From c6275ef2ba863e066a28cde6a09551508751b675 Mon Sep 17 00:00:00 2001 From: snowykami Date: Fri, 6 Sep 2024 07:44:53 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20docs=20from=20@=20snowykami/mb?= =?UTF-8?q?cp@114d262b68c78005341f464ed32c73ff6393a96c=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 404.html | 6 +- api/index.html | 8 +- api/mp_math/angle.html | 8 +- api/mp_math/const.html | 8 +- api/mp_math/equation.html | 8 +- api/mp_math/function.html | 8 +- api/mp_math/index.html | 8 +- api/mp_math/line.html | 8 +- api/mp_math/mp_math_typing.html | 8 +- api/mp_math/plane.html | 63 +++-- api/mp_math/point.html | 8 +- api/mp_math/segment.html | 8 +- api/mp_math/utils.html | 8 +- api/mp_math/vector.html | 83 ++++--- api/particle/index.html | 8 +- api/presets/index.html | 8 +- api/presets/model/index.html | 8 +- assets/api_mp_math_plane.md.DQhjzD06.js | 206 ---------------- assets/api_mp_math_plane.md.DQhjzD06.lean.js | 1 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+- en/api/mp_math/vector.html | 83 ++++--- en/api/particle/index.html | 8 +- en/api/presets/index.html | 8 +- en/api/presets/model/index.html | 8 +- en/demo/best-practice.html | 8 +- en/guide/index.html | 8 +- en/index.html | 8 +- en/refer/index.html | 8 +- guide/index.html | 8 +- hashmap.json | 2 +- index.html | 8 +- ja/api/index.html | 8 +- ja/api/mp_math/angle.html | 8 +- ja/api/mp_math/const.html | 8 +- ja/api/mp_math/equation.html | 8 +- ja/api/mp_math/function.html | 8 +- ja/api/mp_math/index.html | 8 +- ja/api/mp_math/line.html | 8 +- ja/api/mp_math/mp_math_typing.html | 8 +- ja/api/mp_math/plane.html | 63 +++-- ja/api/mp_math/point.html | 8 +- ja/api/mp_math/segment.html | 8 +- ja/api/mp_math/utils.html | 8 +- ja/api/mp_math/vector.html | 83 ++++--- ja/api/particle/index.html | 8 +- ja/api/presets/index.html | 8 +- ja/api/presets/model/index.html | 8 +- ja/demo/best-practice.html | 8 +- ja/guide/index.html | 8 +- ja/index.html | 8 +- ja/refer/index.html | 8 +- 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refer/7-differential-euqtion/index.html diff --git a/404.html b/404.html index 670edb4..8572951 100644 --- a/404.html +++ b/404.html @@ -6,9 +6,9 @@ 404 | MBCP 文档 - + - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index 557156d..82df417 100644 --- a/api/index.html +++ b/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

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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 d4428d3..848d457 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP 文档 - + - - + + @@ -117,7 +117,7 @@ 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 dc1c25a..e3993b1 100644 --- a/api/mp_math/const.html +++ b/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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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 ad41426..bf860ef 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP 文档 - + - - + + @@ -83,7 +83,7 @@ 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 4e57bc9..24881a3 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP 文档 - + - - + + @@ -60,7 +60,7 @@ """@litedoc-hide""" 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 91aa36d..4a196e5 100644 --- a/api/mp_math/index.html +++ b/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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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 945d2d5..ec26be4 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -6,10 +6,10 @@ mbcp.mp_math.line | MBCP 文档 - + - - + + @@ -192,7 +192,7 @@ [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价 """ 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 1257d08..a1b12dc 100644 --- a/api/mp_math/mp_math_typing.html +++ b/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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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 046e74c..879a5a4 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP 文档 - + - - + + - + @@ -48,9 +48,19 @@ k = other.c / self.c return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k) else: - return False

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

说明: 计算平面与平面之间的夹角。

参数:

返回: AnyAngle: 夹角

引发:

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

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

说明: 计算平面与平面之间的夹角。

TIP

平面间夹角计算公式:

θ=arccos⁡(n1⋅n2|n1|⋅|n2|)

其中 n1 和 n2 分别为两个平面的法向量

TIP

平面与直线夹角计算公式:

θ=arccos⁡(n⋅d|n|⋅|d|)

其中 n 为平面的法向量，d 为直线的方向向量

参数:

返回: AnyAngle: 夹角

引发:

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n1 \\cdot n2}{|n1| \\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n \\cdot d}{|n| \\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
         Args:
             other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
         Returns:
@@ -63,7 +73,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

说明: 计算平面与平面或点之间的距离。

参数:

返回: float: 距离

引发:

源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

说明: 计算平面与平面或点之间的距离。

参数:

返回: float: 距离

引发:

源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,9 +88,20 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

说明: 计算两平面的交线。

参数:

返回: Line3: 交线

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

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

说明: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点，依次假设x=0, y=0, z=0，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

或

x−x0m=y−y0n=z−z0p

参数:

返回: Line3: 交线

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\begin{cases} x = x_0 + dt \\\\ y = y_0 + dt \\\\ z = z_0 + dt \\end{cases} $$
+        或
+        $$ \\frac{x - x_0}{m} = \\frac{y - y_0}{n} = \\frac{z - z_0}{p} $$
+        :::
+
         Args:
             other ([`Plane3`](./plane#class-plane3)): 另一个平面
         Returns:
@@ -104,7 +125,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

说明: 计算平面与直线的交点。

参数:

返回: Point3: 交点

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

说明: 计算平面与直线的交点。

参数:

返回: Point3: 交点

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +139,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

说明: 计算平行于该平面且过指定点的平面。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

说明: 计算平行于该平面且过指定点的平面。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +147,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

说明: 判断两个平面是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

说明: 判断两个平面是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +155,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

说明: 平面的法向量。

返回: Vector3: 法向量

源代码 或 在GitHub上查看
python
@property
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

说明: 平面的法向量。

返回: Vector3: 法向量

源代码 或 在GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +174,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

说明: 工厂函数 由三点构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

说明: 工厂函数 由三点构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +188,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

说明: 工厂函数 由两直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

说明: 工厂函数 由两直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +202,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +212,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

@overload

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

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

@overload

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

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

method __and__(self, other) ​

说明: 取两平面的交集（人话：交线）

参数:

返回: Line3 | Point3 | None: 交集

引发:

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

method __and__(self, other) ​

说明: 取两平面的交集（人话：交线）

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码 或 在GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +235,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +243,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)

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

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.approx(other)

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

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
- + \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html index 685b5eb..1c8cf0d 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP 文档 - + - - + + @@ -70,7 +70,7 @@ """ 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 01974fd..e12f835 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP 文档 - + - - + + @@ -33,7 +33,7 @@ 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 56dc6ed..b5af2c5 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP 文档 - + - - + + @@ -87,7 +87,7 @@ 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 76d759a..b21d4a5 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -6,12 +6,12 @@ mbcp.mp_math.vector | MBCP 文档 - + - - + + - + @@ -38,35 +38,34 @@ Returns: [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等 """ - 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。

参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    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。

TIP

向量夹角计算公式:

θ=arccos⁡(v1⋅v2|v1|⋅|v2|)

参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\theta = \\arccos(\\frac{v1 \\cdot v2}{|v1| \\cdot |v2|})$$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

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':
+    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

TIP

叉乘运算法则为:

v1×v2=(v1y⋅v2z−v1z⋅v2y,v1z⋅v2x−v1x⋅v2z,v1x⋅v2y−v1y⋅v2x)

转换为行列式形式:

v1×v2=|ijkv1xv1yv1zv2xv2yv2z|

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':
     """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        ``i  j  k``
-
-        ``x1 y1 z1``
-
-        ``x2 y2 z2``
+        向量积 叉乘：v1 x v2 -> v3
 
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\times v2 = (v1_y \\cdot v2_z - v1_z \\cdot v2_y, v1_z \\cdot v2_x - v1_x \\cdot v2_z, v1_x \\cdot v2_y - v1_y \\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\times v2 = \\begin{vmatrix} i & j & k \\\\ v1_x & v1_y & v1_z \\\\ v2_x & v2_y & v2_z \\end{vmatrix} $$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    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:
+    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:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +74,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    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:
+    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:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +82,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    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):
+    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):
     """
         将向量归一化。
 
@@ -92,33 +91,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length

@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
+    self.z /= length

@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':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    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
+    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
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    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
+    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
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

源代码 或 在GitHub上查看
python
@overload
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V + P -> P
 
@@ -133,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +140,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    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':
+    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':
     """
         P + V -> P
 
@@ -151,11 +150,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    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
+    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
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V - P -> P
 
@@ -170,7 +169,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        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'):
+        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'):
     """
         P - V -> P
         Args:
@@ -181,11 +180,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        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
+        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
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    ...

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':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +197,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        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':
-    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':
+        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':
+    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':
     """
         点乘。
         Args:
@@ -207,15 +206,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    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 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':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
     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 3f8e5d1..6bf7659 100644 --- a/api/particle/index.html +++ b/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.particle ​

本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- + \ No newline at end of file diff --git a/api/presets/index.html b/api/presets/index.html index a0ca1b8..ab0a6b0 100644 --- a/api/presets/index.html +++ b/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

模块 mbcp.presets ​

本模块塞了一些预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- + \ No newline at end of file diff --git a/api/presets/model/index.html b/api/presets/model/index.html index 3f92def..d64cce4 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP 文档 - + - - + + @@ -36,7 +36,7 @@ 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_plane.md.DQhjzD06.js b/assets/api_mp_math_plane.md.DQhjzD06.js deleted file mode 100644 index 81624c4..0000000 --- a/assets/api_mp_math_plane.md.DQhjzD06.js +++ /dev/null @@ -1,206 +0,0 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n(`

模块 mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

说明: 平面方程：ax + by + cz + d = 0

参数:

源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
-    """
-        平面方程：ax + by + cz + d = 0
-        Args:
-            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
-            b (\`float\`): y系数
-            c (\`float\`): z系数
-            d (\`float\`): 常数项
-        """
-    self.a = a
-    self.b = b
-    self.c = c
-    self.d = d

method approx(self, other: Plane3) -> bool ​

说明: 判断两个平面是否近似相等。

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: 'Plane3') -> bool:
-    """
-        判断两个平面是否近似相等。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    if self.a != 0:
-        k = other.a / self.a
-        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.b != 0:
-        k = other.b / self.b
-        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.c != 0:
-        k = other.c / self.c
-        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
-    else:
-        return False

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

说明: 计算平面与平面之间的夹角。

参数:

返回: AnyAngle: 夹角

引发:

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
-    """
-        计算平面与平面之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Line3):
-        return self.normal.cal_angle(other.direction).complementary
-    elif isinstance(other, Plane3):
-        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

说明: 计算平面与平面或点之间的距离。

参数:

返回: float: 距离

引发:

源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
-    """
-        计算平面与平面或点之间的距离。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        return 0
-    elif isinstance(other, Point3):
-        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

说明: 计算两平面的交线。

参数:

返回: Line3: 交线

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-    """
-        计算两平面的交线。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`Line3\`](./line#class-line3): 交线
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
-        """
-    if self.normal.is_parallel(other.normal):
-        raise ValueError('Planes are parallel and have no intersection.')
-    direction = self.normal.cross(other.normal)
-    x, y, z = (0, 0, 0)
-    if self.a != 0 and other.a != 0:
-        A = np.array([[self.b, self.c], [other.b, other.c]])
-        B = np.array([-self.d, -other.d])
-        y, z = np.linalg.solve(A, B)
-    elif self.b != 0 and other.b != 0:
-        A = np.array([[self.a, self.c], [other.a, other.c]])
-        B = np.array([-self.d, -other.d])
-        x, z = np.linalg.solve(A, B)
-    elif self.c != 0 and other.c != 0:
-        A = np.array([[self.a, self.b], [other.a, other.b]])
-        B = np.array([-self.d, -other.d])
-        x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

说明: 计算平面与直线的交点。

参数:

返回: Point3: 交点

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
-    """
-        计算平面与直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
-        """
-    if self.normal @ other.direction == 0:
-        raise ValueError('The plane and the line are parallel or coincident.')
-    x, y, z = other.get_parametric_equations()
-    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

说明: 计算平行于该平面且过指定点的平面。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    """
-        计算平行于该平面且过指定点的平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

说明: 判断两个平面是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
-    """
-        判断两个平面是否平行。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

说明: 平面的法向量。

返回: Vector3: 法向量

源代码 或 在GitHub上查看
python
@property
-def normal(self) -> 'Vector3':
-    """
-        平面的法向量。
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 法向量
-        """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
@classmethod
-def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
-    """
-        工厂函数 由点和法向量构造平面(点法式构造)。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    a, b, c = (normal.x, normal.y, normal.z)
-    d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

说明: 工厂函数 由三点构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
-def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
-    """
-        工厂函数 由三点构造平面。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 (\`Point3\`): 点2
-            p3 (\`Point3\`): 点3
-        Returns:
-            平面
-        """
-    v1 = p2 - p1
-    v2 = p3 - p1
-    normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

说明: 工厂函数 由两直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
-def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由两直线构造平面。
-        Args:
-            l1 ([\`Line3\`](./line#class-line3)): 直线
-            l2 (\`Line3\`): 直线
-        Returns:
-            平面
-        """
-    v1 = l1.direction
-    v2 = l2.point - l1.point
-    if v2 == zero_vector3:
-        v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
-def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由点和直线构造平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            line ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            平面
-        """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

说明: 取两平面的交集（人话：交线）

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码 或 在GitHub上查看
python
def __and__(self, other):
-    """
-        取两平面的交集（人话：交线）
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        if self.normal.is_parallel(other.normal):
-            return None
-        return self.cal_intersection_line3(other)
-    elif isinstance(other, Line3):
-        if self.normal @ other.direction == 0:
-            return None
-        return self.cal_intersection_point3(other)
-    else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        判断两个平面是否等价。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
-        """
-    return self.approx(other)

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

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_plane.md.DQhjzD06.lean.js b/assets/api_mp_math_plane.md.DQhjzD06.lean.js deleted file mode 100644 index 217bc99..0000000 --- a/assets/api_mp_math_plane.md.DQhjzD06.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/api_mp_math_plane.md.dDWoDJrS.js b/assets/api_mp_math_plane.md.dDWoDJrS.js new file mode 100644 index 0000000..57cde13 --- /dev/null +++ b/assets/api_mp_math_plane.md.dDWoDJrS.js @@ -0,0 +1,227 @@ +import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const qs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),e={name:"api/mp_math/plane.md"},h=t(`

模块 mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

说明: 平面方程：ax + by + cz + d = 0

参数:

源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
+            b (\`float\`): y系数
+            c (\`float\`): z系数
+            d (\`float\`): 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d

method approx(self, other: Plane3) -> bool ​

说明: 判断两个平面是否近似相等。

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: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False

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

说明: 计算平面与平面之间的夹角。

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参数:

返回: AnyAngle: 夹角

引发:

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n1 \\\\cdot n2}{|n1| \\\\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n \\\\cdot d}{|n| \\\\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

说明: 计算平面与平面或点之间的距离。

参数:

返回: float: 距离

引发:

源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

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

说明: 计算两平面的交线。

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参数:

返回: Line3: 交线

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\\\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\\\begin{cases} x = x_0 + dt \\\\\\\\ y = y_0 + dt \\\\\\\\ z = z_0 + dt \\\\end{cases} $$
+        或
+        $$ \\\\frac{x - x_0}{m} = \\\\frac{y - y_0}{n} = \\\\frac{z - z_0}{p} $$
+        :::
+
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`Line3\`](./line#class-line3): 交线
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

说明: 计算平面与直线的交点。

参数:

返回: Point3: 交点

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            [\`Point3\`](./point#class-point3): 交点
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

说明: 计算平行于该平面且过指定点的平面。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 指定点
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

说明: 判断两个平面是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

说明: 平面的法向量。

返回: Vector3: 法向量

源代码 或 在GitHub上查看
python
@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            [\`Vector3\`](./vector#class-vector3): 法向量
+        """
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

说明: 工厂函数 由点和法向量构造平面(点法式构造)。

参数:

返回: Plane3: 平面

源代码 或 在GitHub上查看
python
@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

说明: 工厂函数 由三点构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1 ([\`Point3\`](./point#class-point3)): 点1
+            p2 (\`Point3\`): 点2
+            p3 (\`Point3\`): 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

说明: 工厂函数 由两直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1 ([\`Line3\`](./line#class-line3)): 直线
+            l2 (\`Line3\`): 直线
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

说明: 工厂函数 由点和直线构造平面。

参数:

返回: 平面

源代码 或 在GitHub上查看
python
@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            line ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

说明: 取两平面的交集（人话：交线）

参数:

返回: Line3 | Point3 | None: 交集

引发:

源代码 或 在GitHub上查看
python
def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

说明: 判断两个平面是否等价。

参数:

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
+    """
+        判断两个平面是否等价。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
+        """
+    return self.approx(other)

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

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
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E=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"},e=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):
-    """
-        3维向量
-        Args:
-            x ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量
-            y (\`float\`): y轴分量
-            z (\`float\`): z轴分量
-        """
-    self.x = x
-    self.y = y
-    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:
-    """
-        判断两个向量是否近似相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    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。

参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
-    """
-        计算两个向量之间的夹角。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

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':
-    """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        \`\`i  j  k\`\`
-
-        \`\`x1 y1 z1\`\`
-
-        \`\`x2 y2 z2\`\`
-
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`Vector3\`](#class-vector3): 叉乘结果
-        """
-    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:
-    """
-        判断两个向量是否近似平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
-        """
-    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:
-    """
-        判断两个向量是否平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    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):
-    """
-        将向量归一化。
-
-        自体归一化，不返回值。
-        """
-    length = self.length
-    self.x /= length
-    self.y /= length
-    self.z /= length

@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':
-    """
-        返回numpy数组
-        Returns:
-            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
-        """
-    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
-def length(self) -> float:
-    """
-        向量的模。
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
-        """
-    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
-def unit(self) -> 'Vector3':
-    """
-        获取该向量的单位向量。
-        Returns:
-            [\`Vector3\`](#class-vector3): 单位向量
-        """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
-    """
-        V + P -> P
-
-        V + V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
-    else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
-    """
-        判断两个向量是否相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
-        """
-    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':
-    """
-        P + V -> P
-
-        别去点那边实现了。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    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
-def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
-    """
-        V - P -> P
-
-        V - V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
-    else:
-        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'):
-    """
-        P - V -> P
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    if isinstance(other, Point3):
-        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
-    else:
-        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
-def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
-    """
-        数组运算 非点乘。点乘使用@，叉乘使用cross。
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
-        Returns:
-            [\`Vector3\`](#class-vector): 数组运算结果
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
-    elif isinstance(other, (float, int)):
-        return Vector3(self.x * other, self.y * other, self.z * other)
-    else:
-        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':
-    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':
-    """
-        点乘。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
-        """
-    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':
-    """
-        取负。
-        Returns:
-            [\`Vector3\`](#class-vector3): 负向量
-        """
-    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

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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    """\n        3维向量\n        Args:\n            x ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量\n            y (`float`): y轴分量\n            z (`float`): z轴分量\n        """\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    """\n        判断两个向量是否近似相等。\n        Args:\n            other ([`Vector3`](#class-vector3)): 另一个向量\n            epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差\n\n        Returns:\n            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等\n        """\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。

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参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    """
+        计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{v1 \\\\cdot v2}{|v1| \\\\cdot |v2|})$$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        """
+    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

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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':
+    """
+        向量积 叉乘：v1 x v2 -> v3
+
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\\\times v2 = (v1_y \\\\cdot v2_z - v1_z \\\\cdot v2_y, v1_z \\\\cdot v2_x - v1_x \\\\cdot v2_z, v1_x \\\\cdot v2_y - v1_y \\\\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\\\times v2 = \\\\begin{vmatrix} i & j & k \\\\\\\\ v1_x & v1_y & v1_z \\\\\\\\ v2_x & v2_y & v2_z \\\\end{vmatrix} $$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`Vector3\`](#class-vector3): 叉乘结果
+        """
+    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:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
+        """
+    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:
+    """
+        判断两个向量是否平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    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):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length

@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':
+    """
+        返回numpy数组
+        Returns:
+            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
+        """
+    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
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
+        """
+    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
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            [\`Vector3\`](#class-vector3): 单位向量
+        """
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+    """
+        判断两个向量是否相等。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
+        """
+    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':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    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
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        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'):
+    """
+        P - V -> P
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        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
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
+        Returns:
+            [\`Vector3\`](#class-vector): 数组运算结果
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        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':
+    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':
+    """
+        点乘。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
+        """
+    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':
+    """
+        取负。
+        Returns:
+            [\`Vector3\`](#class-vector3): 负向量
+        """
+    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

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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 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mbcp.mp_math.plane","class Plane3"]},"96":{"title":"Module mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["Module mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["Module mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["Module mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["Module mbcp.mp_math.point","class Point3"]},"105":{"title":"Module mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["Module mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["Module mbcp.mp_math.segment","class Segment3"]},"108":{"title":"Module mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["Module mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["Module mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["Module mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["Module mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["Module mbcp.mp_math.utils"]},"118":{"title":"Module mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["Module mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["Module mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["Module mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["Module mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["Module mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> 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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 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AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["模块 mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"模块 mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["模块 mbcp.mp_math.const"]},"25":{"title":"var E","titles":["模块 mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["模块 mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["模块 mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["模块 mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["模块 mbcp.mp_math.const"]},"30":{"title":"模块 mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["模块 mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["模块 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模块 mbcp.mp_math.equation"]},"35":{"title":"模块 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模块 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模块 mbcp.mp_math.function"]},"38":{"title":"模块 mbcp.mp_math","titles":[]},"39":{"title":"模块 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模块 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模块 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模块 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模块 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模块 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模块 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模块 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模块 mbcp.mp_math.line","class Line3"]},"56":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["模块 mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["模块 mbcp.mp_math.line","class Line3"]},"58":{"title":"模块 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模块 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模块 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模块 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模块 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模块 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模块 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模块 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method __and__(self, other)","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["模块 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模块 mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["模块 mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["模块 mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["模块 mbcp.mp_math.point","class Point3"]},"105":{"title":"模块 mbcp.mp_math.utils","titles":[]},"106":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模块 mbcp.mp_math.utils"]},"107":{"title":"class Approx","titles":["模块 mbcp.mp_math.utils"]},"108":{"title":"method __init__(self, value: RealNumber)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"109":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"110":{"title":"method raise_type_error(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"111":{"title":"method __ne__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"112":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.utils"]},"113":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"114":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"115":{"title":"模块 mbcp.mp_math.segment","titles":[]},"116":{"title":"class Segment3","titles":["模块 mbcp.mp_math.segment"]},"117":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模块 mbcp.mp_math.segment","class Segment3"]},"118":{"title":"模块 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模块 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - other","titles":["模块 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OneVarFunc)","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["模組 mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["模組 mbcp.mp_math.equation"]},"35":{"title":"模組 mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["模組 mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["模組 mbcp.mp_math.function"]},"38":{"title":"模組 mbcp.mp_math","titles":[]},"39":{"title":"模組 mbcp.mp_math.line","titles":[]},"40":{"title":"class Line3","titles":["模組 mbcp.mp_math.line"]},"41":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["模組 mbcp.mp_math.line","class Line3"]},"42":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"43":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["模組 mbcp.mp_math.line","class Line3"]},"44":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["模組 mbcp.mp_math.line","class Line3"]},"45":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"46":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"47":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["模組 mbcp.mp_math.line","class Line3"]},"48":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["模組 mbcp.mp_math.line","class Line3"]},"49":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"50":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"51":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"52":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"53":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"54":{"title":"method simplify(self)","titles":["模組 mbcp.mp_math.line","class Line3"]},"55":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["模組 mbcp.mp_math.line","class Line3"]},"56":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["模組 mbcp.mp_math.line","class Line3"]},"57":{"title":"method __eq__(self, other) -> bool","titles":["模組 mbcp.mp_math.line","class Line3"]},"58":{"title":"模組 mbcp.mp_math.mp_math_typing","titles":[]},"59":{"title":"var RealNumber","titles":["模組 mbcp.mp_math.mp_math_typing"]},"60":{"title":"var Number","titles":["模組 mbcp.mp_math.mp_math_typing"]},"61":{"title":"var SingleVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"62":{"title":"var ArrayVar","titles":["模組 mbcp.mp_math.mp_math_typing"]},"63":{"title":"var Var","titles":["模組 mbcp.mp_math.mp_math_typing"]},"64":{"title":"var OneSingleVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"65":{"title":"var OneArrayFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"66":{"title":"var OneVarFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"67":{"title":"var TwoSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"68":{"title":"var TwoArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"69":{"title":"var TwoVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"70":{"title":"var ThreeSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"71":{"title":"var ThreeArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"72":{"title":"var ThreeVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"73":{"title":"var MultiSingleVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"74":{"title":"var MultiArraysFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"75":{"title":"var MultiVarsFunc","titles":["模組 mbcp.mp_math.mp_math_typing"]},"76":{"title":"模組 mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["模組 mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method __and__(self, other)","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["模組 mbcp.mp_math.plane","class Plane3"]},"96":{"title":"模組 mbcp.mp_math.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 __eq__(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 __eq__(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["模組 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模組 mbcp.mp_math.utils"]},"118":{"title":"模組 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模組 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模組 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - 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qs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),e={name:"en/api/mp_math/plane.md"},h=t(`

Module mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

Description: 平面方程：ax + by + cz + d = 0

Arguments:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
+            b (\`float\`): y系数
+            c (\`float\`): z系数
+            d (\`float\`): 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d

method approx(self, other: Plane3) -> bool ​

Description: 判断两个平面是否近似相等。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False

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

Description: 计算平面与平面之间的夹角。

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Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n1 \\\\cdot n2}{|n1| \\\\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n \\\\cdot d}{|n| \\\\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

Description: 计算平面与平面或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

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

Description: 计算两平面的交线。

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Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\\\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\\\begin{cases} x = x_0 + dt \\\\\\\\ y = y_0 + dt \\\\\\\\ z = z_0 + dt \\\\end{cases} $$
+        或
+        $$ \\\\frac{x - x_0}{m} = \\\\frac{y - y_0}{n} = \\\\frac{z - z_0}{p} $$
+        :::
+
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`Line3\`](./line#class-line3): 交线
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

Description: 计算平面与直线的交点。

Arguments:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            [\`Point3\`](./point#class-point3): 交点
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

Description: 计算平行于该平面且过指定点的平面。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 指定点
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            [\`Vector3\`](./vector#class-vector3): 法向量
+        """
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

Description: 工厂函数 由三点构造平面。

Arguments:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1 ([\`Point3\`](./point#class-point3)): 点1
+            p2 (\`Point3\`): 点2
+            p3 (\`Point3\`): 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

Description: 工厂函数 由两直线构造平面。

Arguments:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1 ([\`Line3\`](./line#class-line3)): 直线
+            l2 (\`Line3\`): 直线
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            line ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

Description: 判断两个平面是否等价。

Arguments:

  • 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:
+    """
+        判断两个平面是否等价。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
+        """
+    return self.approx(other)

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

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
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Module mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

Description: 平面方程：ax + by + cz + d = 0

Arguments:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
-    """
-        平面方程：ax + by + cz + d = 0
-        Args:
-            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
-            b (\`float\`): y系数
-            c (\`float\`): z系数
-            d (\`float\`): 常数项
-        """
-    self.a = a
-    self.b = b
-    self.c = c
-    self.d = d

method approx(self, other: Plane3) -> bool ​

Description: 判断两个平面是否近似相等。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
-    """
-        判断两个平面是否近似相等。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    if self.a != 0:
-        k = other.a / self.a
-        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.b != 0:
-        k = other.b / self.b
-        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.c != 0:
-        k = other.c / self.c
-        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
-    else:
-        return False

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

Description: 计算平面与平面之间的夹角。

Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
-    """
-        计算平面与平面之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Line3):
-        return self.normal.cal_angle(other.direction).complementary
-    elif isinstance(other, Plane3):
-        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

Description: 计算平面与平面或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
-    """
-        计算平面与平面或点之间的距离。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        return 0
-    elif isinstance(other, Point3):
-        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

Description: 计算两平面的交线。

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-    """
-        计算两平面的交线。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`Line3\`](./line#class-line3): 交线
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
-        """
-    if self.normal.is_parallel(other.normal):
-        raise ValueError('Planes are parallel and have no intersection.')
-    direction = self.normal.cross(other.normal)
-    x, y, z = (0, 0, 0)
-    if self.a != 0 and other.a != 0:
-        A = np.array([[self.b, self.c], [other.b, other.c]])
-        B = np.array([-self.d, -other.d])
-        y, z = np.linalg.solve(A, B)
-    elif self.b != 0 and other.b != 0:
-        A = np.array([[self.a, self.c], [other.a, other.c]])
-        B = np.array([-self.d, -other.d])
-        x, z = np.linalg.solve(A, B)
-    elif self.c != 0 and other.c != 0:
-        A = np.array([[self.a, self.b], [other.a, other.b]])
-        B = np.array([-self.d, -other.d])
-        x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

Description: 计算平面与直线的交点。

Arguments:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
-    """
-        计算平面与直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
-        """
-    if self.normal @ other.direction == 0:
-        raise ValueError('The plane and the line are parallel or coincident.')
-    x, y, z = other.get_parametric_equations()
-    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

Description: 计算平行于该平面且过指定点的平面。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    """
-        计算平行于该平面且过指定点的平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
-    """
-        判断两个平面是否平行。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
-def normal(self) -> 'Vector3':
-    """
-        平面的法向量。
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 法向量
-        """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
-def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
-    """
-        工厂函数 由点和法向量构造平面(点法式构造)。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    a, b, c = (normal.x, normal.y, normal.z)
-    d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

Description: 工厂函数 由三点构造平面。

Arguments:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
-def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
-    """
-        工厂函数 由三点构造平面。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 (\`Point3\`): 点2
-            p3 (\`Point3\`): 点3
-        Returns:
-            平面
-        """
-    v1 = p2 - p1
-    v2 = p3 - p1
-    normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

Description: 工厂函数 由两直线构造平面。

Arguments:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
-def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由两直线构造平面。
-        Args:
-            l1 ([\`Line3\`](./line#class-line3)): 直线
-            l2 (\`Line3\`): 直线
-        Returns:
-            平面
-        """
-    v1 = l1.direction
-    v2 = l2.point - l1.point
-    if v2 == zero_vector3:
-        v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
-def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由点和直线构造平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            line ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            平面
-        """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
-    """
-        取两平面的交集（人话：交线）
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        if self.normal.is_parallel(other.normal):
-            return None
-        return self.cal_intersection_line3(other)
-    elif isinstance(other, Line3):
-        if self.normal @ other.direction == 0:
-            return None
-        return self.cal_intersection_point3(other)
-    else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

Description: 判断两个平面是否等价。

Arguments:

  • 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:
-    """
-        判断两个平面是否等价。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
-        """
-    return self.approx(other)

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

Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{y as __pageData,c as default}; diff --git a/assets/en_api_mp_math_plane.md.op2OK8nC.lean.js b/assets/en_api_mp_math_plane.md.op2OK8nC.lean.js deleted file mode 100644 index 96be146..0000000 --- a/assets/en_api_mp_math_plane.md.op2OK8nC.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},t=n("",113),h=[t];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{y as __pageData,c as default}; diff --git a/assets/en_api_mp_math_vector.md.DpzqycDg.js b/assets/en_api_mp_math_vector.md.DpzqycDg.js deleted file mode 100644 index 14b69fb..0000000 --- a/assets/en_api_mp_math_vector.md.DpzqycDg.js +++ /dev/null @@ -1,197 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=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"},e=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):
-    """
-        3维向量
-        Args:
-            x ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量
-            y (\`float\`): y轴分量
-            z (\`float\`): z轴分量
-        """
-    self.x = x
-    self.y = y
-    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:
-    """
-        判断两个向量是否近似相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    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。

Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
-    """
-        计算两个向量之间的夹角。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
-    """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        \`\`i  j  k\`\`
-
-        \`\`x1 y1 z1\`\`
-
-        \`\`x2 y2 z2\`\`
-
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`Vector3\`](#class-vector3): 叉乘结果
-        """
-    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:
-    """
-        判断两个向量是否近似平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
-        """
-    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:
-    """
-        判断两个向量是否平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    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):
-    """
-        将向量归一化。
-
-        自体归一化，不返回值。
-        """
-    length = self.length
-    self.x /= length
-    self.y /= length
-    self.z /= length

@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':
-    """
-        返回numpy数组
-        Returns:
-            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
-        """
-    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
-def length(self) -> float:
-    """
-        向量的模。
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
-        """
-    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
-def unit(self) -> 'Vector3':
-    """
-        获取该向量的单位向量。
-        Returns:
-            [\`Vector3\`](#class-vector3): 单位向量
-        """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
-    """
-        V + P -> P
-
-        V + V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
-    else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
-    """
-        判断两个向量是否相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
-        """
-    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':
-    """
-        P + V -> P
-
-        别去点那边实现了。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    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
-def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
-    """
-        V - P -> P
-
-        V - V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
-    else:
-        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'):
-    """
-        P - V -> P
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    if isinstance(other, Point3):
-        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
-    else:
-        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
-def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
-    """
-        数组运算 非点乘。点乘使用@，叉乘使用cross。
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
-        Returns:
-            [\`Vector3\`](#class-vector): 数组运算结果
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
-    elif isinstance(other, (float, int)):
-        return Vector3(self.x * other, self.y * other, self.z * other)
-    else:
-        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':
-    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':
-    """
-        点乘。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
-        """
-    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':
-    """
-        取负。
-        Returns:
-            [\`Vector3\`](#class-vector3): 负向量
-        """
-    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)

`,138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_vector.md.DpzqycDg.lean.js b/assets/en_api_mp_math_vector.md.DpzqycDg.lean.js deleted file mode 100644 index c32f366..0000000 --- a/assets/en_api_mp_math_vector.md.DpzqycDg.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=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"},e=t("",138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_vector.md.OzaLDP6e.js b/assets/en_api_mp_math_vector.md.OzaLDP6e.js new file mode 100644 index 0000000..ff07c55 --- /dev/null +++ b/assets/en_api_mp_math_vector.md.OzaLDP6e.js @@ -0,0 +1,176 @@ +import{_ as n,c as i,j as s,a4 as a,o as t}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"}'),e={name:"en/api/mp_math/vector.md"},l=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    """\n        3维向量\n        Args:\n            x ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量\n            y (`float`): y轴分量\n            z (`float`): z轴分量\n        """\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    """\n        判断两个向量是否近似相等。\n        Args:\n            other ([`Vector3`](#class-vector3)): 另一个向量\n            epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差\n\n        Returns:\n            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等\n        """\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。

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Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    """
+        计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{v1 \\\\cdot v2}{|v1| \\\\cdot |v2|})$$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        """
+    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

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Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    """
+        向量积 叉乘：v1 x v2 -> v3
+
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\\\times v2 = (v1_y \\\\cdot v2_z - v1_z \\\\cdot v2_y, v1_z \\\\cdot v2_x - v1_x \\\\cdot v2_z, v1_x \\\\cdot v2_y - v1_y \\\\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\\\times v2 = \\\\begin{vmatrix} i & j & k \\\\\\\\ v1_x & v1_y & v1_z \\\\\\\\ v2_x & v2_y & v2_z \\\\end{vmatrix} $$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`Vector3\`](#class-vector3): 叉乘结果
+        """
+    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:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
+        """
+    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:
+    """
+        判断两个向量是否平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    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):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length

@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':
+    """
+        返回numpy数组
+        Returns:
+            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
+        """
+    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
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
+        """
+    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
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            [\`Vector3\`](#class-vector3): 单位向量
+        """
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+    """
+        判断两个向量是否相等。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
+        """
+    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':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    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
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        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'):
+    """
+        P - V -> P
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        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
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
+        Returns:
+            [\`Vector3\`](#class-vector): 数组运算结果
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        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':
+    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':
+    """
+        点乘。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
+        """
+    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':
+    """
+        取负。
+        Returns:
+            [\`Vector3\`](#class-vector3): 负向量
+        """
+    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)

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D(w,q,A,L,M,P){return t(),i("div",null,[l,s("div",h,[p,r,s("mjx-container",o,[(t(),i("svg",k,T)),Q])]),g,s("div",c,[m,y,s("mjx-container",E,[(t(),i("svg",F,b)),f]),C,s("mjx-container",v,[(t(),i("svg",B,V)),H])]),x])}const R=n(e,[["render",D]]);export{z as __pageData,R as default}; diff --git a/assets/ja_api_mp_math_plane.md.D8ltDTI9.js b/assets/ja_api_mp_math_plane.md.D8ltDTI9.js deleted file mode 100644 index b06affe..0000000 --- a/assets/ja_api_mp_math_plane.md.D8ltDTI9.js +++ /dev/null @@ -1,206 +0,0 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},t=n(`

モジュール mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

説明: 平面方程：ax + by + cz + d = 0

引数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
-    """
-        平面方程：ax + by + cz + d = 0
-        Args:
-            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
-            b (\`float\`): y系数
-            c (\`float\`): z系数
-            d (\`float\`): 常数项
-        """
-    self.a = a
-    self.b = b
-    self.c = c
-    self.d = d

method approx(self, other: Plane3) -> bool ​

説明: 判断两个平面是否近似相等。

引数:

  • other (Plane3): 另一个平面

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: 'Plane3') -> bool:
-    """
-        判断两个平面是否近似相等。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    if self.a != 0:
-        k = other.a / self.a
-        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.b != 0:
-        k = other.b / self.b
-        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.c != 0:
-        k = other.c / self.c
-        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
-    else:
-        return False

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

説明: 计算平面与平面之间的夹角。

引数:

戻り値: AnyAngle: 夹角

例外:

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
-    """
-        计算平面与平面之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Line3):
-        return self.normal.cal_angle(other.direction).complementary
-    elif isinstance(other, Plane3):
-        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
-    """
-        计算平面与平面或点之间的距离。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        return 0
-    elif isinstance(other, Point3):
-        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-    """
-        计算两平面的交线。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`Line3\`](./line#class-line3): 交线
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
-        """
-    if self.normal.is_parallel(other.normal):
-        raise ValueError('Planes are parallel and have no intersection.')
-    direction = self.normal.cross(other.normal)
-    x, y, z = (0, 0, 0)
-    if self.a != 0 and other.a != 0:
-        A = np.array([[self.b, self.c], [other.b, other.c]])
-        B = np.array([-self.d, -other.d])
-        y, z = np.linalg.solve(A, B)
-    elif self.b != 0 and other.b != 0:
-        A = np.array([[self.a, self.c], [other.a, other.c]])
-        B = np.array([-self.d, -other.d])
-        x, z = np.linalg.solve(A, B)
-    elif self.c != 0 and other.c != 0:
-        A = np.array([[self.a, self.b], [other.a, other.b]])
-        B = np.array([-self.d, -other.d])
-        x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

引数:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
-    """
-        计算平面与直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
-        """
-    if self.normal @ other.direction == 0:
-        raise ValueError('The plane and the line are parallel or coincident.')
-    x, y, z = other.get_parametric_equations()
-    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    """
-        计算平行于该平面且过指定点的平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

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: 'Plane3') -> bool:
-    """
-        判断两个平面是否平行。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
-def normal(self) -> 'Vector3':
-    """
-        平面的法向量。
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 法向量
-        """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
-def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
-    """
-        工厂函数 由点和法向量构造平面(点法式构造)。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    a, b, c = (normal.x, normal.y, normal.z)
-    d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

引数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
-def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
-    """
-        工厂函数 由三点构造平面。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 (\`Point3\`): 点2
-            p3 (\`Point3\`): 点3
-        Returns:
-            平面
-        """
-    v1 = p2 - p1
-    v2 = p3 - p1
-    normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

引数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
-def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由两直线构造平面。
-        Args:
-            l1 ([\`Line3\`](./line#class-line3)): 直线
-            l2 (\`Line3\`): 直线
-        Returns:
-            平面
-        """
-    v1 = l1.direction
-    v2 = l2.point - l1.point
-    if v2 == zero_vector3:
-        v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
-def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由点和直线构造平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            line ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            平面
-        """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
-    """
-        取两平面的交集（人话：交线）
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        if self.normal.is_parallel(other.normal):
-            return None
-        return self.cal_intersection_line3(other)
-    elif isinstance(other, Line3):
-        if self.normal @ other.direction == 0:
-            return None
-        return self.cal_intersection_point3(other)
-    else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
-    """
-        判断两个平面是否等价。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
-        """
-    return self.approx(other)

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

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/ja_api_mp_math_plane.md.D8ltDTI9.lean.js b/assets/ja_api_mp_math_plane.md.D8ltDTI9.lean.js deleted file mode 100644 index 8a72354..0000000 --- a/assets/ja_api_mp_math_plane.md.D8ltDTI9.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/ja_api_mp_math_plane.md.DmM6KUUe.js b/assets/ja_api_mp_math_plane.md.DmM6KUUe.js new file mode 100644 index 0000000..2759a9d --- /dev/null +++ b/assets/ja_api_mp_math_plane.md.DmM6KUUe.js @@ -0,0 +1,227 @@ +import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const qs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),e={name:"ja/api/mp_math/plane.md"},h=t(`

モジュール mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

説明: 平面方程：ax + by + cz + d = 0

引数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
+            b (\`float\`): y系数
+            c (\`float\`): z系数
+            d (\`float\`): 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d

method approx(self, other: Plane3) -> bool ​

説明: 判断两个平面是否近似相等。

引数:

  • other (Plane3): 另一个平面

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: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False

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

説明: 计算平面与平面之间的夹角。

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引数:

戻り値: AnyAngle: 夹角

例外:

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n1 \\\\cdot n2}{|n1| \\\\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n \\\\cdot d}{|n| \\\\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

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引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\\\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\\\begin{cases} x = x_0 + dt \\\\\\\\ y = y_0 + dt \\\\\\\\ z = z_0 + dt \\\\end{cases} $$
+        或
+        $$ \\\\frac{x - x_0}{m} = \\\\frac{y - y_0}{n} = \\\\frac{z - z_0}{p} $$
+        :::
+
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`Line3\`](./line#class-line3): 交线
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

引数:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            [\`Point3\`](./point#class-point3): 交点
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 指定点
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

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: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            [\`Vector3\`](./vector#class-vector3): 法向量
+        """
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

引数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1 ([\`Point3\`](./point#class-point3)): 点1
+            p2 (\`Point3\`): 点2
+            p3 (\`Point3\`): 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

引数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1 ([\`Line3\`](./line#class-line3)): 直线
+            l2 (\`Line3\`): 直线
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            line ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+    """
+        判断两个平面是否等价。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
+        """
+    return self.approx(other)

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

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
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E=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"},e=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):
-    """
-        3维向量
-        Args:
-            x ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量
-            y (\`float\`): y轴分量
-            z (\`float\`): z轴分量
-        """
-    self.x = x
-    self.y = y
-    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:
-    """
-        判断两个向量是否近似相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    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。

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':
-    """
-        计算两个向量之间的夹角。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

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':
-    """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        \`\`i  j  k\`\`
-
-        \`\`x1 y1 z1\`\`
-
-        \`\`x2 y2 z2\`\`
-
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`Vector3\`](#class-vector3): 叉乘结果
-        """
-    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:
-    """
-        判断两个向量是否近似平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
-        """
-    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:
-    """
-        判断两个向量是否平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    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):
-    """
-        将向量归一化。
-
-        自体归一化，不返回值。
-        """
-    length = self.length
-    self.x /= length
-    self.y /= length
-    self.z /= length

@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':
-    """
-        返回numpy数组
-        Returns:
-            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
-        """
-    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
-def length(self) -> float:
-    """
-        向量的模。
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
-        """
-    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
-def unit(self) -> 'Vector3':
-    """
-        获取该向量的单位向量。
-        Returns:
-            [\`Vector3\`](#class-vector3): 单位向量
-        """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
-    """
-        V + P -> P
-
-        V + V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
-    else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
-    """
-        判断两个向量是否相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
-        """
-    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':
-    """
-        P + V -> P
-
-        别去点那边实现了。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    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
-def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
-    """
-        V - P -> P
-
-        V - V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
-    else:
-        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'):
-    """
-        P - V -> P
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    if isinstance(other, Point3):
-        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
-    else:
-        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
-def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
-    """
-        数组运算 非点乘。点乘使用@，叉乘使用cross。
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
-        Returns:
-            [\`Vector3\`](#class-vector): 数组运算结果
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
-    elif isinstance(other, (float, int)):
-        return Vector3(self.x * other, self.y * other, self.z * other)
-    else:
-        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':
-    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':
-    """
-        点乘。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
-        """
-    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':
-    """
-        取负。
-        Returns:
-            [\`Vector3\`](#class-vector3): 负向量
-        """
-    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)

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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    """\n        3维向量\n        Args:\n            x ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量\n            y (`float`): y轴分量\n            z (`float`): z轴分量\n        """\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    """\n        判断两个向量是否近似相等。\n        Args:\n            other ([`Vector3`](#class-vector3)): 另一个向量\n            epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差\n\n        Returns:\n            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等\n        """\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。

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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':
+    """
+        计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{v1 \\\\cdot v2}{|v1| \\\\cdot |v2|})$$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        """
+    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

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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':
+    """
+        向量积 叉乘：v1 x v2 -> v3
+
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\\\times v2 = (v1_y \\\\cdot v2_z - v1_z \\\\cdot v2_y, v1_z \\\\cdot v2_x - v1_x \\\\cdot v2_z, v1_x \\\\cdot v2_y - v1_y \\\\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\\\times v2 = \\\\begin{vmatrix} i & j & k \\\\\\\\ v1_x & v1_y & v1_z \\\\\\\\ v2_x & v2_y & v2_z \\\\end{vmatrix} $$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`Vector3\`](#class-vector3): 叉乘结果
+        """
+    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:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
+        """
+    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:
+    """
+        判断两个向量是否平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    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):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length

@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':
+    """
+        返回numpy数组
+        Returns:
+            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
+        """
+    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
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
+        """
+    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
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            [\`Vector3\`](#class-vector3): 单位向量
+        """
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+    """
+        判断两个向量是否相等。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
+        """
+    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':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    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
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        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'):
+    """
+        P - V -> P
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        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
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
+        Returns:
+            [\`Vector3\`](#class-vector): 数组运算结果
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        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':
+    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':
+    """
+        点乘。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
+        """
+    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':
+    """
+        取负。
+        Returns:
+            [\`Vector3\`](#class-vector3): 负向量
+        """
+    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)

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y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},t=n(`

模組 mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

説明: 平面方程：ax + by + cz + d = 0

變數説明:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
-    """
-        平面方程：ax + by + cz + d = 0
-        Args:
-            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
-            b (\`float\`): y系数
-            c (\`float\`): z系数
-            d (\`float\`): 常数项
-        """
-    self.a = a
-    self.b = b
-    self.c = c
-    self.d = d

method approx(self, other: Plane3) -> bool ​

説明: 判断两个平面是否近似相等。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
-    """
-        判断两个平面是否近似相等。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    if self.a != 0:
-        k = other.a / self.a
-        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.b != 0:
-        k = other.b / self.b
-        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
-    elif self.c != 0:
-        k = other.c / self.c
-        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
-    else:
-        return False

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

説明: 计算平面与平面之间的夹角。

變數説明:

返回: AnyAngle: 夹角

抛出:

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
-    """
-        计算平面与平面之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Line3):
-        return self.normal.cal_angle(other.direction).complementary
-    elif isinstance(other, Plane3):
-        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

變數説明:

返回: float: 距离

抛出:

源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
-    """
-        计算平面与平面或点之间的距离。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        return 0
-    elif isinstance(other, Point3):
-        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
-    else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-    """
-        计算两平面的交线。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`Line3\`](./line#class-line3): 交线
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
-        """
-    if self.normal.is_parallel(other.normal):
-        raise ValueError('Planes are parallel and have no intersection.')
-    direction = self.normal.cross(other.normal)
-    x, y, z = (0, 0, 0)
-    if self.a != 0 and other.a != 0:
-        A = np.array([[self.b, self.c], [other.b, other.c]])
-        B = np.array([-self.d, -other.d])
-        y, z = np.linalg.solve(A, B)
-    elif self.b != 0 and other.b != 0:
-        A = np.array([[self.a, self.c], [other.a, other.c]])
-        B = np.array([-self.d, -other.d])
-        x, z = np.linalg.solve(A, B)
-    elif self.c != 0 and other.c != 0:
-        A = np.array([[self.a, self.b], [other.a, other.b]])
-        B = np.array([-self.d, -other.d])
-        x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

變數説明:

返回: Point3: 交点

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
-    """
-        计算平面与直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
-        """
-    if self.normal @ other.direction == 0:
-        raise ValueError('The plane and the line are parallel or coincident.')
-    x, y, z = other.get_parametric_equations()
-    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
-    """
-        计算平行于该平面且过指定点的平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
-    """
-        判断两个平面是否平行。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

返回: Vector3: 法向量

源碼 或 於GitHub上查看
python
@property
-def normal(self) -> 'Vector3':
-    """
-        平面的法向量。
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 法向量
-        """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
@classmethod
-def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
-    """
-        工厂函数 由点和法向量构造平面(点法式构造)。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
-        Returns:
-            [\`Plane3\`](./plane#class-plane3): 平面
-        """
-    a, b, c = (normal.x, normal.y, normal.z)
-    d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

變數説明:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
-def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
-    """
-        工厂函数 由三点构造平面。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 (\`Point3\`): 点2
-            p3 (\`Point3\`): 点3
-        Returns:
-            平面
-        """
-    v1 = p2 - p1
-    v2 = p3 - p1
-    normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

變數説明:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
-def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由两直线构造平面。
-        Args:
-            l1 ([\`Line3\`](./line#class-line3)): 直线
-            l2 (\`Line3\`): 直线
-        Returns:
-            平面
-        """
-    v1 = l1.direction
-    v2 = l2.point - l1.point
-    if v2 == zero_vector3:
-        v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
-def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
-    """
-        工厂函数 由点和直线构造平面。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 平面上一点
-            line ([\`Line3\`](./line#class-line3)): 直线
-        Returns:
-            平面
-        """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼 或 於GitHub上查看
python
def __and__(self, other):
-    """
-        取两平面的交集（人话：交线）
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
-        Raises:
-            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
-        """
-    if isinstance(other, Plane3):
-        if self.normal.is_parallel(other.normal):
-            return None
-        return self.cal_intersection_line3(other)
-    elif isinstance(other, Line3):
-        if self.normal @ other.direction == 0:
-            return None
-        return self.cal_intersection_point3(other)
-    else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        判断两个平面是否等价。
-        Args:
-            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
-        """
-    return self.approx(other)

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

源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/zht_api_mp_math_plane.md.C-9IgWh_.lean.js b/assets/zht_api_mp_math_plane.md.C-9IgWh_.lean.js deleted file mode 100644 index 43a9b72..0000000 --- a/assets/zht_api_mp_math_plane.md.C-9IgWh_.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default}; diff --git a/assets/zht_api_mp_math_plane.md.DHKntbKb.js b/assets/zht_api_mp_math_plane.md.DHKntbKb.js new file mode 100644 index 0000000..3a597e9 --- /dev/null +++ b/assets/zht_api_mp_math_plane.md.DHKntbKb.js @@ -0,0 +1,227 @@ +import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const qs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),e={name:"zht/api/mp_math/plane.md"},h=t(`

模組 mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

method __init__(self, a: float, b: float, c: float, d: float) ​

説明: 平面方程：ax + by + cz + d = 0

變數説明:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+    """
+        平面方程：ax + by + cz + d = 0
+        Args:
+            a ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x系数
+            b (\`float\`): y系数
+            c (\`float\`): z系数
+            d (\`float\`): 常数项
+        """
+    self.a = a
+    self.b = b
+    self.c = c
+    self.d = d

method approx(self, other: Plane3) -> bool ​

説明: 判断两个平面是否近似相等。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否近似相等。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
+        """
+    if self.a != 0:
+        k = other.a / self.a
+        return approx(other.b, self.b * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.b != 0:
+        k = other.b / self.b
+        return approx(other.a, self.a * k) and approx(other.c, self.c * k) and approx(other.d, self.d * k)
+    elif self.c != 0:
+        k = other.c / self.c
+        return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
+    else:
+        return False

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

説明: 计算平面与平面之间的夹角。

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變數説明:

返回: AnyAngle: 夹角

抛出:

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+    """
+        计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n1 \\\\cdot n2}{|n1| \\\\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{n \\\\cdot d}{|n| \\\\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Line3):
+        return self.normal.cal_angle(other.direction).complementary
+    elif isinstance(other, Plane3):
+        return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

變數説明:

返回: float: 距离

抛出:

源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+    """
+        计算平面与平面或点之间的距离。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3) | [\`Point3\`](./point#class-point3)): 另一个平面或点
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 距离
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        return 0
+    elif isinstance(other, Point3):
+        return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
+    else:
+        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

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變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+    """
+        计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\\\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\\\begin{cases} x = x_0 + dt \\\\\\\\ y = y_0 + dt \\\\\\\\ z = z_0 + dt \\\\end{cases} $$
+        或
+        $$ \\\\frac{x - x_0}{m} = \\\\frac{y - y_0}{n} = \\\\frac{z - z_0}{p} $$
+        :::
+
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`Line3\`](./line#class-line3): 交线
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面平行且无交线
+        """
+    if self.normal.is_parallel(other.normal):
+        raise ValueError('Planes are parallel and have no intersection.')
+    direction = self.normal.cross(other.normal)
+    x, y, z = (0, 0, 0)
+    if self.a != 0 and other.a != 0:
+        A = np.array([[self.b, self.c], [other.b, other.c]])
+        B = np.array([-self.d, -other.d])
+        y, z = np.linalg.solve(A, B)
+    elif self.b != 0 and other.b != 0:
+        A = np.array([[self.a, self.c], [other.a, other.c]])
+        B = np.array([-self.d, -other.d])
+        x, z = np.linalg.solve(A, B)
+    elif self.c != 0 and other.c != 0:
+        A = np.array([[self.a, self.b], [other.a, other.b]])
+        B = np.array([-self.d, -other.d])
+        x, y = np.linalg.solve(A, B)
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

變數説明:

返回: Point3: 交点

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    """
+        计算平面与直线的交点。
+        Args:
+            other ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            [\`Point3\`](./point#class-point3): 交点
+        Raises:
+            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#ValueError): 平面与直线平行或重合
+        """
+    if self.normal @ other.direction == 0:
+        raise ValueError('The plane and the line are parallel or coincident.')
+    x, y, z = other.get_parametric_equations()
+    t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    """
+        计算平行于该平面且过指定点的平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 指定点
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    """
+        判断两个平面是否平行。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

返回: Vector3: 法向量

源碼 或 於GitHub上查看
python
@property
+def normal(self) -> 'Vector3':
+    """
+        平面的法向量。
+        Returns:
+            [\`Vector3\`](./vector#class-vector3): 法向量
+        """
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
@classmethod
+def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
+    """
+        工厂函数 由点和法向量构造平面(点法式构造)。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            normal ([\`Vector3\`](./vector#class-vector3)): 法向量
+        Returns:
+            [\`Plane3\`](./plane#class-plane3): 平面
+        """
+    a, b, c = (normal.x, normal.y, normal.z)
+    d = -a * point.x - b * point.y - c * point.z
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

變數説明:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
+def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
+    """
+        工厂函数 由三点构造平面。
+        Args:
+            p1 ([\`Point3\`](./point#class-point3)): 点1
+            p2 (\`Point3\`): 点2
+            p3 (\`Point3\`): 点3
+        Returns:
+            平面
+        """
+    v1 = p2 - p1
+    v2 = p3 - p1
+    normal = v1.cross(v2)
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

變數説明:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
+def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由两直线构造平面。
+        Args:
+            l1 ([\`Line3\`](./line#class-line3)): 直线
+            l2 (\`Line3\`): 直线
+        Returns:
+            平面
+        """
+    v1 = l1.direction
+    v2 = l2.point - l1.point
+    if v2 == zero_vector3:
+        v2 = l2.get_point(1) - l1.point
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
+def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
+    """
+        工厂函数 由点和直线构造平面。
+        Args:
+            point ([\`Point3\`](./point#class-point3)): 平面上一点
+            line ([\`Line3\`](./line#class-line3)): 直线
+        Returns:
+            平面
+        """
+    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼 或 於GitHub上查看
python
def __and__(self, other):
+    """
+        取两平面的交集（人话：交线）
+        Args:
+            other ([\`Line3\`](./line#class-line3) | [\`Plane3\`](./plane#class-plane3)): 另一个平面或直线
+        Returns:
+            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https%3A//docs.python.org/3/library/constants.html#None): 交集
+        Raises:
+            [\`TypeError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 不支持的类型
+        """
+    if isinstance(other, Plane3):
+        if self.normal.is_parallel(other.normal):
+            return None
+        return self.cal_intersection_line3(other)
+    elif isinstance(other, Line3):
+        if self.normal @ other.direction == 0:
+            return None
+        return self.cal_intersection_point3(other)
+    else:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
+    """
+        判断两个平面是否等价。
+        Args:
+            other ([\`Plane3\`](./plane#class-plane3)): 另一个平面
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
+        """
+    return self.approx(other)

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

源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
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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    """\n        3维向量\n        Args:\n            x ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量\n            y (`float`): y轴分量\n            z (`float`): z轴分量\n        """\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    """\n        判断两个向量是否近似相等。\n        Args:\n            other ([`Vector3`](#class-vector3)): 另一个向量\n            epsilon ([`float`](https%3A//docs.python.org/3/library/functions.html#float)): 误差\n\n        Returns:\n            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等\n        """\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。

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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':
+    """
+        计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\\\theta = \\\\arccos(\\\\frac{v1 \\\\cdot v2}{|v1| \\\\cdot |v2|})$$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`AnyAngle\`](./angle#class-anyangle): 夹角
+        """
+    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

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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':
+    """
+        向量积 叉乘：v1 x v2 -> v3
+
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\\\times v2 = (v1_y \\\\cdot v2_z - v1_z \\\\cdot v2_y, v1_z \\\\cdot v2_x - v1_x \\\\cdot v2_z, v1_x \\\\cdot v2_y - v1_y \\\\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\\\times v2 = \\\\begin{vmatrix} i & j & k \\\\\\\\ v1_x & v1_y & v1_z \\\\\\\\ v2_x & v2_y & v2_z \\\\end{vmatrix} $$
+        :::
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`Vector3\`](#class-vector3): 叉乘结果
+        """
+    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:
+    """
+        判断两个向量是否近似平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
+        """
+    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:
+    """
+        判断两个向量是否平行。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
+        """
+    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):
+    """
+        将向量归一化。
+
+        自体归一化，不返回值。
+        """
+    length = self.length
+    self.x /= length
+    self.y /= length
+    self.z /= length

@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':
+    """
+        返回numpy数组
+        Returns:
+            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
+        """
+    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
+def length(self) -> float:
+    """
+        向量的模。
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
+        """
+    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
+def unit(self) -> 'Vector3':
+    """
+        获取该向量的单位向量。
+        Returns:
+            [\`Vector3\`](#class-vector3): 单位向量
+        """
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    """
+        V + P -> P
+
+        V + V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
+    else:
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+    """
+        判断两个向量是否相等。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
+        """
+    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':
+    """
+        P + V -> P
+
+        别去点那边实现了。
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    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
+def __sub__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
+    """
+        V - P -> P
+
+        V - V -> V
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
+        Returns:
+            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
+    elif isinstance(other, Point3):
+        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
+    else:
+        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'):
+    """
+        P - V -> P
+        Args:
+            other ([\`Point3\`](./point#class-point3)): 另一个点
+        Returns:
+            [\`Point3\`](./point#class-point3): 新的点
+        """
+    if isinstance(other, Point3):
+        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
+    else:
+        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
+def __mul__(self, other: 'Vector3') -> 'Vector3':
+    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    """
+        数组运算 非点乘。点乘使用@，叉乘使用cross。
+        Args:
+            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
+        Returns:
+            [\`Vector3\`](#class-vector): 数组运算结果
+        """
+    if isinstance(other, Vector3):
+        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
+    elif isinstance(other, (float, int)):
+        return Vector3(self.x * other, self.y * other, self.z * other)
+    else:
+        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':
+    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':
+    """
+        点乘。
+        Args:
+            other ([\`Vector3\`](#class-vector3)): 另一个向量
+        Returns:
+            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
+        """
+    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':
+    """
+        取负。
+        Returns:
+            [\`Vector3\`](#class-vector3): 负向量
+        """
+    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)

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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):
-    """
-        3维向量
-        Args:
-            x ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): x轴分量
-            y (\`float\`): y轴分量
-            z (\`float\`): z轴分量
-        """
-    self.x = x
-    self.y = y
-    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:
-    """
-        判断两个向量是否近似相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
-    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。

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':
-    """
-        计算两个向量之间的夹角。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

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':
-    """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        \`\`i  j  k\`\`
-
-        \`\`x1 y1 z1\`\`
-
-        \`\`x2 y2 z2\`\`
-
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`Vector3\`](#class-vector3): 叉乘结果
-        """
-    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:
-    """
-        判断两个向量是否近似平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-            epsilon ([\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
-        """
-    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:
-    """
-        判断两个向量是否平行。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
-    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):
-    """
-        将向量归一化。
-
-        自体归一化，不返回值。
-        """
-    length = self.length
-    self.x /= length
-    self.y /= length
-    self.z /= length

@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':
-    """
-        返回numpy数组
-        Returns:
-            [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
-        """
-    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
-def length(self) -> float:
-    """
-        向量的模。
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
-        """
-    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
-def unit(self) -> 'Vector3':
-    """
-        获取该向量的单位向量。
-        Returns:
-            [\`Vector3\`](#class-vector3): 单位向量
-        """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
-    """
-        V + P -> P
-
-        V + V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量或点
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x + other.x, self.y + other.y, self.z + other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
-    else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
-    """
-        判断两个向量是否相等。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
-        """
-    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':
-    """
-        P + V -> P
-
-        别去点那边实现了。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    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
-def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

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):
-    """
-        V - P -> P
-
-        V - V -> V
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个向量或点
-        Returns:
-            [\`Vector3\`](#class-vector3) | [\`Point3\`](./point#class-point3): 新的向量
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
-    elif isinstance(other, Point3):
-        return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
-    else:
-        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'):
-    """
-        P - V -> P
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    if isinstance(other, Point3):
-        return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
-    else:
-        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
-def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

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':
-    """
-        数组运算 非点乘。点乘使用@，叉乘使用cross。
-        Args:
-            other ([\`Vector3\`](#class-vector3) | [\`float\`](https%3A//docs.python.org/3/library/functions.html#float)): 另一个向量或数
-        Returns:
-            [\`Vector3\`](#class-vector): 数组运算结果
-        """
-    if isinstance(other, Vector3):
-        return Vector3(self.x * other.x, self.y * other.y, self.z * other.z)
-    elif isinstance(other, (float, int)):
-        return Vector3(self.x * other, self.y * other, self.z * other)
-    else:
-        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':
-    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':
-    """
-        点乘。
-        Args:
-            other ([\`Vector3\`](#class-vector3)): 另一个向量
-        Returns:
-            [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
-        """
-    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':
-    """
-        取负。
-        Returns:
-            [\`Vector3\`](#class-vector3): 负向量
-        """
-    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)

`,138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_vector.md.hAG56fdm.lean.js b/assets/zht_api_mp_math_vector.md.hAG56fdm.lean.js deleted file mode 100644 index 484aa50..0000000 --- a/assets/zht_api_mp_math_vector.md.hAG56fdm.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=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"},e=t("",138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default}; diff --git a/demo/best-practice.html b/demo/best-practice.html index a5714d6..d87dbd3 100644 --- a/demo/best-practice.html +++ b/demo/best-practice.html @@ -6,10 +6,10 @@ 最佳实践 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/demo/index.html b/demo/index.html index 4c5c9d1..51356f2 100644 --- a/demo/index.html +++ b/demo/index.html @@ -6,10 +6,10 @@ demo | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
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繁體中文

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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 d97ba5b..98a8f2f 100644 --- a/en/api/index.html +++ b/en/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

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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 49ef4a4..9943c31 100644 --- a/en/api/mp_math/angle.html +++ b/en/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP docs - + - - + + @@ -117,7 +117,7 @@ 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 cae1832..2b528ed 100644 --- a/en/api/mp_math/const.html +++ b/en/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

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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 1c9512e..ab5a958 100644 --- a/en/api/mp_math/equation.html +++ b/en/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP docs - + - - + + @@ -83,7 +83,7 @@ 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 838cbcb..9e82275 100644 --- a/en/api/mp_math/function.html +++ b/en/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP docs - + - - + + @@ -60,7 +60,7 @@ """@litedoc-hide""" 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 77bdd7f..5ace721 100644 --- a/en/api/mp_math/index.html +++ b/en/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

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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 9d42483..e959851 100644 --- a/en/api/mp_math/line.html +++ b/en/api/mp_math/line.html @@ -6,10 +6,10 @@ mbcp.mp_math.line | MBCP docs - + - - + + @@ -192,7 +192,7 @@ [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价 """ 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 93f7fb9..a06c404 100644 --- a/en/api/mp_math/mp_math_typing.html +++ b/en/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

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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 e5d4a22..2f8303e 100644 --- a/en/api/mp_math/plane.html +++ b/en/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP docs - + - - + + - + @@ -48,9 +48,19 @@ k = other.c / self.c return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k) else: - return False

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

Description: 计算平面与平面之间的夹角。

Arguments:

Return: AnyAngle: 夹角

Raises:

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

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

Description: 计算平面与平面之间的夹角。

TIP

平面间夹角计算公式:

θ=arccos⁡(n1⋅n2|n1|⋅|n2|)

其中 n1 和 n2 分别为两个平面的法向量

TIP

平面与直线夹角计算公式:

θ=arccos⁡(n⋅d|n|⋅|d|)

其中 n 为平面的法向量，d 为直线的方向向量

Arguments:

Return: AnyAngle: 夹角

Raises:

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n1 \\cdot n2}{|n1| \\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n \\cdot d}{|n| \\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
         Args:
             other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
         Returns:
@@ -63,7 +73,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

Description: 计算平面与平面或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

Description: 计算平面与平面或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,9 +88,20 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

Description: 计算两平面的交线。

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

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

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

Description: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点，依次假设x=0, y=0, z=0，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

或

x−x0m=y−y0n=z−z0p

Arguments:

  • other (Plane3): 另一个平面

Return: Line3: 交线

Raises:

Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\begin{cases} x = x_0 + dt \\\\ y = y_0 + dt \\\\ z = z_0 + dt \\end{cases} $$
+        或
+        $$ \\frac{x - x_0}{m} = \\frac{y - y_0}{n} = \\frac{z - z_0}{p} $$
+        :::
+
         Args:
             other ([`Plane3`](./plane#class-plane3)): 另一个平面
         Returns:
@@ -104,7 +125,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

Description: 计算平面与直线的交点。

Arguments:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

Description: 计算平面与直线的交点。

Arguments:

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +139,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

Description: 计算平行于该平面且过指定点的平面。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

Description: 计算平行于该平面且过指定点的平面。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +147,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

Description: 判断两个平面是否平行。

Arguments:

  • other (Plane3): 另一个平面

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +155,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

Description: 平面的法向量。

Return: Vector3: 法向量

Source code or View on GitHub
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

Description: 工厂函数 由点和法向量构造平面(点法式构造)。

Arguments:

Return: Plane3: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +174,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

Description: 工厂函数 由三点构造平面。

Arguments:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

Description: 工厂函数 由三点构造平面。

Arguments:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +188,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

Description: 工厂函数 由两直线构造平面。

Arguments:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

Description: 工厂函数 由两直线构造平面。

Arguments:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +202,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

Description: 工厂函数 由点和直线构造平面。

Arguments:

Return: 平面

Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +212,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

@overload

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

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

@overload

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

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

method __and__(self, other) ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

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

method __and__(self, other) ​

Description: 取两平面的交集（人话：交线）

Arguments:

Return: Line3 | Point3 | None: 交集

Raises:

Source code or View on GitHub
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +235,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

Description: 判断两个平面是否等价。

Arguments:

  • 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:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

Description: 判断两个平面是否等价。

Arguments:

  • 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:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +243,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)

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

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

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

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

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 4b06a65..722dae2 100644 --- a/en/api/mp_math/point.html +++ b/en/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP docs - + - - + + @@ -70,7 +70,7 @@ """ 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 caa6d29..e8e7451 100644 --- a/en/api/mp_math/segment.html +++ b/en/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP docs - + - - + + @@ -33,7 +33,7 @@ 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 01523c6..c1c5bdb 100644 --- a/en/api/mp_math/utils.html +++ b/en/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP docs - + - - + + @@ -87,7 +87,7 @@ 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 f28a8f8..f742b9f 100644 --- a/en/api/mp_math/vector.html +++ b/en/api/mp_math/vector.html @@ -6,12 +6,12 @@ mbcp.mp_math.vector | MBCP docs - + - - + + - + @@ -38,35 +38,34 @@ Returns: [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等 """ - 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。

Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    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。

TIP

向量夹角计算公式:

θ=arccos⁡(v1⋅v2|v1|⋅|v2|)

Arguments:

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\theta = \\arccos(\\frac{v1 \\cdot v2}{|v1| \\cdot |v2|})$$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    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

TIP

叉乘运算法则为:

v1×v2=(v1y⋅v2z−v1z⋅v2y,v1z⋅v2x−v1x⋅v2z,v1x⋅v2y−v1y⋅v2x)

转换为行列式形式:

v1×v2=|ijkv1xv1yv1zv2xv2yv2z|

Arguments:

Return: Vector3: 叉乘结果

Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        ``i  j  k``
-
-        ``x1 y1 z1``
-
-        ``x2 y2 z2``
+        向量积 叉乘：v1 x v2 -> v3
 
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\times v2 = (v1_y \\cdot v2_z - v1_z \\cdot v2_y, v1_z \\cdot v2_x - v1_x \\cdot v2_z, v1_x \\cdot v2_y - v1_y \\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\times v2 = \\begin{vmatrix} i & j & k \\\\ v1_x & v1_y & v1_z \\\\ v2_x & v2_y & v2_z \\end{vmatrix} $$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    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:
+    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:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +74,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    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:
+    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:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +82,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    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):
+    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):
     """
         将向量归一化。
 
@@ -92,33 +91,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

Source code or View on GitHub
python
@property
+    self.z /= length

@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':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    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
+    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
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    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
+    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
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

Source code or View on GitHub
python
@overload
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V + P -> P
 
@@ -133,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +140,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    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':
+    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':
     """
         P + V -> P
 
@@ -151,11 +150,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    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
+    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
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V - P -> P
 
@@ -170,7 +169,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        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'):
+        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'):
     """
         P - V -> P
         Args:
@@ -181,11 +180,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        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
+        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
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    ...

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':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +197,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        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':
-    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':
+        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':
+    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':
     """
         点乘。
         Args:
@@ -207,15 +206,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    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 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':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
     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 f86d3d2..b108c16 100644 --- a/en/api/particle/index.html +++ b/en/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP docs - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/index.html b/en/api/presets/index.html index 6928f1d..8d97d03 100644 --- a/en/api/presets/index.html +++ b/en/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP docs - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html index 7db6ca4..d326eb5 100644 --- a/en/api/presets/model/index.html +++ b/en/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP docs - + - - + + @@ -36,7 +36,7 @@ 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 fe9ed19..33a0a9d 100644 --- a/en/demo/best-practice.html +++ b/en/demo/best-practice.html @@ -6,10 +6,10 @@ Best Practice | MBCP docs - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/en/guide/index.html b/en/guide/index.html index 01fa2d2..b7c052e 100644 --- a/en/guide/index.html +++ b/en/guide/index.html @@ -6,10 +6,10 @@ 开始不了一点 | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

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开始不了一点 ​

∫12x111

Documentation built with VitePress | API references generated by litedoc

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- + \ No newline at end of file diff --git a/en/index.html b/en/index.html index 47c9daa..b3a136c 100644 --- a/en/index.html +++ b/en/index.html @@ -6,10 +6,10 @@ MBCP docs - + - - + + @@ -19,7 +19,7 @@
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MBCP

More basic change particle

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

Get Started
API Reference
Best Practice
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🛠️

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 6a6fa4b..5efc36c 100644 --- a/en/refer/index.html +++ b/en/refer/index.html @@ -6,10 +6,10 @@ Reference | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

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Reference ​

help us to improve the documentation

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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 a28d678..30ea9ae 100644 --- a/guide/index.html +++ b/guide/index.html @@ -6,10 +6,10 @@ 快速开始 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

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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

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- + \ No newline at end of file diff --git a/hashmap.json b/hashmap.json index 01aee1c..e9c53e5 100644 --- a/hashmap.json +++ b/hashmap.json @@ -1 +1 @@ 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diff --git a/index.html b/index.html index 1515f23..5c821a1 100644 --- a/index.html +++ b/index.html @@ -6,10 +6,10 @@ MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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MBCP

更多基础变换粒子

用于几何运算和Minecraft粒子制作的库

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API文档
最佳实践
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🛠️

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

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- + \ No newline at end of file diff --git a/ja/api/index.html b/ja/api/index.html index a20d269..ae32fba 100644 --- a/ja/api/index.html +++ b/ja/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
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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

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- + \ No newline at end of file diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html index 6bac679..1a8e439 100644 --- a/ja/api/mp_math/angle.html +++ b/ja/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP ドキュメント - + - - + + @@ -117,7 +117,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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- + \ No newline at end of file diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html index 2523363..a5d82e7 100644 --- a/ja/api/mp_math/const.html +++ b/ja/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
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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 e29ff80..6011cf6 100644 --- a/ja/api/mp_math/equation.html +++ b/ja/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP ドキュメント - + - - + + @@ -83,7 +83,7 @@ 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 dad4cf8..7a56cd1 100644 --- a/ja/api/mp_math/function.html +++ b/ja/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP ドキュメント - + - - + + @@ -60,7 +60,7 @@ """@litedoc-hide""" 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 8243410..65b7de9 100644 --- a/ja/api/mp_math/index.html +++ b/ja/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.mp_math ​

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

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

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

- + \ No newline at end of file diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html index ff8169c..edaccea 100644 --- a/ja/api/mp_math/line.html +++ b/ja/api/mp_math/line.html @@ -6,10 +6,10 @@ mbcp.mp_math.line | MBCP ドキュメント - + - - + + @@ -192,7 +192,7 @@ [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价 """ 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 4f4304a..5342df3 100644 --- a/ja/api/mp_math/mp_math_typing.html +++ b/ja/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 説明: 实数

  • タイプ: TypeAlias

  • デフォルト: int | float

var Number ​

  • 説明: 数

  • タイプ: TypeAlias

  • デフォルト: RealNumber | complex

var SingleVar ​

  • 説明: 单变量

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

var ArrayVar ​

  • 説明: 数组变量

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

var Var ​

  • 説明: 变量

  • タイプ: TypeAlias

  • デフォルト: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 説明: 一元单变量函数

  • タイプ: TypeAlias

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

var OneArrayFunc ​

  • 説明: 一元数组函数

  • タイプ: TypeAlias

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

var OneVarFunc ​

  • 説明: 一元函数

  • タイプ: TypeAlias

  • デフォルト: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 説明: 二元单变量函数

  • タイプ: TypeAlias

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

var TwoArraysFunc ​

  • 説明: 二元数组函数

  • タイプ: TypeAlias

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

var TwoVarsFunc ​

  • 説明: 二元函数

  • タイプ: TypeAlias

  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 説明: 三元单变量函数

  • タイプ: TypeAlias

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

var ThreeArraysFunc ​

  • 説明: 三元数组函数

  • タイプ: TypeAlias

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

var ThreeVarsFunc ​

  • 説明: 三元函数

  • タイプ: TypeAlias

  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 説明: 多元单变量函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 説明: 多元数组函数

  • タイプ: TypeAlias

  • デフォルト: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 説明: 多元函数

  • タイプ: TypeAlias

  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc

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

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

- + \ No newline at end of file diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html index d97a6ce..b7bfdf0 100644 --- a/ja/api/mp_math/plane.html +++ b/ja/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP ドキュメント - + - - + + - + @@ -48,9 +48,19 @@ k = other.c / self.c return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k) else: - return False

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

説明: 计算平面与平面之间的夹角。

引数:

戻り値: AnyAngle: 夹角

例外:

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

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

説明: 计算平面与平面之间的夹角。

TIP

平面间夹角计算公式:

θ=arccos⁡(n1⋅n2|n1|⋅|n2|)

其中 n1 和 n2 分别为两个平面的法向量

TIP

平面与直线夹角计算公式:

θ=arccos⁡(n⋅d|n|⋅|d|)

其中 n 为平面的法向量，d 为直线的方向向量

引数:

戻り値: AnyAngle: 夹角

例外:

ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n1 \\cdot n2}{|n1| \\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n \\cdot d}{|n| \\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
         Args:
             other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
         Returns:
@@ -63,7 +73,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

引数:

戻り値: float: 距离

例外:

ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,9 +88,20 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点，依次假设x=0, y=0, z=0，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

或

x−x0m=y−y0n=z−z0p

引数:

  • other (Plane3): 另一个平面

戻り値: Line3: 交线

例外:

ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\begin{cases} x = x_0 + dt \\\\ y = y_0 + dt \\\\ z = z_0 + dt \\end{cases} $$
+        或
+        $$ \\frac{x - x_0}{m} = \\frac{y - y_0}{n} = \\frac{z - z_0}{p} $$
+        :::
+
         Args:
             other ([`Plane3`](./plane#class-plane3)): 另一个平面
         Returns:
@@ -104,7 +125,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

引数:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

引数:

戻り値: Point3: 交点

例外:

ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +139,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +147,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

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: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

引数:

  • other (Plane3): 另一个平面

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: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +155,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

戻り値: Vector3: 法向量

ソースコード または GitHubで表示
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

引数:

戻り値: Plane3: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +174,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

引数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

引数:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +188,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

引数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

引数:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +202,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

引数:

戻り値: 平面

ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +212,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

@overload

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

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

@overload

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

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

引数:

戻り値: Line3 | Point3 | None: 交集

例外:

ソースコード または GitHubで表示
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +235,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

引数:

  • other (Plane3): 另一个平面

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +243,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)

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

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.approx(other)

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

ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

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 ca46e34..ac35501 100644 --- a/ja/api/mp_math/point.html +++ b/ja/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP ドキュメント - + - - + + @@ -70,7 +70,7 @@ """ 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 ca76e95..f5702e4 100644 --- a/ja/api/mp_math/segment.html +++ b/ja/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP ドキュメント - + - - + + @@ -33,7 +33,7 @@ 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 184bf0d..7923271 100644 --- a/ja/api/mp_math/utils.html +++ b/ja/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP ドキュメント - + - - + + @@ -87,7 +87,7 @@ 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 5b58f3d..3f30e2e 100644 --- a/ja/api/mp_math/vector.html +++ b/ja/api/mp_math/vector.html @@ -6,12 +6,12 @@ mbcp.mp_math.vector | MBCP ドキュメント - + - - + + - + @@ -38,35 +38,34 @@ Returns: [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等 """ - 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。

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':
+    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。

TIP

向量夹角计算公式:

θ=arccos⁡(v1⋅v2|v1|⋅|v2|)

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':
     """
         计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\theta = \\arccos(\\frac{v1 \\cdot v2}{|v1| \\cdot |v2|})$$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

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':
+    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

TIP

叉乘运算法则为:

v1×v2=(v1y⋅v2z−v1z⋅v2y,v1z⋅v2x−v1x⋅v2z,v1x⋅v2y−v1y⋅v2x)

转换为行列式形式:

v1×v2=|ijkv1xv1yv1zv2xv2yv2z|

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':
     """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        ``i  j  k``
-
-        ``x1 y1 z1``
-
-        ``x2 y2 z2``
+        向量积 叉乘：v1 x v2 -> v3
 
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\times v2 = (v1_y \\cdot v2_z - v1_z \\cdot v2_y, v1_z \\cdot v2_x - v1_x \\cdot v2_z, v1_x \\cdot v2_y - v1_y \\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\times v2 = \\begin{vmatrix} i & j & k \\\\ v1_x & v1_y & v1_z \\\\ v2_x & v2_y & v2_z \\end{vmatrix} $$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    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:
+    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:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +74,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    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:
+    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:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +82,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    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):
+    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):
     """
         将向量归一化。
 
@@ -92,33 +91,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length

@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
+    self.z /= length

@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':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    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
+    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
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    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
+    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
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

ソースコード または GitHubで表示
python
@overload
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V + P -> P
 
@@ -133,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +140,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    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':
+    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':
     """
         P + V -> P
 
@@ -151,11 +150,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    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
+    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
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V - P -> P
 
@@ -170,7 +169,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        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'):
+        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'):
     """
         P - V -> P
         Args:
@@ -181,11 +180,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        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
+        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
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    ...

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':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +197,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        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':
-    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':
+        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':
+    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':
     """
         点乘。
         Args:
@@ -207,15 +206,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    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 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':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
     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

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- + \ No newline at end of file diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html index 4839f5b..1cd588f 100644 --- a/ja/api/particle/index.html +++ b/ja/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html index 2a29a27..fcc894c 100644 --- a/ja/api/presets/index.html +++ b/ja/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html index 1901a18..21dc400 100644 --- a/ja/api/presets/model/index.html +++ b/ja/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP ドキュメント - + - - + + @@ -36,7 +36,7 @@ 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)]

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- + \ No newline at end of file diff --git a/ja/demo/best-practice.html b/ja/demo/best-practice.html index d0ff381..38915d4 100644 --- a/ja/demo/best-practice.html +++ b/ja/demo/best-practice.html @@ -6,10 +6,10 @@ ベストプラクティス | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/ja/guide/index.html b/ja/guide/index.html index 55b0ab4..46e139e 100644 --- a/ja/guide/index.html +++ b/ja/guide/index.html @@ -6,10 +6,10 @@ 开始不了一点 | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
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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 cc5d8c9..998beb9 100644 --- a/ja/index.html +++ b/ja/index.html @@ -6,10 +6,10 @@ MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
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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

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- + \ No newline at end of file diff --git a/ja/refer/index.html b/ja/refer/index.html index dc7f898..388fd38 100644 --- a/ja/refer/index.html +++ b/ja/refer/index.html @@ -6,10 +6,10 @@ Reference | MBCP ドキュメント - + - - + + @@ -19,7 +19,7 @@
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Reference ​

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- + \ No newline at end of file diff --git a/refer/7-differential-euqtion/index.html b/refer/7-differential-euqtion/index.html new file mode 100644 index 0000000..99a472a --- /dev/null +++ b/refer/7-differential-euqtion/index.html @@ -0,0 +1,25 @@ + + + + + + 微分方程 | MBCP 文档 + + + + + + + + + + + + + + +
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+ + + + \ No newline at end of file diff --git a/refer/function/curry.html b/refer/function/curry.html index 4dd6da0..da0bfa5 100644 --- a/refer/function/curry.html +++ b/refer/function/curry.html @@ -6,10 +6,10 @@ 柯里化 | MBCP 文档 - + - - + + @@ -18,8 +18,8 @@ -
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+ \ No newline at end of file diff --git a/refer/index.html b/refer/index.html index a00689b..7687578 100644 --- a/refer/index.html +++ b/refer/index.html @@ -6,10 +6,10 @@ 参考 | MBCP 文档 - + - - + + @@ -18,8 +18,8 @@ -
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+ \ No newline at end of file diff --git a/sitemap.xml b/sitemap.xml index bb915ee..5e148c9 100644 --- a/sitemap.xml +++ b/sitemap.xml @@ -1 +1 @@ -https://mbcp.sfkm.me/en/api/https://mbcp.sfkm.me/ja/api/https://mbcp.sfkm.me/api/https://mbcp.sfkm.me/zht/api/https://mbcp.sfkm.me/en/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/en/api/mp_math/const.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/const.htmlhttps://mbcp.sfkm.me/api/mp_math/const.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/const.htmlhttps://mbcp.sfkm.me/en/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/en/api/mp_math/function.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/function.htmlhttps://mbcp.sfkm.me/api/mp_math/function.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/function.htmlhttps://mbcp.sfkm.me/en/api/mp_math/https://mbcp.sfkm.me/ja/api/mp_math/https://mbcp.sfkm.me/api/mp_math/https://mbcp.sfkm.me/zht/api/mp_math/https://mbcp.sfkm.me/en/api/mp_math/line.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/line.htmlhttps://mbcp.sfkm.me/api/mp_math/line.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/line.htmlhttps://mbcp.sfkm.me/en/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/en/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/en/api/mp_math/point.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/point.htmlhttps://mbcp.sfkm.me/api/mp_math/point.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/point.htmlhttps://mbcp.sfkm.me/en/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/en/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/en/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/en/api/particle/https://mbcp.sfkm.me/ja/api/particle/https://mbcp.sfkm.me/api/particle/https://mbcp.sfkm.me/zht/api/particle/https://mbcp.sfkm.me/en/api/presets/https://mbcp.sfkm.me/ja/api/presets/https://mbcp.sfkm.me/api/presets/https://mbcp.sfkm.me/zht/api/presets/https://mbcp.sfkm.me/en/api/presets/model/https://mbcp.sfkm.me/ja/api/presets/model/https://mbcp.sfkm.me/api/presets/model/https://mbcp.sfkm.me/zht/api/presets/model/https://mbcp.sfkm.me/en/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/ja/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/zht/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/en/guide/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/ja/guide/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/guide/2024-09-03T14:29:26.000Zhttps://mbcp.sfkm.me/zht/guide/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/en/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/ja/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/zht/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/en/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/ja/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/zht/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/demo/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/refer/function/curry.html2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/refer/function/function.html2024-08-30T09:56:01.000Z \ No newline at end of file +https://mbcp.sfkm.me/en/api/https://mbcp.sfkm.me/ja/api/https://mbcp.sfkm.me/api/https://mbcp.sfkm.me/zht/api/https://mbcp.sfkm.me/en/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/angle.htmlhttps://mbcp.sfkm.me/en/api/mp_math/const.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/const.htmlhttps://mbcp.sfkm.me/api/mp_math/const.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/const.htmlhttps://mbcp.sfkm.me/en/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/equation.htmlhttps://mbcp.sfkm.me/en/api/mp_math/function.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/function.htmlhttps://mbcp.sfkm.me/api/mp_math/function.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/function.htmlhttps://mbcp.sfkm.me/en/api/mp_math/https://mbcp.sfkm.me/ja/api/mp_math/https://mbcp.sfkm.me/api/mp_math/https://mbcp.sfkm.me/zht/api/mp_math/https://mbcp.sfkm.me/en/api/mp_math/line.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/line.htmlhttps://mbcp.sfkm.me/api/mp_math/line.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/line.htmlhttps://mbcp.sfkm.me/en/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/mp_math_typing.htmlhttps://mbcp.sfkm.me/en/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/plane.htmlhttps://mbcp.sfkm.me/en/api/mp_math/point.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/point.htmlhttps://mbcp.sfkm.me/api/mp_math/point.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/point.htmlhttps://mbcp.sfkm.me/en/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/segment.htmlhttps://mbcp.sfkm.me/en/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/utils.htmlhttps://mbcp.sfkm.me/en/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/ja/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/zht/api/mp_math/vector.htmlhttps://mbcp.sfkm.me/en/api/particle/https://mbcp.sfkm.me/ja/api/particle/https://mbcp.sfkm.me/api/particle/https://mbcp.sfkm.me/zht/api/particle/https://mbcp.sfkm.me/en/api/presets/https://mbcp.sfkm.me/ja/api/presets/https://mbcp.sfkm.me/api/presets/https://mbcp.sfkm.me/zht/api/presets/https://mbcp.sfkm.me/en/api/presets/model/https://mbcp.sfkm.me/ja/api/presets/model/https://mbcp.sfkm.me/api/presets/model/https://mbcp.sfkm.me/zht/api/presets/model/https://mbcp.sfkm.me/en/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/ja/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/zht/demo/best-practice.html2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/en/guide/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/ja/guide/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/guide/2024-09-03T14:29:26.000Zhttps://mbcp.sfkm.me/zht/guide/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/en/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/ja/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/zht/2024-08-31T02:12:28.000Zhttps://mbcp.sfkm.me/en/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/ja/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/zht/refer/2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/demo/2024-08-29T11:00:01.000Zhttps://mbcp.sfkm.me/refer/7-differential-euqtion/2024-09-06T07:42:16.000Zhttps://mbcp.sfkm.me/refer/function/curry.html2024-08-30T09:56:01.000Zhttps://mbcp.sfkm.me/refer/function/function.html2024-08-30T09:56:01.000Z \ No newline at end of file diff --git a/zht/api/index.html b/zht/api/index.html index 5cf291d..eee3661 100644 --- a/zht/api/index.html +++ b/zht/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
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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

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- + \ No newline at end of file diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html index 05ae3f3..c436e7a 100644 --- a/zht/api/mp_math/angle.html +++ b/zht/api/mp_math/angle.html @@ -6,10 +6,10 @@ mbcp.mp_math.angle | MBCP 文檔 - + - - + + @@ -117,7 +117,7 @@ if isinstance(other, AnyAngle): return self.radian / other.radian return AnyAngle(self.radian / other, is_radian=True)

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- + \ No newline at end of file diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html index 7c92957..4732eab 100644 --- a/zht/api/mp_math/const.html +++ b/zht/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
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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

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- + \ No newline at end of file diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html index 86ac30f..e9c93e3 100644 --- a/zht/api/mp_math/equation.html +++ b/zht/api/mp_math/equation.html @@ -6,10 +6,10 @@ mbcp.mp_math.equation | MBCP 文檔 - + - - + + @@ -83,7 +83,7 @@ return high_order_partial_derivative_func else: raise ValueError('Invalid var type')

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- + \ No newline at end of file diff --git a/zht/api/mp_math/function.html b/zht/api/mp_math/function.html index 81286ff..d00474c 100644 --- a/zht/api/mp_math/function.html +++ b/zht/api/mp_math/function.html @@ -6,10 +6,10 @@ mbcp.mp_math.function | MBCP 文檔 - + - - + + @@ -60,7 +60,7 @@ """@litedoc-hide""" return func(*args, *args2) return curried_func

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- + \ No newline at end of file diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html index 398daf6..5a69c65 100644 --- a/zht/api/mp_math/index.html +++ b/zht/api/mp_math/index.html @@ -6,10 +6,10 @@ mbcp.mp_math | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
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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 5286d24..98f28ba 100644 --- a/zht/api/mp_math/line.html +++ b/zht/api/mp_math/line.html @@ -6,10 +6,10 @@ mbcp.mp_math.line | MBCP 文檔 - + - - + + @@ -192,7 +192,7 @@ [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价 """ 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 07757e1..0124ece 100644 --- a/zht/api/mp_math/mp_math_typing.html +++ b/zht/api/mp_math/mp_math_typing.html @@ -6,10 +6,10 @@ mbcp.mp_math.mp_math_typing | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

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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 686d1c8..e55ed3c 100644 --- a/zht/api/mp_math/plane.html +++ b/zht/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP 文檔 - + - - + + - + @@ -48,9 +48,19 @@ k = other.c / self.c return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k) else: - return False

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

説明: 计算平面与平面之间的夹角。

變數説明:

返回: AnyAngle: 夹角

抛出:

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False

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

説明: 计算平面与平面之间的夹角。

TIP

平面间夹角计算公式:

θ=arccos⁡(n1⋅n2|n1|⋅|n2|)

其中 n1 和 n2 分别为两个平面的法向量

TIP

平面与直线夹角计算公式:

θ=arccos⁡(n⋅d|n|⋅|d|)

其中 n 为平面的法向量，d 为直线的方向向量

變數説明:

返回: AnyAngle: 夹角

抛出:

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
+        :::tip
+        平面间夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n1 \\cdot n2}{|n1| \\cdot |n2|})$$
+        其中 $n1$ 和 $n2$ 分别为两个平面的法向量
+        :::
+        :::tip
+        平面与直线夹角计算公式:
+        $$\\theta = \\arccos(\\frac{n \\cdot d}{|n| \\cdot |d|})$$
+        其中 $n$ 为平面的法向量，$d$ 为直线的方向向量
+        :::
         Args:
             other ([`Line3`](./line#class-line3) | [`Plane3`](./plane#class-plane3)): 另一个平面或直线
         Returns:
@@ -63,7 +73,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

變數説明:

返回: float: 距离

抛出:

源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')

method cal_distance(self, other: Plane3 | Point3) -> float ​

説明: 计算平面与平面或点之间的距离。

變數説明:

返回: float: 距离

抛出:

源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,9 +88,20 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')

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

説明: 计算两平面的交线。

TIP

计算两平面交线的一般步骤:

  1. 求两平面的法向量的叉乘得到方向向量
d=n1×n2
  1. 寻找直线上的一点，依次假设x=0, y=0, z=0，并代入两平面方程求出合适的点 直线最终可用参数方程或点向式表示
{x=x0+dty=y0+dtz=z0+dt

或

x−x0m=y−y0n=z−z0p

變數説明:

  • other (Plane3): 另一个平面

返回: Line3: 交线

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
+        :::tip
+        计算两平面交线的一般步骤:
+        1. 求两平面的法向量的叉乘得到方向向量
+        $$ d = n1 \\times n2 $$
+        2. 寻找直线上的一点，依次假设$x=0$, $y=0$, $z=0$，并代入两平面方程求出合适的点
+        直线最终可用参数方程或点向式表示
+        $$ \\begin{cases} x = x_0 + dt \\\\ y = y_0 + dt \\\\ z = z_0 + dt \\end{cases} $$
+        或
+        $$ \\frac{x - x_0}{m} = \\frac{y - y_0}{n} = \\frac{z - z_0}{p} $$
+        :::
+
         Args:
             other ([`Plane3`](./plane#class-plane3)): 另一个平面
         Returns:
@@ -104,7 +125,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

變數説明:

返回: Point3: 交点

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)

method cal_intersection_point3(self, other: Line3) -> Point3 ​

説明: 计算平面与直线的交点。

變數説明:

返回: Point3: 交点

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +139,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))

method cal_parallel_plane3(self, point: Point3) -> Plane3 ​

説明: 计算平行于该平面且过指定点的平面。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +147,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)

method is_parallel(self, other: Plane3) -> bool ​

説明: 判断两个平面是否平行。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否平行

源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +155,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

返回: Vector3: 法向量

源碼 或 於GitHub上查看
python
@property
+    return self.normal.is_parallel(other.normal)

@property

method normal(self) -> Vector3 ​

説明: 平面的法向量。

返回: Vector3: 法向量

源碼 或 於GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)

@classmethod

method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​

説明: 工厂函数 由点和法向量构造平面(点法式构造)。

變數説明:

返回: Plane3: 平面

源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +174,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

變數説明:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)

@classmethod

method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​

説明: 工厂函数 由三点构造平面。

變數説明:

  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +188,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

變數説明:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)

@classmethod

method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​

説明: 工厂函数 由两直线构造平面。

變數説明:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +202,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))

@classmethod

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

説明: 工厂函数 由点和直线构造平面。

變數説明:

返回: 平面

源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +212,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)

@overload

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

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

@overload

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

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

@overload

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

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

@overload

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

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

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

method __and__(self, other) ​

説明: 取两平面的交集（人话：交线）

變數説明:

返回: Line3 | Point3 | None: 交集

抛出:

源碼 或 於GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +235,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")

method __eq__(self, other) -> bool ​

説明: 判断两个平面是否等价。

變數説明:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +243,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)

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

源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.approx(other)

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

源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

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 ffacfe3..1f4b4cc 100644 --- a/zht/api/mp_math/point.html +++ b/zht/api/mp_math/point.html @@ -6,10 +6,10 @@ mbcp.mp_math.point | MBCP 文檔 - + - - + + @@ -70,7 +70,7 @@ """ 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 0e50b40..3d08a12 100644 --- a/zht/api/mp_math/segment.html +++ b/zht/api/mp_math/segment.html @@ -6,10 +6,10 @@ mbcp.mp_math.segment | MBCP 文檔 - + - - + + @@ -33,7 +33,7 @@ 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 41bc170..2cd52f2 100644 --- a/zht/api/mp_math/utils.html +++ b/zht/api/mp_math/utils.html @@ -6,10 +6,10 @@ mbcp.mp_math.utils | MBCP 文檔 - + - - + + @@ -87,7 +87,7 @@ 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 857ed14..93a7007 100644 --- a/zht/api/mp_math/vector.html +++ b/zht/api/mp_math/vector.html @@ -6,12 +6,12 @@ mbcp.mp_math.vector | MBCP 文檔 - + - - + + - + @@ -38,35 +38,34 @@ Returns: [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等 """ - 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。

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':
+    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。

TIP

向量夹角计算公式:

θ=arccos⁡(v1⋅v2|v1|⋅|v2|)

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':
     """
         计算两个向量之间的夹角。
+        :::tip
+        向量夹角计算公式:
+        $$\\theta = \\arccos(\\frac{v1 \\cdot v2}{|v1| \\cdot |v2|})$$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    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 cross v2 -> v3

叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。

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':
+    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

TIP

叉乘运算法则为:

v1×v2=(v1y⋅v2z−v1z⋅v2y,v1z⋅v2x−v1x⋅v2z,v1x⋅v2y−v1y⋅v2x)

转换为行列式形式:

v1×v2=|ijkv1xv1yv1zv2xv2yv2z|

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':
     """
-        向量积 叉乘：v1 cross v2 -> v3
-
-        叉乘为0，则两向量平行。
-        其余结果的模为平行四边形的面积。
-
-        返回如下行列式的结果：
-
-        ``i  j  k``
-
-        ``x1 y1 z1``
-
-        ``x2 y2 z2``
+        向量积 叉乘：v1 x v2 -> v3
 
+        :::tip
+        叉乘运算法则为:
+        $$ v1 \\times v2 = (v1_y \\cdot v2_z - v1_z \\cdot v2_y, v1_z \\cdot v2_x - v1_x \\cdot v2_z, v1_x \\cdot v2_y - v1_y \\cdot v2_x) $$
+        转换为行列式形式:
+        $$ v1 \\times v2 = \\begin{vmatrix} i & j & k \\\\ v1_x & v1_y & v1_z \\\\ v2_x & v2_y & v2_z \\end{vmatrix} $$
+        :::
         Args:
             other ([`Vector3`](#class-vector3)): 另一个向量
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    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:
+    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:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +74,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    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:
+    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:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +82,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    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):
+    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):
     """
         将向量归一化。
 
@@ -92,33 +91,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

源碼 或 於GitHub上查看
python
@property
+    self.z /= length

@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':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    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
+    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
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    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
+    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
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

源碼 或 於GitHub上查看
python
@overload
+    return self / self.length

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V + P -> P
 
@@ -133,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")

method __eq__(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):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +140,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    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':
+    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':
     """
         P + V -> P
 
@@ -151,11 +150,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    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
+    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
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self - other: Point3 => Point3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

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):
+    ...

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):
     """
         V - P -> P
 
@@ -170,7 +169,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        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'):
+        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'):
     """
         P - V -> P
         Args:
@@ -181,11 +180,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        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
+        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
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...

@overload

method self * other: RealNumber => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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':
+    ...

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':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +197,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        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':
-    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':
+        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':
+    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':
     """
         点乘。
         Args:
@@ -207,15 +206,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    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 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':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
     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 459693a..a54c0ee 100644 --- a/zht/api/particle/index.html +++ b/zht/api/particle/index.html @@ -6,10 +6,10 @@ mbcp.particle | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html index 5cffdce..4fa6fe4 100644 --- a/zht/api/presets/index.html +++ b/zht/api/presets/index.html @@ -6,10 +6,10 @@ mbcp.presets | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html index 5b488cb..2b53da5 100644 --- a/zht/api/presets/model/index.html +++ b/zht/api/presets/model/index.html @@ -6,10 +6,10 @@ mbcp.presets.model | MBCP 文檔 - + - - + + @@ -36,7 +36,7 @@ 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 9c4e325..86b66a8 100644 --- a/zht/demo/best-practice.html +++ b/zht/demo/best-practice.html @@ -6,10 +6,10 @@ 最佳實踐 | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@ - + \ No newline at end of file diff --git a/zht/guide/index.html b/zht/guide/index.html index 834aa55..0df8272 100644 --- a/zht/guide/index.html +++ b/zht/guide/index.html @@ -6,10 +6,10 @@ 开始不了一点 | MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
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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 6af7732..5cab41b 100644 --- a/zht/index.html +++ b/zht/index.html @@ -6,10 +6,10 @@ MBCP 文檔 - + - - + + @@ -19,7 +19,7 @@
MBCP 文檔

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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

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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

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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

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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

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文檔由 VitePress 構建 | API引用由 litedoc 生成

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