",{"2":{"140":1}}],["reference",{"0":{"160":1}}],["realnumber",{"0":{"47":1,"59":1,"111":1,"142":1,"144":1,"145":1,"146":1},"2":{"47":2,"60":1,"111":2,"142":1,"144":1,"145":1,"146":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,"131":1,"134":2,"135":1,"136":1,"139":2,"140":1,"143":2,"144":1,"145":1,"146":1,"147":1,"156":1}}],["range",{"2":{"156":2}}],["rand",{"2":{"95":1}}],["radius",{"0":{"156":1},"2":{"156":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":{"136":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,"134":1,"139":1,"140":1,"143":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,"130":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"156":1}}],["can",{"2":{"158":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",{"2":{"33":1}}],["cz",{"2":{"78":1}}],["clamp",{"0":{"109":1},"2":{"109":1,"156":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,"155":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,"147":1,"156":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,"156":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,"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,"147":1,"156":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,"147":1,"156":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,"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,"147":1,"156":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,"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,"127":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"156":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,"129":1,"130":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"145":1,"147":1,"148":1,"149":1,"150":1,"151":1,"156":1}}],["f",{"2":{"80":1,"81":1,"93":1,"113":1,"117":3,"134":1,"139":1,"140":1,"143":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,"158":1}}],["format",{"0":{"117":1},"2":{"117":1}}],["for",{"2":{"33":1,"34":1,"93":1,"134":1,"139":1,"140":1,"143":1,"156":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,"129":1,"143":1,"156":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,"129":2,"143":3,"145":1,"156":2}}],["==",{"0":{"17":1,"57":1,"94":1,"103":1,"112":1,"135":1},"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,"33":1,"34":1,"36":1,"42":1,"49":1,"56":1,"57":1,"91":1,"92":1,"94":1,"95":1,"99":1,"100":1,"101":1,"104":1,"114":1,"115":2,"116":1,"117":1,"121":1,"124":1,"132":1,"133":1,"136":1,"137":1,"138":1,"141":1,"142":1,"143":1,"144":1,"145":1,"146":1,"147":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,"156":7}}],["improve",{"2":{"160":1}}],["import",{"2":{"104":1}}],["i",{"2":{"156":4,"158":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,"143":1},"2":{"34":3,"37":4,"59":1,"112":2,"143":2,"156":1}}],["in",{"2":{"33":1,"34":1,"156":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,"134":1,"139":1,"140":1,"143":1,"158":1}}],["isinstance",{"2":{"22":1,"34":2,"44":2,"80":2,"81":2,"93":2,"112":4,"134":2,"139":2,"140":1,"143":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":{"156":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":{"153":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,"134":2,"136":2,"139":2,"140":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,"133":2,"136":2,"138":2,"140":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,"133":2,"134":4,"136":5,"138":2,"139":4,"140":5,"156":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,"128":1,"129":1,"130":1,"132":1,"133":1,"137":1,"138":1,"141":1,"142":1,"156":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,"127":1,"131":1,"134":1,"135":1,"136":1,"139":1,"140":1,"143":1,"144":1,"145":1,"146":1,"147":1}}],["project",{"0":{"127":1},"2":{"127":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,"127":1,"128":2,"129":2,"130":1}}],["presets",{"0":{"152":1,"154":1},"1":{"155":1,"156":1},"2":{"0":1}}],["pi",{"0":{"24":1},"2":{"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"24":1,"156":2}}],["粒子生成工具",{"2":{"0":1}}],["mc特效红石音乐",{"2":{"158":1}}],["model",{"0":{"154":1},"1":{"155":1,"156":1}}],["midpoint",{"2":{"107":1}}],["minecraft",{"2":{"158":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,"141":1,"142":1,"143":1,"144":1}}],["matmul",{"2":{"145":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,"151":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,"129":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,"147":1,"156":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,"151":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,"152":1,"153":1,"154":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,"151":1,"155":1,"156":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.xTIJuz0Z.js b/assets/chunks/VPLocalSearchBox.IDVxz8uj.js similarity index 99% rename from assets/chunks/VPLocalSearchBox.xTIJuz0Z.js rename to assets/chunks/VPLocalSearchBox.IDVxz8uj.js index 5d7245d..5dcb0f0 100644 --- a/assets/chunks/VPLocalSearchBox.xTIJuz0Z.js +++ b/assets/chunks/VPLocalSearchBox.IDVxz8uj.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.DVJrRbLX.js";const as={en:()=>ye(()=>import("./@localSearchIndexen.CXLYQH14.js"),[]),ja:()=>ye(()=>import("./@localSearchIndexja.BCRaXGU0.js"),[]),root:()=>ye(()=>import("./@localSearchIndexroot.CVf1h8jm.js"),[]),zht:()=>ye(()=>import("./@localSearchIndexzht.o8aepsrg.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.5eFoszBF.js";const as={en:()=>ye(()=>import("./@localSearchIndexen.ke4OFQjO.js"),[]),ja:()=>ye(()=>import("./@localSearchIndexja.COlRHLLs.js"),[]),root:()=>ye(()=>import("./@localSearchIndexroot.xPvxH6jA.js"),[]),zht:()=>ye(()=>import("./@localSearchIndexzht.Buw3O8cF.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)$/.test(e.tagName))for(var t=e.parentElement;t;){if(t.tagName==="FIELDSET"&&t.disabled){for(var s=0;s=0)},ws=function a(e){var t=[],s=[];return e.forEach(function(n,r){var i=!!n.scopeParent,o=i?n.scopeParent:n,c=cs(o,i),l=i?a(n.candidates):o;c===0?i?t.push.apply(t,l):t.push(o):s.push({documentOrder:r,tabIndex:c,item:n,isScope:i,content:l})}),s.sort(ls).reduce(function(n,r){return r.isScope?n.push.apply(n,r.content):n.push(r.content),n},[]).concat(t)},_s=function(e,t){t=t||{};var s;return t.getShadowRoot?s=wt([e],t.includeContainer,{filter:Be.bind(null,t),flatten:!1,getShadowRoot:t.getShadowRoot,shadowRootFilter:ys}):s=yt(e,t.includeContainer,Be.bind(null,t)),ws(s)},xs=function(e,t){t=t||{};var s;return t.getShadowRoot?s=wt([e],t.includeContainer,{filter:Oe.bind(null,t),flatten:!0,getShadowRoot:t.getShadowRoot}):s=yt(e,t.includeContainer,Oe.bind(null,t)),s},ae=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return re.call(e,Ne)===!1?!1:Be(t,e)},Ss=gt.concat("iframe").join(","),Le=function(e,t){if(t=t||{},!e)throw new Error("No node provided");return re.call(e,Ss)===!1?!1:Oe(t,e)};/*! diff --git a/assets/chunks/theme.DVJrRbLX.js b/assets/chunks/theme.5eFoszBF.js similarity index 99% rename from assets/chunks/theme.DVJrRbLX.js rename to assets/chunks/theme.5eFoszBF.js index 80e25e9..8950447 100644 --- a/assets/chunks/theme.DVJrRbLX.js +++ b/assets/chunks/theme.5eFoszBF.js @@ -1,2 +1,2 @@ -const __vite__mapDeps=(i,m=__vite__mapDeps,d=(m.f||(m.f=["assets/chunks/VPLocalSearchBox.xTIJuz0Z.js","assets/chunks/framework.DpC1ZpOZ.js"])))=>i.map(i=>d[i]); -import{d as _,o as a,c,r as l,n as N,a as O,t as I,b as k,w as d,e as f,T as ve,_ as b,u as Ge,i as Ue,f as je,g as pe,h as y,j as v,k as r,p as C,l as H,m as K,q as ie,s as w,v as G,x as Z,y as W,z as he,A as fe,B as ze,C as qe,D as R,F as M,E,G as Pe,H as x,I as m,J as F,K as Ve,L as ee,M as q,N as te,O as Ke,P as Le,Q as le,R as We,S as Se,U as oe,V as Re,W as Je,X as Xe,Y as Te,Z as Ie,$ 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.xTIJuz0Z.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.$slots,"layout-bottom",{},void 0,!0)],2)):(a(),k(L,{key:1}))}}}),fr=b(hr,[["__scopeId","data-v-3b4648ff"]]),mr={Layout:fr,enhanceApp:({app:o})=>{o.component("Badge",tt)}};export{Us as c,mr as t,P as u}; +const __vite__mapDeps=(i,m=__vite__mapDeps,d=(m.f||(m.f=["assets/chunks/VPLocalSearchBox.IDVxz8uj.js","assets/chunks/framework.DpC1ZpOZ.js"])))=>i.map(i=>d[i]); +import{d as _,o as a,c,r as l,n as N,a as O,t as I,b as k,w as d,e as f,T as ve,_ as b,u as Ge,i as Ue,f as je,g as pe,h as y,j as v,k as r,p as C,l as H,m as K,q as ie,s as w,v as G,x as Z,y as W,z as he,A as fe,B as ze,C as qe,D as R,F as M,E,G as Pe,H as x,I as m,J as F,K as Ve,L as ee,M as q,N as te,O as Ke,P as Le,Q as le,R as We,S as Se,U as oe,V as Re,W as Je,X as Xe,Y as Te,Z as Ie,$ 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.IDVxz8uj.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_vector.md.C89tx4nd.js b/assets/en_api_mp_math_vector.md.C89tx4nd.js deleted file mode 100644 index 0ad14f7..0000000 --- a/assets/en_api_mp_math_vector.md.C89tx4nd.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),l={name:"en/api/mp_math/vector.md"},n=a('

Module mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

Description: 3维向量

Arguments:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

Description: 判断两个向量是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

Description: 计算两个向量之间的夹角。

',16),h={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"向量夹角计算公式:",-1),p={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a('',1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a('

Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

Description: 向量积 叉乘：v1 x v2 -> v3

',6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a('',1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},_=a('',1),H=[_],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a('

Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

Description: 判断两个向量是否近似平行。

Arguments:

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

Description: 判断两个向量是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

Description: 将向量归一化。

自体归一化，不返回值。

Source code or View on GitHub
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

Source code or View on GitHub
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

Description: 获取该向量的单位向量。

Return: Vector3: 单位向量

Source code or View on GitHub
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

Source code or View on GitHub
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

Description: V + P -> P

V + V -> V

Arguments:

Return: Vector3 | Point3: 新的向量或点

Source code or View on GitHub
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

Description: 判断两个向量是否相等。

Arguments:

Return: bool: 是否相等

Source code or View on GitHub
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

Description: P + V -> P

别去点那边实现了。

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

Description: V - P -> P

V - V -> V

Arguments:

Return: Vector3 | Point3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

Description: P - V -> P

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。

Arguments:

Return: Vector3: 数组运算结果

Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

Description: 点乘。

Arguments:

Return: float: 点乘结果

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

var zero_vector3 ​

  • Description: 零向量

  • Type: Vector3

  • Default: Vector3(0, 0, 0)

var x_axis ​

  • Description: x轴单位向量

  • Type: Vector3

  • Default: Vector3(1, 0, 0)

var y_axis ​

  • Description: y轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 1, 0)

var z_axis ​

  • Description: z轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 0, 1)

',120);function w(B,A,L,M,Z,q){return i(),t("div",null,[n,s("div",h,[r,o,s("mjx-container",p,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",V,H)),x])]),D])}const S=e(l,[["render",w]]);export{z as __pageData,S as default}; diff --git a/assets/en_api_mp_math_vector.md.C89tx4nd.lean.js b/assets/en_api_mp_math_vector.md.C89tx4nd.lean.js deleted file mode 100644 index cd0471a..0000000 --- a/assets/en_api_mp_math_vector.md.C89tx4nd.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),l={name:"en/api/mp_math/vector.md"},n=a("",16),h={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"向量夹角计算公式:",-1),p={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a("",1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a("",6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a("",1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},_=a("",1),H=[_],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a("",120);function w(B,A,L,M,Z,q){return i(),t("div",null,[n,s("div",h,[r,o,s("mjx-container",p,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",V,H)),x])]),D])}const S=e(l,[["render",w]]);export{z as __pageData,S as default}; diff --git a/assets/en_api_mp_math_vector.md.DJV8Xiz8.js b/assets/en_api_mp_math_vector.md.DJV8Xiz8.js new file mode 100644 index 0000000..6a8dab9 --- /dev/null +++ b/assets/en_api_mp_math_vector.md.DJV8Xiz8.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t('

Module mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

Description: 3维向量

Arguments:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

Description: 判断两个向量是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

Description: 计算两个向量之间的夹角。

',16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),d={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t('',1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t('

Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

Description: 向量积 叉乘：v1 x v2 -> v3

',6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t('',1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},x=t('',1),H=[x],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t('

Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

Description: 判断两个向量是否近似平行。

Arguments:

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

Description: 判断两个向量是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

Description: 将向量归一化。

自体归一化，不返回值。

Source code or View on GitHub
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

Description: 计算自向量在另一个向量上的投影向量。

',22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t('',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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),j=[R],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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t('',1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t('

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

Source code or View on GitHub
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

Description: 获取该向量的单位向量。

Return: Vector3: 单位向量

Source code or View on GitHub
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

Source code or View on GitHub
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

Description: V + P -> P

V + V -> V

Arguments:

Return: Vector3 | Point3: 新的向量或点

Source code or View on GitHub
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

Description: 判断两个向量是否相等。

Arguments:

Return: bool: 是否相等

Source code or View on GitHub
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

Description: P + V -> P

别去点那边实现了。

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

Description: V - P -> P

V - V -> V

Arguments:

Return: Vector3 | Point3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

Description: P - V -> P

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。

Arguments:

Return: Vector3: 数组运算结果

Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

Description: 点乘。

Arguments:

Return: float: 点乘结果

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

var zero_vector3 ​

  • Description: 零向量

  • Type: Vector3

  • Default: Vector3(0, 0, 0)

var x_axis ​

  • Description: x轴单位向量

  • Type: Vector3

  • Default: Vector3(1, 0, 0)

var y_axis ​

  • Description: y轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 1, 0)

var z_axis ​

  • Description: z轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 0, 1)

',99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",d,[(i(),a("svg",T,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",V,H)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",S,j)),G]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/en_api_mp_math_vector.md.DJV8Xiz8.lean.js b/assets/en_api_mp_math_vector.md.DJV8Xiz8.lean.js new file mode 100644 index 0000000..c1fe1d4 --- /dev/null +++ b/assets/en_api_mp_math_vector.md.DJV8Xiz8.lean.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t("",16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),d={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},T={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t("",1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t("",6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t("",1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},V={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},x=t("",1),H=[x],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t("",22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t("",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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},S={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),j=[R],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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t("",1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t("",99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",d,[(i(),a("svg",T,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",V,H)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",S,j)),G]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/ja_api_mp_math_vector.md.Dg61_-jz.js b/assets/ja_api_mp_math_vector.md.Dg61_-jz.js deleted file mode 100644 index a97a60b..0000000 --- a/assets/ja_api_mp_math_vector.md.Dg61_-jz.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),l={name:"ja/api/mp_math/vector.md"},h=a('

モジュール mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

説明: 3维向量

引数:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似相等。

引数:

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

説明: 计算两个向量之间的夹角。

',16),n={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),o={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a('',1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a('

引数:

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

説明: 向量积 叉乘：v1 x v2 -> v3

',6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a('',1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},V=a('',1),H=[V],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a('

引数:

戻り値: Vector3: 叉乘结果

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

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似平行。

引数:

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

説明: 判断两个向量是否平行。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

ソースコード または GitHubで表示
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

ソースコード または GitHubで表示
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

ソースコード または GitHubで表示
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

戻り値: Vector3: 单位向量

ソースコード または GitHubで表示
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

ソースコード または GitHubで表示
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

説明: V + P -> P

V + V -> V

引数:

戻り値: Vector3 | Point3: 新的向量或点

ソースコード または GitHubで表示
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

説明: 判断两个向量是否相等。

引数:

戻り値: bool: 是否相等

ソースコード または GitHubで表示
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

説明: V - P -> P

V - V -> V

引数:

戻り値: Vector3 | Point3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

引数:

戻り値: Vector3: 数组运算结果

ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

引数:

戻り値: float: 点乘结果

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

var zero_vector3 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

',120);function B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",_,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/assets/ja_api_mp_math_vector.md.Dg61_-jz.lean.js b/assets/ja_api_mp_math_vector.md.Dg61_-jz.lean.js deleted file mode 100644 index 768a932..0000000 --- a/assets/ja_api_mp_math_vector.md.Dg61_-jz.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),l={name:"ja/api/mp_math/vector.md"},h=a("",16),n={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),o={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a("",1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a("",6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a("",1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},V=a("",1),H=[V],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a("",120);function B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",_,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/assets/ja_api_mp_math_vector.md.XtCcd31y.js b/assets/ja_api_mp_math_vector.md.XtCcd31y.js new file mode 100644 index 0000000..7a4f412 --- /dev/null +++ b/assets/ja_api_mp_math_vector.md.XtCcd31y.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t('

モジュール mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

説明: 3维向量

引数:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似相等。

引数:

戻り値: bool: 是否近似相等

ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

説明: 计算两个向量之间的夹角。

',16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t('',1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t('

引数:

戻り値: AnyAngle: 夹角

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

説明: 向量积 叉乘：v1 x v2 -> v3

',6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t('',1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t('',1),V=[H],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t('

引数:

戻り値: Vector3: 叉乘结果

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

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似平行。

引数:

戻り値: bool: 是否近似平行

ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

説明: 判断两个向量是否平行。

引数:

戻り値: bool: 是否平行

ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

ソースコード または GitHubで表示
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

説明: 计算自向量在另一个向量上的投影向量。

',22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t('',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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t('',1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t('

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

ソースコード または GitHubで表示
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

ソースコード または GitHubで表示
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

戻り値: Vector3: 单位向量

ソースコード または GitHubで表示
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

ソースコード または GitHubで表示
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

説明: V + P -> P

V + V -> V

引数:

戻り値: Vector3 | Point3: 新的向量或点

ソースコード または GitHubで表示
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

説明: 判断两个向量是否相等。

引数:

戻り値: bool: 是否相等

ソースコード または GitHubで表示
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

説明: V - P -> P

V - V -> V

引数:

戻り値: Vector3 | Point3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

引数:

戻り値: Point3: 新的点

ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

引数:

戻り値: Vector3: 数组运算结果

ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

引数:

戻り値: float: 点乘结果

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

var zero_vector3 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

',99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/ja_api_mp_math_vector.md.XtCcd31y.lean.js b/assets/ja_api_mp_math_vector.md.XtCcd31y.lean.js new file mode 100644 index 0000000..66c0113 --- /dev/null +++ b/assets/ja_api_mp_math_vector.md.XtCcd31y.lean.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t("",16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t("",1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t("",6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t("",1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t("",1),V=[H],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t("",22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t("",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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t("",1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t("",99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/zht_api_mp_math_vector.md.BnvyNBhC.js b/assets/zht_api_mp_math_vector.md.BnvyNBhC.js new file mode 100644 index 0000000..f9732bb --- /dev/null +++ b/assets/zht_api_mp_math_vector.md.BnvyNBhC.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t('

模組 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

説明: 3维向量

變數説明:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似相等。

變數説明:

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

説明: 计算两个向量之间的夹角。

',16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t('',1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t('

變數説明:

返回: AnyAngle: 夹角

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

説明: 向量积 叉乘：v1 x v2 -> v3

',6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t('',1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t('',1),V=[H],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t('

變數説明:

返回: Vector3: 叉乘结果

源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似平行。

變數説明:

返回: bool: 是否近似平行

源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

説明: 判断两个向量是否平行。

變數説明:

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

源碼 或 於GitHub上查看
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

説明: 计算自向量在另一个向量上的投影向量。

',22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t('',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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t('',1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t('

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

返回: float: 模

源碼 或 於GitHub上查看
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源碼 或 於GitHub上查看
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

源碼 或 於GitHub上查看
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

説明: V + P -> P

V + V -> V

變數説明:

返回: Vector3 | Point3: 新的向量或点

源碼 或 於GitHub上查看
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

説明: 判断两个向量是否相等。

變數説明:

返回: bool: 是否相等

源碼 或 於GitHub上查看
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

説明: V - P -> P

V - V -> V

變數説明:

返回: Vector3 | Point3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

變數説明:

返回: Vector3: 数组运算结果

源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

變數説明:

返回: float: 点乘结果

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

var zero_vector3 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

',99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/zht_api_mp_math_vector.md.BnvyNBhC.lean.js b/assets/zht_api_mp_math_vector.md.BnvyNBhC.lean.js new file mode 100644 index 0000000..d7fbf7f --- /dev/null +++ b/assets/zht_api_mp_math_vector.md.BnvyNBhC.lean.js @@ -0,0 +1 @@ +import{_ as l,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const o1=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",16),r={class:"tip custom-block"},o=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),T={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=t("",1),Q=[k],m=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=t("",6),c={class:"tip custom-block"},y=s("p",{class:"custom-block-title"},"TIP",-1),E=s("p",null,"叉乘运算法则为:",-1),u={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=t("",1),F=[b],C=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),_=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},x={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},H=t("",1),V=[H],w=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=t("",22),L={class:"tip custom-block"},B=s("p",{class:"custom-block-title"},"TIP",-1),A={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},M={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.206ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3626.9 1000","aria-hidden":"true"},Z=t("",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,"p"),s("mi",null,"r"),s("mi",null,"o"),s("msub",null,[s("mi",null,"j"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")")])],-1),z={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},j={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.294ex",height:"1.025ex",role:"img",focusable:"false",viewBox:"0 -442 572 453","aria-hidden":"true"},S=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":"1D462",d:"M21 287Q21 295 30 318T55 370T99 420T158 442Q204 442 227 417T250 358Q250 340 216 246T182 105Q182 62 196 45T238 27T291 44T328 78L339 95Q341 99 377 247Q407 367 413 387T427 416Q444 431 463 431Q480 431 488 421T496 402L420 84Q419 79 419 68Q419 43 426 35T447 26Q469 29 482 57T512 145Q514 153 532 153Q551 153 551 144Q550 139 549 130T540 98T523 55T498 17T462 -8Q454 -10 438 -10Q372 -10 347 46Q345 45 336 36T318 21T296 6T267 -6T233 -11Q189 -11 155 7Q103 38 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",style:{"stroke-width":"3"}})])])],-1),G=[S],R=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,"u")])],-1),N={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},I={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"1.097ex",height:"1.027ex",role:"img",focusable:"false",viewBox:"0 -443 485 454","aria-hidden":"true"},O=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":"1D463",d:"M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z",style:{"stroke-width":"3"}})])])],-1),J=[O],X=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,"v")])],-1),$={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},U={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.193ex"},xmlns:"http://www.w3.org/2000/svg",width:"18.757ex",height:"4.725ex",role:"img",focusable:"false",viewBox:"0 -1119 8290.4 2088.4","aria-hidden":"true"},K=t("",1),W=[K],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("msub",null,[s("mtext",null,"proj"),s("mi",null,"v")]),s("mo",{stretchy:"false"},"("),s("mi",null,"u"),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"u"),s("mo",null,"⋅"),s("mi",null,"v")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("msup",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mn",null,"2")])])]),s("mo",null,"⋅"),s("mi",null,"v")])],-1),s1=t("",99);function t1(a1,i1,e1,l1,n1,h1){return i(),a("div",null,[h,s("div",r,[o,p,s("mjx-container",T,[(i(),a("svg",d,Q)),m])]),g,s("div",c,[y,E,s("mjx-container",u,[(i(),a("svg",f,F)),C]),_,s("mjx-container",v,[(i(),a("svg",x,V)),w])]),D,s("div",L,[B,s("p",null,[e("投影向量计算公式，"),s("mjx-container",A,[(i(),a("svg",M,P)),q]),e("表示向量"),s("mjx-container",z,[(i(),a("svg",j,G)),R]),e("在向量"),s("mjx-container",N,[(i(),a("svg",I,J)),X]),e("上的投影向量:")]),s("mjx-container",$,[(i(),a("svg",U,W)),Y])]),s1])}const p1=l(n,[["render",t1]]);export{o1 as __pageData,p1 as default}; diff --git a/assets/zht_api_mp_math_vector.md.D-o57Jl7.js b/assets/zht_api_mp_math_vector.md.D-o57Jl7.js deleted file mode 100644 index 4aa86f1..0000000 --- a/assets/zht_api_mp_math_vector.md.D-o57Jl7.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),l={name:"zht/api/mp_math/vector.md"},h=a('

模組 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

method __init__(self, x: float, y: float, z: float) ​

説明: 3维向量

變數説明:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):\n    self.x = x\n    self.y = y\n    self.z = z

method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似相等。

變數説明:

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

method cal_angle(self, other: Vector3) -> AnyAngle ​

説明: 计算两个向量之间的夹角。

',16),n={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),o={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a('',1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a('

變數説明:

返回: AnyAngle: 夹角

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

method cross(self, other: Vector3) -> Vector3 ​

説明: 向量积 叉乘：v1 x v2 -> v3

',6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a('',1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},V=a('',1),H=[V],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a('

變數説明:

返回: Vector3: 叉乘结果

源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​

説明: 判断两个向量是否近似平行。

變數説明:

返回: bool: 是否近似平行

源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:\n    return self.cross(other).length < epsilon

method is_parallel(self, other: Vector3) -> bool ​

説明: 判断两个向量是否平行。

變數説明:

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:\n    return self.cross(other).approx(zero_vector3)

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

源碼 或 於GitHub上查看
python
def normalize(self):\n    length = self.length\n    self.x /= length\n    self.y /= length\n    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':\n    return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property\ndef np_array(self) -> 'np.ndarray':\n    return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

返回: float: 模

源碼 或 於GitHub上查看
python
@property\ndef length(self) -> float:\n    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

返回: Vector3: 单位向量

源碼 或 於GitHub上查看
python
@property\ndef unit(self) -> 'Vector3':\n    return self / self.length

method __abs__(self) ​

源碼 或 於GitHub上查看
python
def __abs__(self):\n    return self.length

@overload

method self + other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self + other: Point3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __add__(self, other: 'Point3') -> 'Point3':\n    ...

method self + other ​

説明: V + P -> P

V + V -> V

變數説明:

返回: Vector3 | Point3: 新的向量或点

源碼 或 於GitHub上查看
python
def __add__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method self == other ​

説明: 判断两个向量是否相等。

變數説明:

返回: bool: 是否相等

源碼 或 於GitHub上查看
python
def __eq__(self, other):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

@overload

method self - other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __sub__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self - other: Point3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __sub__(self, other: 'Point3') -> 'Point3':\n    ...

method self - other ​

説明: V - P -> P

V - V -> V

變數説明:

返回: Vector3 | Point3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other):\n    if isinstance(other, Vector3):\n        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)\n    elif isinstance(other, Point3):\n        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)\n    else:\n        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')

method self - other: Point3 ​

説明: P - V -> P

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):\n    if isinstance(other, Point3):\n        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)\n    else:\n        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")

@overload

method self * other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __mul__(self, other: 'Vector3') -> 'Vector3':\n    ...

@overload

method self * other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __mul__(self, other: RealNumber) -> 'Vector3':\n    ...

method self * other: int | float | Vector3 => Vector3 ​

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

變數説明:

返回: Vector3: 数组运算结果

源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':\n    if isinstance(other, Vector3):\n        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)\n    elif isinstance(other, (float, int)):\n        return Vector3(self.x * other, self.y * other, self.z * other)\n    else:\n        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")

method self * other: RealNumber => Vector3 ​

源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':\n    return self.__mul__(other)

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

變數説明:

返回: float: 点乘结果

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

var zero_vector3 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

',120);function B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",_,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/assets/zht_api_mp_math_vector.md.D-o57Jl7.lean.js b/assets/zht_api_mp_math_vector.md.D-o57Jl7.lean.js deleted file mode 100644 index 228732f..0000000 --- a/assets/zht_api_mp_math_vector.md.D-o57Jl7.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),l={name:"zht/api/mp_math/vector.md"},h=a("",16),n={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),p=s("p",null,"向量夹角计算公式:",-1),o={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:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},k=a("",1),T=[k],Q=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,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),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,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a("",6),m={class:"tip custom-block"},c=s("p",{class:"custom-block-title"},"TIP",-1),y=s("p",null,"叉乘运算法则为:",-1),E={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},u={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.667ex"},xmlns:"http://www.w3.org/2000/svg",width:"70.883ex",height:"2.364ex",role:"img",focusable:"false",viewBox:"0 -750 31330.3 1045","aria-hidden":"true"},b=a("",1),f=[b],F=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mo",{stretchy:"false"},"("),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")]),s("mo",null,","),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")]),s("mo",null,"−"),s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")]),s("mo",null,"⋅"),s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")]),s("mo",{stretchy:"false"},")")])],-1),C=s("p",null,"转换为行列式形式:",-1),v={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},_={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-3.835ex"},xmlns:"http://www.w3.org/2000/svg",width:"25.963ex",height:"8.801ex",role:"img",focusable:"false",viewBox:"0 -2195 11475.8 3889.9","aria-hidden":"true"},V=a("",1),H=[V],x=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,"v"),s("mn",null,"1"),s("mo",null,"×"),s("mi",null,"v"),s("mn",null,"2"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"|"),s("mtable",{columnspacing:"1em",rowspacing:"4pt"},[s("mtr",null,[s("mtd",null,[s("mi",null,"i")]),s("mtd",null,[s("mi",null,"j")]),s("mtd",null,[s("mi",null,"k")])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"1"),s("mi",null,"z")])])]),s("mtr",null,[s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"x")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"y")])]),s("mtd",null,[s("mi",null,"v"),s("msub",null,[s("mn",null,"2"),s("mi",null,"z")])])])]),s("mo",{"data-mjx-texclass":"CLOSE"},"|")])])],-1),D=a("",120);function B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",v,[(i(),t("svg",_,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/demo/best-practice.html b/demo/best-practice.html index 71ff9d6..fbfc974 100644 --- a/demo/best-practice.html +++ b/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/demo/index.html b/demo/index.html index 4f9bff8..377255e 100644 --- a/demo/index.html +++ b/demo/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 28d0da7..272c7c2 100644 --- a/en/api/index.html +++ b/en/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 6522a9a..781cd7a 100644 --- a/en/api/mp_math/angle.html +++ b/en/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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/const.html b/en/api/mp_math/const.html index 7889768..8be7ee6 100644 --- a/en/api/mp_math/const.html +++ b/en/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -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 1bd247f..a94b104 100644 --- a/en/api/mp_math/equation.html +++ b/en/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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/function.html b/en/api/mp_math/function.html index 3f14c95..931f2a7 100644 --- a/en/api/mp_math/function.html +++ b/en/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

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/index.html b/en/api/mp_math/index.html index 79d6220..b1518b3 100644 --- a/en/api/mp_math/index.html +++ b/en/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 660ed0d..566cd3d 100644 --- a/en/api/mp_math/line.html +++ b/en/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

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)

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/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html index 8165235..9b8ddb7 100644 --- a/en/api/mp_math/mp_math_typing.html +++ b/en/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -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 bccd2a3..9db5190 100644 --- a/en/api/mp_math/plane.html +++ b/en/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method self == other => bool ​

Description: 判断两个平面是否等价。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否等价

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

method self & other: Line3 => Point3 ​

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

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/point.html b/en/api/mp_math/point.html index 3e853dc..9ebb2b2 100644 --- a/en/api/mp_math/point.html +++ b/en/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -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)

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/segment.html b/en/api/mp_math/segment.html index 75de8e3..57f91e2 100644 --- a/en/api/mp_math/segment.html +++ b/en/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -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)

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/utils.html b/en/api/mp_math/utils.html index 4672a2f..265f578 100644 --- a/en/api/mp_math/utils.html +++ b/en/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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/vector.html b/en/api/mp_math/vector.html index 6281105..5cd75e3 100644 --- a/en/api/mp_math/vector.html +++ b/en/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

method project(self, other: Vector3) -> Vector3 ​

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

Description: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

Arguments:

Return: Vector3: 投影向量

Source code or View on GitHub
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

Source code or View on GitHub
python
@property
@@ -79,7 +79,7 @@
     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 ​

  • Description: 零向量

  • Type: Vector3

  • Default: Vector3(0, 0, 0)

var x_axis ​

  • Description: x轴单位向量

  • Type: Vector3

  • Default: Vector3(1, 0, 0)

var y_axis ​

  • Description: y轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 1, 0)

var z_axis ​

  • Description: z轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 0, 1)

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/particle/index.html b/en/api/particle/index.html index c243c3c..2667563 100644 --- a/en/api/particle/index.html +++ b/en/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/index.html b/en/api/presets/index.html index 9aad9c7..6bf607a 100644 --- a/en/api/presets/index.html +++ b/en/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html index 5270a2c..927b520 100644 --- a/en/api/presets/model/index.html +++ b/en/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -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)]

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/demo/best-practice.html b/en/demo/best-practice.html index 88c03a4..7f95cf4 100644 --- a/en/demo/best-practice.html +++ b/en/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/guide/index.html b/en/guide/index.html index 61c25b7..e1bd0f7 100644 --- a/en/guide/index.html +++ b/en/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 00ae943..2ac1a0d 100644 --- a/en/index.html +++ b/en/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 83d8533..900a7a9 100644 --- a/en/refer/index.html +++ b/en/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 d07ac7c..a14b4e5 100644 --- a/guide/index.html +++ b/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 540ad9c..a435f5e 100644 --- a/hashmap.json +++ b/hashmap.json @@ -1 +1 @@ -{"api_index.md":"BO3OGCZm","api_mp_math_angle.md":"o2FjFJVM","api_mp_math_const.md":"B_APaY-d","api_mp_math_equation.md":"7eZhFpxb","api_mp_math_function.md":"CDW7K4aO","api_mp_math_index.md":"BfSAi6YB","api_mp_math_line.md":"BufsPjQ4","api_mp_math_mp_math_typing.md":"D0jHaHho","api_mp_math_plane.md":"BI-yBOVt","api_mp_math_point.md":"9lQO7e_B","api_mp_math_segment.md":"JYVgLepk","api_mp_math_utils.md":"BRgMKXyU","api_mp_math_vector.md":"DjjcwrqW","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":"BxI_io2D","en_api_mp_math_const.md":"f-2wQHW5","en_api_mp_math_equation.md":"BDw5boDN","en_api_mp_math_function.md":"l19FY4Hu","en_api_mp_math_index.md":"BiDCWhuz","en_api_mp_math_line.md":"N84NCcFr","en_api_mp_math_mp_math_typing.md":"A2oAWINP","en_api_mp_math_plane.md":"Dcl5f694","en_api_mp_math_point.md":"BtS25597","en_api_mp_math_segment.md":"D0wpX8Us","en_api_mp_math_utils.md":"C-COPCw_","en_api_mp_math_vector.md":"C89tx4nd","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":"BsVW1_45","ja_api_mp_math_const.md":"kKAd6ihV","ja_api_mp_math_equation.md":"Cvdc0kei","ja_api_mp_math_function.md":"pJM1NJ2m","ja_api_mp_math_index.md":"BCReRKfD","ja_api_mp_math_line.md":"ACj3eb2t","ja_api_mp_math_mp_math_typing.md":"CzEPV5Ep","ja_api_mp_math_plane.md":"BLythjEi","ja_api_mp_math_point.md":"gujIoqh8","ja_api_mp_math_segment.md":"DZAkmIjJ","ja_api_mp_math_utils.md":"crOIcdWW","ja_api_mp_math_vector.md":"Dg61_-jz","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":"DK9un2Dh","zht_api_mp_math_const.md":"D9eBwcNw","zht_api_mp_math_equation.md":"U4JCwJwD","zht_api_mp_math_function.md":"3Rru8vfk","zht_api_mp_math_index.md":"DVqLRZhm","zht_api_mp_math_line.md":"CqvSdHr8","zht_api_mp_math_mp_math_typing.md":"DWzRfFJe","zht_api_mp_math_plane.md":"u8cWUecu","zht_api_mp_math_point.md":"CGqDeaEv","zht_api_mp_math_segment.md":"CqQitARa","zht_api_mp_math_utils.md":"CFas0PJL","zht_api_mp_math_vector.md":"D-o57Jl7","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":"o2FjFJVM","api_mp_math_const.md":"B_APaY-d","api_mp_math_equation.md":"7eZhFpxb","api_mp_math_function.md":"CDW7K4aO","api_mp_math_index.md":"BfSAi6YB","api_mp_math_line.md":"BufsPjQ4","api_mp_math_mp_math_typing.md":"D0jHaHho","api_mp_math_plane.md":"BI-yBOVt","api_mp_math_point.md":"9lQO7e_B","api_mp_math_segment.md":"JYVgLepk","api_mp_math_utils.md":"BRgMKXyU","api_mp_math_vector.md":"Bmtslkkm","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":"BxI_io2D","en_api_mp_math_const.md":"f-2wQHW5","en_api_mp_math_equation.md":"BDw5boDN","en_api_mp_math_function.md":"l19FY4Hu","en_api_mp_math_index.md":"BiDCWhuz","en_api_mp_math_line.md":"N84NCcFr","en_api_mp_math_mp_math_typing.md":"A2oAWINP","en_api_mp_math_plane.md":"Dcl5f694","en_api_mp_math_point.md":"BtS25597","en_api_mp_math_segment.md":"D0wpX8Us","en_api_mp_math_utils.md":"C-COPCw_","en_api_mp_math_vector.md":"DJV8Xiz8","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":"BsVW1_45","ja_api_mp_math_const.md":"kKAd6ihV","ja_api_mp_math_equation.md":"Cvdc0kei","ja_api_mp_math_function.md":"pJM1NJ2m","ja_api_mp_math_index.md":"BCReRKfD","ja_api_mp_math_line.md":"ACj3eb2t","ja_api_mp_math_mp_math_typing.md":"CzEPV5Ep","ja_api_mp_math_plane.md":"BLythjEi","ja_api_mp_math_point.md":"gujIoqh8","ja_api_mp_math_segment.md":"DZAkmIjJ","ja_api_mp_math_utils.md":"crOIcdWW","ja_api_mp_math_vector.md":"XtCcd31y","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":"DK9un2Dh","zht_api_mp_math_const.md":"D9eBwcNw","zht_api_mp_math_equation.md":"U4JCwJwD","zht_api_mp_math_function.md":"3Rru8vfk","zht_api_mp_math_index.md":"DVqLRZhm","zht_api_mp_math_line.md":"CqvSdHr8","zht_api_mp_math_mp_math_typing.md":"DWzRfFJe","zht_api_mp_math_plane.md":"u8cWUecu","zht_api_mp_math_point.md":"CGqDeaEv","zht_api_mp_math_segment.md":"CqQitARa","zht_api_mp_math_utils.md":"CFas0PJL","zht_api_mp_math_vector.md":"BnvyNBhC","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 e4d0003..d31ccf8 100644 --- a/index.html +++ b/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 b7a82d5..bb2428f 100644 --- a/ja/api/index.html +++ b/ja/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 d9ac6cd..00bc318 100644 --- a/ja/api/mp_math/angle.html +++ b/ja/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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/const.html b/ja/api/mp_math/const.html index 3280369..ae21848 100644 --- a/ja/api/mp_math/const.html +++ b/ja/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -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 5743443..f7ff8ca 100644 --- a/ja/api/mp_math/equation.html +++ b/ja/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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/function.html b/ja/api/mp_math/function.html index 16698ca..c6c4fec 100644 --- a/ja/api/mp_math/function.html +++ b/ja/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

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/index.html b/ja/api/mp_math/index.html index d18f489..ea15bef 100644 --- a/ja/api/mp_math/index.html +++ b/ja/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 fa22273..176a80a 100644 --- a/ja/api/mp_math/line.html +++ b/ja/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

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)

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/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html index e3a765c..b49a50f 100644 --- a/ja/api/mp_math/mp_math_typing.html +++ b/ja/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -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 c2992e3..eb93964 100644 --- a/ja/api/mp_math/plane.html +++ b/ja/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method 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 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)

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/point.html b/ja/api/mp_math/point.html index d6ee23b..809a0af 100644 --- a/ja/api/mp_math/point.html +++ b/ja/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -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)

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/segment.html b/ja/api/mp_math/segment.html index f024754..a847af1 100644 --- a/ja/api/mp_math/segment.html +++ b/ja/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -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)

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/utils.html b/ja/api/mp_math/utils.html index 3d8d263..e260ba5 100644 --- a/ja/api/mp_math/utils.html +++ b/ja/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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/vector.html b/ja/api/mp_math/vector.html index 4754f3d..7e88e55 100644 --- a/ja/api/mp_math/vector.html +++ b/ja/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

method project(self, other: Vector3) -> Vector3 ​

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

説明: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

引数:

戻り値: Vector3: 投影向量

ソースコード または GitHubで表示
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

ソースコード または GitHubで表示
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

ソースコード または GitHubで表示
python
@property
@@ -79,7 +79,7 @@
     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 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

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/particle/index.html b/ja/api/particle/index.html index 534b783..40cd1e7 100644 --- a/ja/api/particle/index.html +++ b/ja/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html index 94e7c6d..aed80e6 100644 --- a/ja/api/presets/index.html +++ b/ja/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html index 12cb837..e2ebb14 100644 --- a/ja/api/presets/model/index.html +++ b/ja/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -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)]

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/demo/best-practice.html b/ja/demo/best-practice.html index d9f0306..be81b05 100644 --- a/ja/demo/best-practice.html +++ b/ja/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/guide/index.html b/ja/guide/index.html index d6847f2..ed903d8 100644 --- a/ja/guide/index.html +++ b/ja/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 7d13ba5..85c8f56 100644 --- a/ja/index.html +++ b/ja/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 e4b5b58..4dfa5fd 100644 --- a/ja/refer/index.html +++ b/ja/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 70aef65..ac49686 100644 --- a/refer/7-differential-euqtion/index.html +++ b/refer/7-differential-euqtion/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 1daa583..418569b 100644 --- a/refer/function/curry.html +++ b/refer/function/curry.html @@ -8,8 +8,8 @@ - - + + @@ -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 0ba7b22..d86c8d1 100644 --- a/refer/function/function.html +++ b/refer/function/function.html @@ -8,8 +8,8 @@ - - + + @@ -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 66f155d..ca1fc1b 100644 --- a/refer/index.html +++ b/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 8eba367..105cb74 100644 --- a/zht/api/index.html +++ b/zht/api/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 47b61c3..4cdf0a3 100644 --- a/zht/api/mp_math/angle.html +++ b/zht/api/mp_math/angle.html @@ -8,8 +8,8 @@ - - + + @@ -56,7 +56,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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/const.html b/zht/api/mp_math/const.html index 05ec460..3322bcc 100644 --- a/zht/api/mp_math/const.html +++ b/zht/api/mp_math/const.html @@ -8,8 +8,8 @@ - - + + @@ -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 7c1121a..e62593e 100644 --- a/zht/api/mp_math/equation.html +++ b/zht/api/mp_math/equation.html @@ -8,8 +8,8 @@ - - + + @@ -45,7 +45,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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/function.html b/zht/api/mp_math/function.html index 9bf83af..1cf6048 100644 --- a/zht/api/mp_math/function.html +++ b/zht/api/mp_math/function.html @@ -8,8 +8,8 @@ - - + + @@ -30,7 +30,7 @@ def curried_func(*args2: Var) -> Var: return func(*args, *args2) return curried_func

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/index.html b/zht/api/mp_math/index.html index 47475b7..47d26ea 100644 --- a/zht/api/mp_math/index.html +++ b/zht/api/mp_math/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 61bd6ef..426abf9 100644 --- a/zht/api/mp_math/line.html +++ b/zht/api/mp_math/line.html @@ -8,8 +8,8 @@ - - + + @@ -66,7 +66,7 @@ else: return self.cal_intersection(other)

method self == other => bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

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)

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/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html index b3e0c87..c6360ce 100644 --- a/zht/api/mp_math/mp_math_typing.html +++ b/zht/api/mp_math/mp_math_typing.html @@ -8,8 +8,8 @@ - - + + @@ -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 5f6c3be..19208f0 100644 --- a/zht/api/mp_math/plane.html +++ b/zht/api/mp_math/plane.html @@ -8,8 +8,8 @@ - - + + @@ -105,7 +105,7 @@ raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method 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 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)

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/point.html b/zht/api/mp_math/point.html index bf758de..535ee6d 100644 --- a/zht/api/mp_math/point.html +++ b/zht/api/mp_math/point.html @@ -8,8 +8,8 @@ - - + + @@ -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)

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/segment.html b/zht/api/mp_math/segment.html index 2b5cb8d..35be59a 100644 --- a/zht/api/mp_math/segment.html +++ b/zht/api/mp_math/segment.html @@ -8,8 +8,8 @@ - - + + @@ -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)

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/utils.html b/zht/api/mp_math/utils.html index c4c38ef..b249d88 100644 --- a/zht/api/mp_math/utils.html +++ b/zht/api/mp_math/utils.html @@ -8,8 +8,8 @@ - - + + @@ -46,7 +46,7 @@ return f'-{abs(x)}' else: return ''

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/vector.html b/zht/api/mp_math/vector.html index 7d1f534..3c04eb8 100644 --- a/zht/api/mp_math/vector.html +++ b/zht/api/mp_math/vector.html @@ -8,10 +8,10 @@ - - + + - + @@ -30,7 +30,7 @@ length = self.length self.x /= length self.y /= length - self.z /= length

method project(self, other: Vector3) -> Vector3 ​

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
+    self.z /= length

method project(self, other: Vector3) -> Vector3 ​

説明: 计算自向量在另一个向量上的投影向量。

TIP

投影向量计算公式，projv(u)表示向量u在向量v上的投影向量:

projv(u)=u⋅v|v|2⋅v

變數説明:

返回: Vector3: 投影向量

源碼 或 於GitHub上查看
python
def project(self, other: 'Vector3') -> 'Vector3':
     return self @ other / other.length * other.unit

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     return np.array([self.x, self.y, self.z])

@property

method length(self) -> float ​

説明: 向量的模。

返回: float: 模

源碼 或 於GitHub上查看
python
@property
@@ -79,7 +79,7 @@
     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 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

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/particle/index.html b/zht/api/particle/index.html index f7e979d..5a83f7c 100644 --- a/zht/api/particle/index.html +++ b/zht/api/particle/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html index 7a25383..2865007 100644 --- a/zht/api/presets/index.html +++ b/zht/api/presets/index.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html index 8a0641f..2a7a74c 100644 --- a/zht/api/presets/model/index.html +++ b/zht/api/presets/model/index.html @@ -8,8 +8,8 @@ - - + + @@ -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)]

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/demo/best-practice.html b/zht/demo/best-practice.html index d49c3a8..943b8a2 100644 --- a/zht/demo/best-practice.html +++ b/zht/demo/best-practice.html @@ -8,8 +8,8 @@ - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/guide/index.html b/zht/guide/index.html index 92959eb..c61f0d9 100644 --- a/zht/guide/index.html +++ b/zht/guide/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 d060b95..538ebe3 100644 --- a/zht/index.html +++ b/zht/index.html @@ -8,8 +8,8 @@ - - + + @@ -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 64eaaef..90ab2bb 100644 --- a/zht/refer/index.html +++ b/zht/refer/index.html @@ -8,8 +8,8 @@ - - + + @@ -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