diff --git a/404.html b/404.html index 8572951..42d03bf 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 82df417..bf11d1d 100644 --- a/api/index.html +++ b/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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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

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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 848d457..5e971c4 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -6,12 +6,12 @@ mbcp.mp_math.angle | MBCP 文档 - + - - + + - + @@ -19,92 +19,31 @@
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模块 mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

说明: 任意角度。

参数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
     if is_radian:
         self.radian = value
     else:
         self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

说明: 余角：两角的和为90°。

返回: 余角

源代码 或 在GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
     return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

说明: 补角：两角的和为180°。

返回: 补角

源代码 或 在GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
     return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

说明: 角度。

返回: 弧度

源代码 或 在GitHub上查看
python
@property
 def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
     return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

说明: 最小正角。

返回: 最小正角度

源代码 或 在GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
     return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

说明: 最大负角。

返回: 最大负角度

源代码 或 在GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
     return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

说明: 正弦值。

返回: 正弦值

源代码 或 在GitHub上查看
python
@property
 def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
     return math.sin(self.radian)

@property

method cos(self) -> float ​

说明: 余弦值。

返回: 余弦值

源代码 或 在GitHub上查看
python
@property
 def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
     return math.cos(self.radian)

@property

method tan(self) -> float ​

说明: 正切值。

返回: 正切值

源代码 或 在GitHub上查看
python
@property
 def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
     return math.tan(self.radian)

@property

method cot(self) -> float ​

说明: 余切值。

返回: 余切值

源代码 或 在GitHub上查看
python
@property
 def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
     return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

说明: 正割值。

返回: 正割值

源代码 或 在GitHub上查看
python
@property
 def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
     return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

说明: 余割值。

返回: 余割值

源代码 或 在GitHub上查看
python
@property
 def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
     return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
     return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
@@ -117,7 +56,7 @@
     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/api/mp_math/const.html b/api/mp_math/const.html index e3993b1..c55967e 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

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- + \ No newline at end of file diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html index bf860ef..14ef05a 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -6,12 +6,12 @@ mbcp.mp_math.equation | MBCP 文档 - + - - + + - + @@ -19,46 +19,16 @@
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模块 mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

说明: 曲线方程。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

说明: 计算曲线上的点。

参数:

  • *t:
  • 参数:

返回: 目标点

源代码 或 在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

参数:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

返回: 偏导函数

引发:

  • ValueError 无效变量类型
源代码 或 在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -68,14 +38,6 @@
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
@@ -83,7 +45,7 @@
         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/api/mp_math/function.html b/api/mp_math/function.html index 24881a3..bc4e85a 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -6,12 +6,12 @@ mbcp.mp_math.function | MBCP 文档 - + - - + + - + @@ -19,18 +19,6 @@
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模块 mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

说明: 计算三元函数在某点的梯度向量。

TIP

已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)

参数:

返回: 梯度

源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\nabla f(x_0, y_0, z_0) = \\left(\\frac{\\partial f}{\\partial x}, \\frac{\\partial f}{\\partial y}, \\frac{\\partial f}{\\partial z}\\right)$
-    Args:
-        func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([`Point3`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -38,29 +26,11 @@
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
源代码 或 在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([`Var`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        ```python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        ```
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func

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- + \ No newline at end of file diff --git a/api/mp_math/index.html b/api/mp_math/index.html index 4a196e5..ae20195 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

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- + \ No newline at end of file diff --git a/api/mp_math/line.html b/api/mp_math/line.html index ec26be4..3877bc3 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP 文档 - + - - + + - + @@ -19,40 +19,10 @@
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模块 mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

说明: 三维空间中的直线。由一个点和一个方向向量确定。

参数:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([`Point3`](./point#class-point3)): 直线上的一点
-            direction ([`Vector3`](./vector#class-vector3)): 方向向量
-        """
     self.point = point
     self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​

说明: 判断两条直线是否近似相等。

参数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似相等

源代码 或 在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

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

说明: 计算直线和直线之间的夹角。

参数:

  • other (Line3): 另一条直线

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`AnyAngle`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float ​

说明: 计算直线和直线或点之间的距离。

参数:

返回: float: 距离

引发:

源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([`Line3`](./line#class-line3) | [`Point3`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -66,91 +36,19 @@
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')

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

说明: 计算两条直线的交点。

参数:

  • other (Line3): 另一条直线

返回: Point3: 交点

引发:

源代码 或 在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Point3`](./point#class-point3): 交点
-        Raises:
-            [`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            `ValueError`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3 ​

说明: 计算直线经过指定点p的垂线。

参数:

返回: Line3: 垂线

源代码 或 在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([`Point3`](./point#class-point3)): 指定点
-        Returns:
-            [`Line3`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3 ​

说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。

参数:

返回: Point3: 点

源代码 或 在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([`RealNumber`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [`Point3`](./point#class-point3): 点
-        """
     return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​

说明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源代码 或 在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​

说明: 判断两条直线是否近似平行。

参数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

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: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool ​

说明: 判断两条直线是否平行。

参数:

返回: bool: 是否平行

源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool ​

说明: 判断两条直线是否共线。

参数:

返回: bool: 是否共线

源代码 或 在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool ​

说明: 判断点是否在直线上。

参数:

返回: bool: 是否在直线上

源代码 或 在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([`Point3`](./point#class-point3)): 点
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool ​

说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

参数:

返回: bool: 是否共面

源代码 或 在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self) ​

说明: 简化直线方程，等价相等。 自体简化，不返回值。

按照可行性一次对x y z 化 0 处理，并对向量单位化

源代码 或 在GitHub上查看
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -159,40 +57,16 @@
     if self.direction.z == 0:
         self.point.z = 0

@classmethod

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

说明: 工厂函数 由两点构造直线。

参数:

返回: Line3: 直线

源代码 或 在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 点1
-            p2 ([`Point3`](./point#class-point3)): 点2
-        Returns:
-            [`Line3`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)

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

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

参数:

  • other (Line3): 另一条直线

返回: Line3 | Point3 | None: 交集

源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

说明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

参数:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`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)

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

- + \ 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 a1b12dc..b7dcad2 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

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- + \ No newline at end of file diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html index 879a5a4..5e4a05a 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -6,12 +6,12 @@ mbcp.mp_math.plane | MBCP 文档 - + - - + + - + @@ -19,25 +19,10 @@
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模块 mbcp.mp_math.plane ​

本模块定义了三维空间中的平面类

class Plane3 ​

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

说明: 平面方程：ax + by + cz + d = 0

参数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
-    """
-        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:

  • other (Plane3): 另一个平面

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)
@@ -49,66 +34,18 @@
         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。

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:
-            [`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。

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:

  • other (Plane3): 另一个平面

返回: Line3: 交线

引发:

源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-    """
-        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)
@@ -126,106 +63,36 @@
         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:

  • other (Plane3): 另一个平面

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:

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

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:

  • l1 (Line3): 直线
  • l2 (Line3): 直线

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
@@ -236,16 +103,9 @@
         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:

  • other (Plane3): 另一个平面

返回: bool: 是否等价

源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        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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- + \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html index 1c8cf0d..6aa37e8 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -6,12 +6,12 @@ mbcp.mp_math.point | MBCP 文档 - + - - + + - + @@ -19,58 +19,19 @@
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模块 mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

说明: 笛卡尔坐标系中的点。

参数:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([`float`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (`float`): y 坐标
-            z (`float`): z 坐标
-        """
     self.x = x
     self.y = y
     self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

说明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://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])

@overload

method self + other: Vector3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
     ...

@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: P + V -> P P + P -> P

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([`Vector3`](./vector#class-vector3) | [`Point3`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [`Point3`](./point#class-point3): 新的点
-        """
     return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

说明: 判断两个点是否相等。

参数:

返回: bool: 是否相等

源代码 或 在GitHub上查看
python
def __eq__(self, other):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`bool`](https://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 => Vector3 ​

说明: P - P -> V

P - V -> P 已在 Vector3 中实现

参数:

返回: Vector3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [`Vector3`](./vector#class-vector3) 中实现
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`Vector3`](./vector#class-vector3): 新的向量
-        """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

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- + \ No newline at end of file diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html index e12f835..8d9acf4 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -6,12 +6,12 @@ mbcp.mp_math.segment | MBCP 文档 - + - - + + - + @@ -19,12 +19,6 @@
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模块 mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

说明: 三维空间中的线段。

参数:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 线段的一个端点
-            p2 ([`Point3`](./point#class-point3)): 线段的另一个端点
-        """
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -33,7 +27,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

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- + \ No newline at end of file diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html index b5af2c5..c61f6b5 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -6,12 +6,12 @@ mbcp.mp_math.utils | MBCP 文档 - + - - + + - + @@ -19,22 +19,7 @@
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模块 mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

说明: 区间限定函数

参数:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

返回: float: 限定在区间内的值

源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (`float`): 最小值
-        max_ (`float`): 最大值
-
-    Returns:
-        `float`: 限定在区间内的值
-    """
     return max(min(x, max_), min_)

class Approx ​

method __init__(self, value: RealNumber) ​

说明: 用于近似比较对象

参数:

源代码 或 在GitHub上查看
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value

method __eq__(self, other) ​

源代码 或 在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -48,46 +33,20 @@
             self.raise_type_error(other)

method raise_type_error(self, other) ​

源代码 或 在GitHub上查看
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')

method __ne__(self, other) ​

源代码 或 在GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)

func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​

说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。

参数:

  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差

返回: bool: 是否近似相等

源代码 或 在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (`float`): 数2
-        epsilon (`float`): 误差
-    Returns:
-        [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon

func sign(x: float, only_neg: bool = False) -> str ​

说明: 获取数的符号。

参数:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

返回: str: 符号 + - ""

源代码 或 在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''

func sign_format(x: float, only_neg: bool = False) -> str ​

说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""

参数:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

返回: str: 符号 + - ""

源代码 或 在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         return f'-{abs(x)}'
     else:
         return ''

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- + \ No newline at end of file diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html index b21d4a5..553ddef 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -6,12 +6,12 @@ mbcp.mp_math.vector | MBCP 文档 - + - - + + - + @@ -19,164 +19,47 @@
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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:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
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。

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 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 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:
@@ -185,13 +68,6 @@
     ...

@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)):
@@ -199,22 +75,10 @@
     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 ​

  • 说明: 零向量

  • 类型: Vector3

  • 默认值: Vector3(0, 0, 0)

var x_axis ​

  • 说明: x轴单位向量

  • 类型: Vector3

  • 默认值: Vector3(1, 0, 0)

var y_axis ​

  • 说明: y轴单位向量

  • 类型: Vector3

  • 默认值: Vector3(0, 1, 0)

var z_axis ​

  • 说明: z轴单位向量

  • 类型: Vector3

  • 默认值: Vector3(0, 0, 1)

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/particle/index.html b/api/particle/index.html index 6bf7659..69c5d59 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 ab0a6b0..c3d6e92 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 d64cce4..4821238 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -6,12 +6,12 @@ mbcp.presets.model | MBCP 文档 - + - - + + - + @@ -20,14 +20,6 @@
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.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

说明: 生成球体上的点集。

参数:

  • radius:
  • density:

返回: List[Point3]: 球体上的点集。

源代码 或 在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -36,7 +28,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

文档由 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/assets/api_mp_math_angle.md.DRCLNUJL.js b/assets/api_mp_math_angle.md.DRCLNUJL.js new file mode 100644 index 0000000..9b44677 --- /dev/null +++ b/assets/api_mp_math_angle.md.DRCLNUJL.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),e={name:"api/mp_math/angle.md"},n=t('

模块 mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

说明: 任意角度。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):\n    if is_radian:\n        self.radian = value\n    else:\n        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

说明: 余角：两角的和为90°。

返回: 余角

源代码 或 在GitHub上查看
python
@property\ndef complementary(self) -> 'AnyAngle':\n    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

说明: 补角：两角的和为180°。

返回: 补角

源代码 或 在GitHub上查看
python
@property\ndef supplementary(self) -> 'AnyAngle':\n    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

说明: 角度。

返回: 弧度

源代码 或 在GitHub上查看
python
@property\ndef degree(self) -> float:\n    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

说明: 最小正角。

返回: 最小正角度

源代码 或 在GitHub上查看
python
@property\ndef minimum_positive(self) -> 'AnyAngle':\n    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

说明: 最大负角。

返回: 最大负角度

源代码 或 在GitHub上查看
python
@property\ndef maximum_negative(self) -> 'AnyAngle':\n    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

说明: 正弦值。

返回: 正弦值

源代码 或 在GitHub上查看
python
@property\ndef sin(self) -> float:\n    return math.sin(self.radian)

@property

method cos(self) -> float ​

说明: 余弦值。

返回: 余弦值

源代码 或 在GitHub上查看
python
@property\ndef cos(self) -> float:\n    return math.cos(self.radian)

@property

method tan(self) -> float ​

说明: 正切值。

返回: 正切值

源代码 或 在GitHub上查看
python
@property\ndef tan(self) -> float:\n    return math.tan(self.radian)

@property

method cot(self) -> float ​

说明: 余切值。

返回: 余切值

源代码 或 在GitHub上查看
python
@property\ndef cot(self) -> float:\n    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

说明: 正割值。

返回: 正割值

源代码 或 在GitHub上查看
python
@property\ndef sec(self) -> float:\n    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

说明: 余割值。

返回: 余割值

源代码 或 在GitHub上查看
python
@property\ndef csc(self) -> float:\n    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

源代码 或 在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':\n    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

源代码 或 在GitHub上查看
python
def __truediv__(self, other):\n    if isinstance(other, AnyAngle):\n        return self.radian / other.radian\n    return AnyAngle(self.radian / other, is_radian=True)
',80),h=[n];function l(p,k,r,o,d,g){return i(),a("div",null,h)}const c=s(e,[["render",l]]);export{m as __pageData,c as default}; diff --git a/assets/api_mp_math_angle.md.DRCLNUJL.lean.js b/assets/api_mp_math_angle.md.DRCLNUJL.lean.js new file mode 100644 index 0000000..4a08902 --- /dev/null +++ b/assets/api_mp_math_angle.md.DRCLNUJL.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),e={name:"api/mp_math/angle.md"},n=t("",80),h=[n];function l(p,k,r,o,d,g){return i(),a("div",null,h)}const c=s(e,[["render",l]]);export{m as __pageData,c as default}; diff --git a/assets/api_mp_math_angle.md.DXjHPMcZ.js b/assets/api_mp_math_angle.md.DXjHPMcZ.js deleted file mode 100644 index 188d692..0000000 --- a/assets/api_mp_math_angle.md.DXjHPMcZ.js +++ /dev/null @@ -1,99 +0,0 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`

模块 mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

说明: 任意角度。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
-    if is_radian:
-        self.radian = value
-    else:
-        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

说明: 余角：两角的和为90°。

返回: 余角

源代码 或 在GitHub上查看
python
@property
-def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

说明: 补角：两角的和为180°。

返回: 补角

源代码 或 在GitHub上查看
python
@property
-def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

说明: 角度。

返回: 弧度

源代码 或 在GitHub上查看
python
@property
-def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
-    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

说明: 最小正角。

返回: 最小正角度

源代码 或 在GitHub上查看
python
@property
-def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
-    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

说明: 最大负角。

返回: 最大负角度

源代码 或 在GitHub上查看
python
@property
-def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

说明: 正弦值。

返回: 正弦值

源代码 或 在GitHub上查看
python
@property
-def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
-    return math.sin(self.radian)

@property

method cos(self) -> float ​

说明: 余弦值。

返回: 余弦值

源代码 或 在GitHub上查看
python
@property
-def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
-    return math.cos(self.radian)

@property

method tan(self) -> float ​

说明: 正切值。

返回: 正切值

源代码 或 在GitHub上查看
python
@property
-def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
-    return math.tan(self.radian)

@property

method cot(self) -> float ​

说明: 余切值。

返回: 余切值

源代码 或 在GitHub上查看
python
@property
-def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
-    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

说明: 正割值。

返回: 正割值

源代码 或 在GitHub上查看
python
@property
-def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
-    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

说明: 余割值。

返回: 余割值

源代码 或 在GitHub上查看
python
@property
-def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
-    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

源代码 或 在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

源代码 或 在GitHub上查看
python
def __truediv__(self, other):
-    if isinstance(other, AnyAngle):
-        return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/api_mp_math_angle.md.DXjHPMcZ.lean.js b/assets/api_mp_math_angle.md.DXjHPMcZ.lean.js deleted file mode 100644 index 5db2722..0000000 --- a/assets/api_mp_math_angle.md.DXjHPMcZ.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/api_mp_math_equation.md.qaTLbds6.js b/assets/api_mp_math_equation.md.Q6tfqPV1.js similarity index 76% rename from assets/api_mp_math_equation.md.qaTLbds6.js rename to assets/api_mp_math_equation.md.Q6tfqPV1.js index 986185a..c157530 100644 --- a/assets/api_mp_math_equation.md.qaTLbds6.js +++ b/assets/api_mp_math_equation.md.Q6tfqPV1.js @@ -1,44 +1,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n(`

模块 mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

说明: 曲线方程。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

说明: 计算曲线上的点。

参数:

返回: 目标点

源代码 或 在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

参数:

返回: 偏导函数

引发:

源代码 或 在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -48,18 +18,10 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default}; + raise ValueError('Invalid var type')`,23),h=[l];function p(e,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",p]]);export{u as __pageData,o as default}; diff --git a/assets/api_mp_math_equation.md.qaTLbds6.lean.js b/assets/api_mp_math_equation.md.Q6tfqPV1.lean.js similarity index 67% rename from assets/api_mp_math_equation.md.qaTLbds6.lean.js rename to assets/api_mp_math_equation.md.Q6tfqPV1.lean.js index 450e361..3cfbaf2 100644 --- a/assets/api_mp_math_equation.md.qaTLbds6.lean.js +++ b/assets/api_mp_math_equation.md.Q6tfqPV1.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default}; +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",23),h=[l];function p(e,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",p]]);export{u as __pageData,o as default}; diff --git a/assets/api_mp_math_function.md.D6Sk-jUO.js b/assets/api_mp_math_function.md.CDW7K4aO.js similarity index 82% rename from assets/api_mp_math_function.md.D6Sk-jUO.js rename to assets/api_mp_math_function.md.CDW7K4aO.js index f907517..f19a152 100644 --- a/assets/api_mp_math_function.md.D6Sk-jUO.js +++ b/assets/api_mp_math_function.md.CDW7K4aO.js @@ -1,16 +1,4 @@ -import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),e={name:"api/mp_math/function.md"},Q=a('

模块 mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

说明: 计算三元函数在某点的梯度向量。

',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`

参数:

返回: 梯度

源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
+import{_ as n,c as s,j as t,a as Q,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),T={name:"api/mp_math/function.md"},e=a('
模块 mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
',4),l={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=a('',1),u=[g],y=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=a('',1),w=[_],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=a(`
参数:
返回: 梯度
源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -18,25 +6,7 @@ import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1Zp
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
源代码 或 在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
+    return curried_func
`,13);function L(H,F,M,v,D,Z){return i(),s("div",null,[e,t("div",l,[h,t("p",null,[Q("已知一个函数"),t("mjx-container",r,[(i(),s("svg",d,o)),m]),Q("，则其在点"),t("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),t("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/api_mp_math_function.md.CDW7K4aO.lean.js b/assets/api_mp_math_function.md.CDW7K4aO.lean.js new file mode 100644 index 0000000..4c93a8e --- /dev/null +++ b/assets/api_mp_math_function.md.CDW7K4aO.lean.js @@ -0,0 +1 @@ +import{_ as n,c as s,j as t,a as Q,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),T={name:"api/mp_math/function.md"},e=a("",4),l={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=a("",1),u=[g],y=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=a("",1),w=[_],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=a("",13);function L(H,F,M,v,D,Z){return i(),s("div",null,[e,t("div",l,[h,t("p",null,[Q("已知一个函数"),t("mjx-container",r,[(i(),s("svg",d,o)),m]),Q("，则其在点"),t("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),t("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/api_mp_math_function.md.D6Sk-jUO.lean.js b/assets/api_mp_math_function.md.D6Sk-jUO.lean.js deleted file mode 100644 index 48b5568..0000000 --- a/assets/api_mp_math_function.md.D6Sk-jUO.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),e={name:"api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default}; diff --git a/assets/api_mp_math_line.md.K-HhIsvU.lean.js b/assets/api_mp_math_line.md.K-HhIsvU.lean.js deleted file mode 100644 index 28b458f..0000000 --- a/assets/api_mp_math_line.md.K-HhIsvU.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 F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default}; diff --git a/assets/api_mp_math_line.md.K-HhIsvU.js b/assets/api_mp_math_line.md.Ld9EytA4.js similarity index 74% rename from assets/api_mp_math_line.md.K-HhIsvU.js rename to assets/api_mp_math_line.md.Ld9EytA4.js index bdce64d..0420ad2 100644 --- a/assets/api_mp_math_line.md.K-HhIsvU.js +++ b/assets/api_mp_math_line.md.Ld9EytA4.js @@ -1,38 +1,8 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n(`

模块 mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

说明: 三维空间中的直线。由一个点和一个方向向量确定。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 直线上的一点
-            direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
-        """
+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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),n={name:"api/mp_math/line.md"},e=t(`
模块 mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     self.point = point
     self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -46,91 +16,19 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other (Line3): 另一条直线
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            \`ValueError\`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
返回: Line3: 垂线
源代码 或 在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Line3\`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
返回: Point3: 点
源代码 或 在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([\`RealNumber\`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [\`Point3\`](./point#class-point3): 点
-        """
     return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源代码 或 在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
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: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
返回: bool: 是否共线
源代码 或 在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
返回: bool: 是否在直线上
源代码 或 在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 点
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
返回: bool: 是否共面
源代码 或 在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码 或 在GitHub上查看
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -139,36 +37,12 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.z == 0:
         self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
返回: Line3: 直线
源代码 或 在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 ([\`Point3\`](./point#class-point3)): 点2
-        Returns:
-            [\`Line3\`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`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)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/api_mp_math_line.md.Ld9EytA4.lean.js b/assets/api_mp_math_line.md.Ld9EytA4.lean.js new file mode 100644 index 0000000..528ed79 --- /dev/null +++ b/assets/api_mp_math_line.md.Ld9EytA4.lean.js @@ -0,0 +1 @@ +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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),n={name:"api/mp_math/line.md"},e=t("",106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/api_mp_math_plane.md.dDWoDJrS.js b/assets/api_mp_math_plane.md.DRZNcHy5.js similarity index 85% rename from assets/api_mp_math_plane.md.dDWoDJrS.js rename to assets/api_mp_math_plane.md.DRZNcHy5.js index 57cde13..e1a9cf1 100644 --- a/assets/api_mp_math_plane.md.dDWoDJrS.js +++ b/assets/api_mp_math_plane.md.DRZNcHy5.js @@ -1,23 +1,8 @@ -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
-        """
+import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=t(`
模块 mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     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:
  • other (Plane3): 另一个平面
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)
@@ -28,67 +13,19 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},k=s("p",{class:"custom-block-title"},"TIP",-1),r=s("p",null,"平面间夹角计算公式:",-1),o={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),g=[Q],c=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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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
-        """
+        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':
     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:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
-    """
-        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
-        """
+        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:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -106,106 +43,36 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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:
  • other (Plane3): 另一个平面
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:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
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:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
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
@@ -216,12 +83,5 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        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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c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),e={name:"api/mp_math/point.md"},h=t('

模块 mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

说明: 笛卡尔坐标系中的点。

参数:

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

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

说明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

@overload

method self + other: Vector3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Point3':\n    ...

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

说明: P + V -> P P + P -> P

参数:

返回: Point3: 新的点

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

method __eq__(self, other) ​

说明: 判断两个点是否相等。

参数:

返回: bool: 是否相等

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

method self - other: Point3 => Vector3 ​

说明: P - P -> V

P - V -> P 已在 Vector3 中实现

参数:

返回: Vector3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':\n    from .vector import Vector3\n    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
',39),n=[h];function l(p,o,k,r,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{c as __pageData,y as default}; diff --git a/assets/api_mp_math_point.md.C4s5FhwG.lean.js b/assets/api_mp_math_point.md.C4s5FhwG.lean.js new file mode 100644 index 0000000..b929e32 --- /dev/null +++ b/assets/api_mp_math_point.md.C4s5FhwG.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),e={name:"api/mp_math/point.md"},h=t("",39),n=[h];function l(p,o,k,r,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{c as __pageData,y as default}; diff --git a/assets/api_mp_math_point.md.NLp_Sg9U.js b/assets/api_mp_math_point.md.NLp_Sg9U.js deleted file mode 100644 index 3c06616..0000000 --- a/assets/api_mp_math_point.md.NLp_Sg9U.js +++ /dev/null @@ -1,52 +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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t(`

模块 mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

说明: 笛卡尔坐标系中的点。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (\`float\`): y 坐标
-            z (\`float\`): z 坐标
-        """
-    self.x = x
-    self.y = y
-    self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

说明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://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])

@overload

method self + other: Vector3 => Point3 ​

源代码 或 在GitHub上查看
python
@overload
-def __add__(self, other: 'Vector3') -> 'Point3':
-    ...

@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: P + V -> P P + P -> P

参数:

返回: Point3: 新的点

源代码 或 在GitHub上查看
python
def __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([\`Vector3\`](./vector#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

说明: 判断两个点是否相等。

参数:

返回: bool: 是否相等

源代码 或 在GitHub上查看
python
def __eq__(self, other):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`bool\`](https://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 => Vector3 ​

说明: P - P -> V

P - V -> P 已在 Vector3 中实现

参数:

返回: Vector3: 新的向量

源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [\`Vector3\`](./vector#class-vector3) 中实现
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 新的向量
-        """
-    from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default}; diff --git a/assets/api_mp_math_point.md.NLp_Sg9U.lean.js b/assets/api_mp_math_point.md.NLp_Sg9U.lean.js deleted file mode 100644 index 0ab8c06..0000000 --- a/assets/api_mp_math_point.md.NLp_Sg9U.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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t("",39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default}; diff --git a/assets/api_mp_math_segment.md.C2PEP6H5.lean.js b/assets/api_mp_math_segment.md.C2PEP6H5.lean.js deleted file mode 100644 index b310795..0000000 --- a/assets/api_mp_math_segment.md.C2PEP6H5.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 F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,o,E){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default}; diff --git a/assets/api_mp_math_segment.md.C2PEP6H5.js b/assets/api_mp_math_segment.md.JYVgLepk.js similarity index 83% rename from assets/api_mp_math_segment.md.C2PEP6H5.js rename to assets/api_mp_math_segment.md.JYVgLepk.js index 5e8b841..861ef9f 100644 --- a/assets/api_mp_math_segment.md.C2PEP6H5.js +++ b/assets/api_mp_math_segment.md.JYVgLepk.js @@ -1,10 +1,4 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n(`

模块 mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

说明: 三维空间中的线段。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 线段的一个端点
-            p2 ([\`Point3\`](./point#class-point3)): 线段的另一个端点
-        """
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),n={name:"api/mp_math/segment.md"},h=t(`
模块 mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。
参数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -12,4 +6,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     '长度'
     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)
`,8),h=[p];function l(e,k,r,d,o,E){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const c=s(n,[["render",e]]);export{m as __pageData,c as default}; diff --git a/assets/api_mp_math_segment.md.JYVgLepk.lean.js b/assets/api_mp_math_segment.md.JYVgLepk.lean.js new file mode 100644 index 0000000..11c604f --- /dev/null +++ b/assets/api_mp_math_segment.md.JYVgLepk.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),n={name:"api/mp_math/segment.md"},h=t("",8),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const c=s(n,[["render",e]]);export{m as __pageData,c as default}; diff --git a/assets/api_mp_math_utils.md.QB0hGGMg.js b/assets/api_mp_math_utils.md.DuXZd_EC.js similarity index 81% rename from assets/api_mp_math_utils.md.QB0hGGMg.js rename to assets/api_mp_math_utils.md.DuXZd_EC.js index 01901d1..19db17d 100644 --- a/assets/api_mp_math_utils.md.QB0hGGMg.js +++ b/assets/api_mp_math_utils.md.DuXZd_EC.js @@ -1,20 +1,5 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),n={name:"api/mp_math/utils.md"},l=t(`

模块 mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

说明: 区间限定函数

参数:

返回: float: 限定在区间内的值

源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (\`float\`): 最小值
-        max_ (\`float\`): 最大值
-
-    Returns:
-        \`float\`: 限定在区间内的值
-    """
+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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},n=t(`
模块 mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
说明: 区间限定函数
参数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
说明: 用于近似比较对象
参数:
源代码 或 在GitHub上查看
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value
method __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -28,42 +13,16 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
             self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码 或 在GitHub上查看
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (\`float\`): 数2
-        epsilon (\`float\`): 误差
-    Returns:
-        [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[n];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{E as __pageData,c as default}; diff --git a/assets/api_mp_math_utils.md.DuXZd_EC.lean.js b/assets/api_mp_math_utils.md.DuXZd_EC.lean.js new file mode 100644 index 0000000..5f34385 --- /dev/null +++ b/assets/api_mp_math_utils.md.DuXZd_EC.lean.js @@ -0,0 +1 @@ +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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},n=t("",38),h=[n];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{E as __pageData,c as default}; diff --git a/assets/api_mp_math_utils.md.QB0hGGMg.lean.js b/assets/api_mp_math_utils.md.QB0hGGMg.lean.js deleted file mode 100644 index db5f944..0000000 --- a/assets/api_mp_math_utils.md.QB0hGGMg.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 F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),n={name:"api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default}; diff --git a/assets/api_mp_math_vector.md.BzTv8qws.js b/assets/api_mp_math_vector.md.BzTv8qws.js deleted file mode 100644 index 22017a8..0000000 --- a/assets/api_mp_math_vector.md.BzTv8qws.js +++ /dev/null @@ -1,176 +0,0 @@ -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":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),l={name:"api/mp_math/vector.md"},e=a('

模块 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

说明: 3维向量

参数:

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

',16),h={class:"tip custom-block"},p=s("p",{class:"custom-block-title"},"TIP",-1),r=s("p",null,"向量夹角计算公式:",-1),o={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},d=a('',1),T=[d],Q=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a(`

参数:

返回: AnyAngle: 夹角

源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
-    """
-        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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模块 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

说明: 3维向量

参数:

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

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

说明: 判断两个向量是否近似相等。

参数:

返回: bool: 是否近似相等

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

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

说明: 计算两个向量之间的夹角。

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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':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

说明: 向量积 叉乘：v1 x v2 -> v3

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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':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

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

说明: 判断两个向量是否近似平行。

参数:

返回: bool: 是否近似平行

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

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

说明: 判断两个向量是否平行。

参数:

返回: bool: 是否平行

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

method normalize(self) ​

说明: 将向量归一化。

自体归一化，不返回值。

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

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

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

@property

method length(self) -> float ​

说明: 向量的模。

返回: float: 模

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

@property

method unit(self) -> Vector3 ​

说明: 获取该向量的单位向量。

返回: Vector3: 单位向量

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

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

说明: V + P -> P

V + V -> V

参数:

返回: Vector3 | Point3: 新的向量或点

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

method __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):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

说明: P + V -> P

别去点那边实现了。

参数:

返回: Point3: 新的点

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

@overload

method self - other: Vector3 => Vector3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

method self - other ​

说明: V - P -> P

V - V -> V

参数:

返回: Vector3 | Point3: 新的向量

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

method self - other: Point3 ​

说明: P - V -> P

参数:

返回: Point3: 新的点

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

@overload

method self * other: Vector3 => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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

说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

参数:

返回: Vector3: 数组运算结果

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

method self * other: RealNumber => Vector3 ​

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

method self @ other: Vector3 => RealNumber ​

说明: 点乘。

参数:

返回: float: 点乘结果

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

method self / other: RealNumber => Vector3 ​

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

method - self => Vector3 ​

说明: 取负。

返回: Vector3: 负向量

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

var zero_vector3 ​

var x_axis ​

var y_axis ​

var z_axis ​

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y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),n={name:"api/presets/model/index.md"},h=t(`

模块 mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

说明: 生成球体上的点集。

参数:

返回: List[Point3]: 球体上的点集。

源代码 或 在GitHub上查看
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),h={name:"api/presets/model/index.md"},n=t(`
模块 mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码 或 在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -15,4 +7,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     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)]
`,10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[n];function e(p,k,r,d,E,o){return a(),i("div",null,l)}const c=s(h,[["render",e]]);export{y as __pageData,c as default}; diff --git a/assets/api_presets_model_index.md.BH3azKA8.lean.js b/assets/api_presets_model_index.md.DTQNHoYw.lean.js similarity index 64% rename from assets/api_presets_model_index.md.BH3azKA8.lean.js rename to assets/api_presets_model_index.md.DTQNHoYw.lean.js index 5dbf3aa..7c01294 100644 --- a/assets/api_presets_model_index.md.BH3azKA8.lean.js +++ b/assets/api_presets_model_index.md.DTQNHoYw.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),n={name:"api/presets/model/index.md"},h=t("",10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default}; +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),h={name:"api/presets/model/index.md"},n=t("",10),l=[n];function e(p,k,r,d,E,o){return a(),i("div",null,l)}const c=s(h,[["render",e]]);export{y as __pageData,c as default}; diff --git a/assets/app.BOTpTV4k.js b/assets/app.BUlGQzcU.js similarity index 95% rename from assets/app.BOTpTV4k.js rename to assets/app.BUlGQzcU.js index d89ae92..cfe0134 100644 --- a/assets/app.BOTpTV4k.js +++ b/assets/app.BUlGQzcU.js @@ -1 +1 @@ -import{t as p}from"./chunks/theme.Uf1cjNk7.js";import{U as o,a5 as u,a6 as c,a7 as l,a8 as f,a9 as d,aa as m,ab as h,ac as g,ad as A,ae as y,d as P,u as v,y as C,x as b,af as w,ag as E,ah as 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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 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mbcp.mp_math.angle","class AnyAngle(Angle)"]},"20":{"title":"method self / other: float => AnyAngle","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"21":{"title":"method self / other: AnyAngle => float","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"22":{"title":"method self / other","titles":["モジュール mbcp.mp_math.angle","class AnyAngle(Angle)"]},"23":{"title":"モジュール mbcp.mp_math.const","titles":[]},"24":{"title":"var PI","titles":["モジュール mbcp.mp_math.const"]},"25":{"title":"var E","titles":["モジュール mbcp.mp_math.const"]},"26":{"title":"var GOLDEN_RATIO","titles":["モジュール mbcp.mp_math.const"]},"27":{"title":"var GAMMA","titles":["モジュール mbcp.mp_math.const"]},"28":{"title":"var EPSILON","titles":["モジュール mbcp.mp_math.const"]},"29":{"title":"var APPROX","titles":["モジュール mbcp.mp_math.const"]},"30":{"title":"モジュール mbcp.mp_math.equation","titles":[]},"31":{"title":"class CurveEquation","titles":["モジュール mbcp.mp_math.equation"]},"32":{"title":"method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc)","titles":["モジュール mbcp.mp_math.equation","class CurveEquation"]},"33":{"title":"method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]","titles":["モジュール mbcp.mp_math.equation","class CurveEquation"]},"34":{"title":"func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc","titles":["モジュール mbcp.mp_math.equation"]},"35":{"title":"モジュール mbcp.mp_math.function","titles":[]},"36":{"title":"func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3","titles":["モジュール mbcp.mp_math.function"]},"37":{"title":"func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc","titles":["モジュール mbcp.mp_math.function"]},"38":{"title":"モジュール mbcp.mp_math","titles":[]},"39":{"title":"モジュール mbcp.mp_math.mp_math_typing","titles":[]},"40":{"title":"var RealNumber","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"41":{"title":"var Number","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"42":{"title":"var SingleVar","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"43":{"title":"var ArrayVar","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"44":{"title":"var Var","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"45":{"title":"var OneSingleVarFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"46":{"title":"var OneArrayFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"47":{"title":"var OneVarFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"48":{"title":"var TwoSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"49":{"title":"var TwoArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"50":{"title":"var TwoVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"51":{"title":"var ThreeSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"52":{"title":"var ThreeArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"53":{"title":"var ThreeVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"54":{"title":"var MultiSingleVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"55":{"title":"var MultiArraysFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"56":{"title":"var MultiVarsFunc","titles":["モジュール mbcp.mp_math.mp_math_typing"]},"57":{"title":"モジュール mbcp.mp_math.line","titles":[]},"58":{"title":"class Line3","titles":["モジュール mbcp.mp_math.line"]},"59":{"title":"method __init__(self, point: Point3, direction: Vector3)","titles":["モジュール mbcp.mp_math.line","class Line3"]},"60":{"title":"method approx(self, other: Line3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"61":{"title":"method cal_angle(self, other: Line3) -> AnyAngle","titles":["モジュール mbcp.mp_math.line","class Line3"]},"62":{"title":"method cal_distance(self, other: Line3 | Point3) -> float","titles":["モジュール mbcp.mp_math.line","class Line3"]},"63":{"title":"method cal_intersection(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"64":{"title":"method cal_perpendicular(self, point: Point3) -> Line3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"65":{"title":"method get_point(self, t: RealNumber) -> Point3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"66":{"title":"method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]","titles":["モジュール mbcp.mp_math.line","class Line3"]},"67":{"title":"method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"68":{"title":"method is_parallel(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"69":{"title":"method is_collinear(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"70":{"title":"method is_point_on(self, point: Point3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"71":{"title":"method is_coplanar(self, other: Line3) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"72":{"title":"method simplify(self)","titles":["モジュール mbcp.mp_math.line","class Line3"]},"73":{"title":"method from_two_points(cls, p1: Point3, p2: Point3) -> Line3","titles":["モジュール mbcp.mp_math.line","class Line3"]},"74":{"title":"method __and__(self, other: Line3) -> Line3 | Point3 | None","titles":["モジュール mbcp.mp_math.line","class Line3"]},"75":{"title":"method __eq__(self, other) -> bool","titles":["モジュール mbcp.mp_math.line","class Line3"]},"76":{"title":"モジュール mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["モジュール mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"85":{"title":"method is_parallel(self, other: Plane3) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"86":{"title":"method normal(self) -> Vector3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"87":{"title":"method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"88":{"title":"method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"89":{"title":"method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"90":{"title":"method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"91":{"title":"method __and__(self, other: Line3) -> Point3 | None","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"92":{"title":"method __and__(self, other: Plane3) -> Line3 | None","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"93":{"title":"method __and__(self, other)","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"94":{"title":"method __eq__(self, other) -> bool","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"95":{"title":"method __rand__(self, other: Line3) -> Point3","titles":["モジュール mbcp.mp_math.plane","class Plane3"]},"96":{"title":"モジュール mbcp.mp_math.point","titles":[]},"97":{"title":"class Point3","titles":["モジュール mbcp.mp_math.point"]},"98":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["モジュール mbcp.mp_math.point","class Point3"]},"99":{"title":"method approx(self, other: Point3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.point","class Point3"]},"100":{"title":"method self + other: Vector3 => Point3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"101":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"102":{"title":"method self + other","titles":["モジュール mbcp.mp_math.point","class Point3"]},"103":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.point","class Point3"]},"104":{"title":"method self - other: Point3 => Vector3","titles":["モジュール mbcp.mp_math.point","class Point3"]},"105":{"title":"モジュール mbcp.mp_math.segment","titles":[]},"106":{"title":"class Segment3","titles":["モジュール mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["モジュール mbcp.mp_math.segment","class Segment3"]},"108":{"title":"モジュール mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["モジュール mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["モジュール mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["モジュール mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["モジュール mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["モジュール mbcp.mp_math.utils"]},"118":{"title":"モジュール mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["モジュール mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["モジュール mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => 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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.segment","titles":[]},"106":{"title":"class Segment3","titles":["模块 mbcp.mp_math.segment"]},"107":{"title":"method __init__(self, p1: Point3, p2: Point3)","titles":["模块 mbcp.mp_math.segment","class Segment3"]},"108":{"title":"模块 mbcp.mp_math.utils","titles":[]},"109":{"title":"func clamp(x: float, min_: float, max_: float) -> float","titles":["模块 mbcp.mp_math.utils"]},"110":{"title":"class Approx","titles":["模块 mbcp.mp_math.utils"]},"111":{"title":"method __init__(self, value: RealNumber)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"112":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"113":{"title":"method raise_type_error(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"114":{"title":"method __ne__(self, other)","titles":["模块 mbcp.mp_math.utils","class Approx"]},"115":{"title":"func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.utils"]},"116":{"title":"func sign(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"117":{"title":"func sign_format(x: float, only_neg: bool = False) -> str","titles":["模块 mbcp.mp_math.utils"]},"118":{"title":"模块 mbcp.mp_math.vector","titles":[]},"119":{"title":"class Vector3","titles":["模块 mbcp.mp_math.vector"]},"120":{"title":"method __init__(self, x: float, y: float, z: float)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"121":{"title":"method approx(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"122":{"title":"method cal_angle(self, other: Vector3) -> AnyAngle","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"123":{"title":"method cross(self, other: Vector3) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"124":{"title":"method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"125":{"title":"method is_parallel(self, other: Vector3) -> bool","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"126":{"title":"method normalize(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"127":{"title":"method np_array(self) -> np.ndarray","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"128":{"title":"method length(self) -> float","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"129":{"title":"method unit(self) -> Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"130":{"title":"method __abs__(self)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"131":{"title":"method self + other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"132":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"133":{"title":"method self + other","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"134":{"title":"method __eq__(self, other)","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"135":{"title":"method self + other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"136":{"title":"method self - other: Vector3 => Vector3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"137":{"title":"method self - other: Point3 => Point3","titles":["模块 mbcp.mp_math.vector","class Vector3"]},"138":{"title":"method self - 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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 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c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n(`

Module mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

Description: 任意角度。

Arguments:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
-    if is_radian:
-        self.radian = value
-    else:
-        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

Description: 余角：两角的和为90°。

Return: 余角

Source code or View on GitHub
python
@property
-def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

Description: 补角：两角的和为180°。

Return: 补角

Source code or View on GitHub
python
@property
-def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

Description: 角度。

Return: 弧度

Source code or View on GitHub
python
@property
-def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
-    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

Description: 最小正角。

Return: 最小正角度

Source code or View on GitHub
python
@property
-def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
-    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

Description: 最大负角。

Return: 最大负角度

Source code or View on GitHub
python
@property
-def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

Description: 正弦值。

Return: 正弦值

Source code or View on GitHub
python
@property
-def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
-    return math.sin(self.radian)

@property

method cos(self) -> float ​

Description: 余弦值。

Return: 余弦值

Source code or View on GitHub
python
@property
-def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
-    return math.cos(self.radian)

@property

method tan(self) -> float ​

Description: 正切值。

Return: 正切值

Source code or View on GitHub
python
@property
-def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
-    return math.tan(self.radian)

@property

method cot(self) -> float ​

Description: 余切值。

Return: 余切值

Source code or View on GitHub
python
@property
-def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
-    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

Description: 正割值。

Return: 正割值

Source code or View on GitHub
python
@property
-def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
-    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

Description: 余割值。

Return: 余割值

Source code or View on GitHub
python
@property
-def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
-    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

Source code or View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

Source code or View on GitHub
python
def __truediv__(self, other):
-    if isinstance(other, AnyAngle):
-        return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/en_api_mp_math_angle.md.B5tdtBiM.lean.js b/assets/en_api_mp_math_angle.md.B5tdtBiM.lean.js deleted file mode 100644 index 8f233a1..0000000 --- a/assets/en_api_mp_math_angle.md.B5tdtBiM.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 c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/en_api_mp_math_angle.md.Bd_SmddI.js b/assets/en_api_mp_math_angle.md.Bd_SmddI.js new file mode 100644 index 0000000..b8762be --- /dev/null +++ b/assets/en_api_mp_math_angle.md.Bd_SmddI.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},n=t('

Module mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

Description: 任意角度。

Arguments:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):\n    if is_radian:\n        self.radian = value\n    else:\n        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

Description: 余角：两角的和为90°。

Return: 余角

Source code or View on GitHub
python
@property\ndef complementary(self) -> 'AnyAngle':\n    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

Description: 补角：两角的和为180°。

Return: 补角

Source code or View on GitHub
python
@property\ndef supplementary(self) -> 'AnyAngle':\n    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

Description: 角度。

Return: 弧度

Source code or View on GitHub
python
@property\ndef degree(self) -> float:\n    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

Description: 最小正角。

Return: 最小正角度

Source code or View on GitHub
python
@property\ndef minimum_positive(self) -> 'AnyAngle':\n    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

Description: 最大负角。

Return: 最大负角度

Source code or View on GitHub
python
@property\ndef maximum_negative(self) -> 'AnyAngle':\n    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

Description: 正弦值。

Return: 正弦值

Source code or View on GitHub
python
@property\ndef sin(self) -> float:\n    return math.sin(self.radian)

@property

method cos(self) -> float ​

Description: 余弦值。

Return: 余弦值

Source code or View on GitHub
python
@property\ndef cos(self) -> float:\n    return math.cos(self.radian)

@property

method tan(self) -> float ​

Description: 正切值。

Return: 正切值

Source code or View on GitHub
python
@property\ndef tan(self) -> float:\n    return math.tan(self.radian)

@property

method cot(self) -> float ​

Description: 余切值。

Return: 余切值

Source code or View on GitHub
python
@property\ndef cot(self) -> float:\n    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

Description: 正割值。

Return: 正割值

Source code or View on GitHub
python
@property\ndef sec(self) -> float:\n    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

Description: 余割值。

Return: 余割值

Source code or View on GitHub
python
@property\ndef csc(self) -> float:\n    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

Source code or View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':\n    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

Source code or View on GitHub
python
def __truediv__(self, other):\n    if isinstance(other, AnyAngle):\n        return self.radian / other.radian\n    return AnyAngle(self.radian / other, is_radian=True)
',80),h=[n];function l(p,r,k,o,d,g){return a(),i("div",null,h)}const m=s(e,[["render",l]]);export{c as __pageData,m as default}; diff --git a/assets/en_api_mp_math_angle.md.Bd_SmddI.lean.js b/assets/en_api_mp_math_angle.md.Bd_SmddI.lean.js new file mode 100644 index 0000000..039f849 --- /dev/null +++ b/assets/en_api_mp_math_angle.md.Bd_SmddI.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},n=t("",80),h=[n];function l(p,r,k,o,d,g){return a(),i("div",null,h)}const m=s(e,[["render",l]]);export{c as __pageData,m as default}; diff --git a/assets/en_api_mp_math_equation.md.N3oP-7Ua.js b/assets/en_api_mp_math_equation.md.B0ThTNcD.js similarity index 77% rename from assets/en_api_mp_math_equation.md.N3oP-7Ua.js rename to assets/en_api_mp_math_equation.md.B0ThTNcD.js index 88be957..d236f29 100644 --- a/assets/en_api_mp_math_equation.md.N3oP-7Ua.js +++ b/assets/en_api_mp_math_equation.md.B0ThTNcD.js @@ -1,44 +1,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n(`

Module mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

Description: 曲线方程。

Arguments:

Source code or View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

Description: 计算曲线上的点。

Arguments:

  • *t:
  • 参数:

Return: 目标点

Source code or View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

Arguments:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

Return: 偏导函数

Raises:

  • ValueError 无效变量类型
Source code or View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -48,18 +18,10 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default}; + raise ValueError('Invalid var type')`,23),h=[l];function e(p,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",e]]);export{u as __pageData,o as default}; diff --git a/assets/en_api_mp_math_equation.md.N3oP-7Ua.lean.js b/assets/en_api_mp_math_equation.md.B0ThTNcD.lean.js similarity index 73% rename from assets/en_api_mp_math_equation.md.N3oP-7Ua.lean.js rename to assets/en_api_mp_math_equation.md.B0ThTNcD.lean.js index ec4bd2d..f5aa0b5 100644 --- a/assets/en_api_mp_math_equation.md.N3oP-7Ua.lean.js +++ b/assets/en_api_mp_math_equation.md.B0ThTNcD.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default}; +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n("",23),h=[l];function e(p,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",e]]);export{u as __pageData,o as default}; diff --git a/assets/en_api_mp_math_function.md.BT0NB_1n.lean.js b/assets/en_api_mp_math_function.md.BT0NB_1n.lean.js deleted file mode 100644 index d2c213a..0000000 --- a/assets/en_api_mp_math_function.md.BT0NB_1n.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),e={name:"en/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 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V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),e={name:"en/api/mp_math/function.md"},Q=a('

Module mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

Description: 计算三元函数在某点的梯度向量。

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Arguments:

Return: 梯度

Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
+import{_ as n,c as s,j as t,a as Q,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),T={name:"en/api/mp_math/function.md"},e=a('
Module mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
',4),l={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},o=a('',1),p=[o],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=a('',1),u=[g],y=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=a('',1),w=[_],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=a(`
Arguments:
Return: 梯度
Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -18,25 +6,7 @@ import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1Zp
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
Source code or View on GitHub
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const Z=l(e,[["render",x]]);export{V as __pageData,Z as default};
+    return curried_func
`,13);function L(H,M,F,v,D,Z){return i(),s("div",null,[e,t("div",l,[h,t("p",null,[Q("已知一个函数"),t("mjx-container",r,[(i(),s("svg",d,p)),m]),Q("，则其在点"),t("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),t("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/en_api_mp_math_function.md.l19FY4Hu.lean.js b/assets/en_api_mp_math_function.md.l19FY4Hu.lean.js new file mode 100644 index 0000000..05c3641 --- /dev/null +++ b/assets/en_api_mp_math_function.md.l19FY4Hu.lean.js @@ -0,0 +1 @@ +import{_ as n,c as s,j as t,a as Q,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),T={name:"en/api/mp_math/function.md"},e=a("",4),l={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},o=a("",1),p=[o],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=a("",1),u=[g],y=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=a("",1),w=[_],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=a("",13);function L(H,M,F,v,D,Z){return i(),s("div",null,[e,t("div",l,[h,t("p",null,[Q("已知一个函数"),t("mjx-container",r,[(i(),s("svg",d,p)),m]),Q("，则其在点"),t("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),t("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/en_api_mp_math_line.md.0bBpZMyn.lean.js b/assets/en_api_mp_math_line.md.0bBpZMyn.lean.js deleted file mode 100644 index 0ed5ff5..0000000 --- a/assets/en_api_mp_math_line.md.0bBpZMyn.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 F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default}; diff --git a/assets/en_api_mp_math_line.md.0bBpZMyn.js b/assets/en_api_mp_math_line.md.Bd5Z3iC3.js similarity index 74% rename from assets/en_api_mp_math_line.md.0bBpZMyn.js rename to assets/en_api_mp_math_line.md.Bd5Z3iC3.js index 1fc957d..30b81c6 100644 --- a/assets/en_api_mp_math_line.md.0bBpZMyn.js +++ b/assets/en_api_mp_math_line.md.Bd5Z3iC3.js @@ -1,38 +1,8 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n(`

Module mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

Description: 三维空间中的直线。由一个点和一个方向向量确定。

Arguments:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 直线上的一点
-            direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
-        """
+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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),e={name:"en/api/mp_math/line.md"},n=t(`
Module mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     self.point = point
     self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other (Line3): 另一条直线
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -46,91 +16,19 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other (Line3): 另一条直线
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            \`ValueError\`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
Return: Line3: 垂线
Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Line3\`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
Return: Point3: 点
Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([\`RealNumber\`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [\`Point3\`](./point#class-point3): 点
-        """
     return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
Return: bool: 是否共线
Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
Return: bool: 是否在直线上
Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 点
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
Return: bool: 是否共面
Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code or View on GitHub
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -139,36 +37,12 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.z == 0:
         self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
Return: Line3: 直线
Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 ([\`Point3\`](./point#class-point3)): 点2
-        Returns:
-            [\`Line3\`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other (Line3): 另一条直线
Return: Line3 | Point3 | None: 交集
Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other (Line3): 另一条直线
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`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)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[n];function h(p,o,r,k,d,g){return a(),i("div",null,l)}const y=s(e,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_line.md.Bd5Z3iC3.lean.js b/assets/en_api_mp_math_line.md.Bd5Z3iC3.lean.js new file mode 100644 index 0000000..ee7ec98 --- /dev/null +++ b/assets/en_api_mp_math_line.md.Bd5Z3iC3.lean.js @@ -0,0 +1 @@ +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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),e={name:"en/api/mp_math/line.md"},n=t("",106),l=[n];function h(p,o,r,k,d,g){return a(),i("div",null,l)}const y=s(e,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_plane.md.BqUredjB.js b/assets/en_api_mp_math_plane.md.D91Vt6aU.js similarity index 84% rename from assets/en_api_mp_math_plane.md.BqUredjB.js rename to assets/en_api_mp_math_plane.md.D91Vt6aU.js index 7e6f2ec..f8a4dc1 100644 --- a/assets/en_api_mp_math_plane.md.BqUredjB.js +++ b/assets/en_api_mp_math_plane.md.D91Vt6aU.js @@ -1,23 +1,8 @@ -import{_ as l,c as i,j as s,a as n,a4 as t,o as a}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":"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
-        """
+import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=t(`
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):
     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)
@@ -28,67 +13,19 @@ import{_ as l,c as i,j as s,a as n,a4 as t,o as a}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
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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
-        """
+        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':
     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
-        """
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
`,16),I={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"x"),s("mo",null,"="),s("mn",null,"0")])],-1),ls={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},hs={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.464ex"},xmlns:"http://www.w3.org/2000/svg",width:"5.257ex",height:"1.971ex",role:"img",focusable:"false",viewBox:"0 -666 2323.6 871","aria-hidden":"true"},ps=t('',1),rs=[ps],os=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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0",position:"relative"}},_s={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.991ex"},xmlns:"http://www.w3.org/2000/svg",width:"27.19ex",height:"4.839ex",role:"img",focusable:"false",viewBox:"0 -1259 12018.1 2139","aria-hidden":"true"},bs=t('',1),Cs=[bs],xs=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mfrac",null,[s("mrow",null,[s("mi",null,"x"),s("mo",null,"−"),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")])]),s("mi",null,"m")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"y"),s("mo",null,"−"),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")])]),s("mi",null,"n")]),s("mo",null,"="),s("mfrac",null,[s("mrow",null,[s("mi",null,"z"),s("mo",null,"−"),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")])]),s("mi",null,"p")])])],-1),ws=t(`
Arguments:
  • 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':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -106,106 +43,36 @@ import{_ as l,c as i,j as s,a as n,a4 as t,o as a}from"./chunks/framework.DpC1Zp
         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
@@ -216,12 +83,5 @@ import{_ as l,c as i,j as s,a as n,a4 as t,o as a}from"./chunks/framework.DpC1Zp
         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.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

Description: 笛卡尔坐标系中的点。

Arguments:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (\`float\`): y 坐标
-            z (\`float\`): z 坐标
-        """
-    self.x = x
-    self.y = y
-    self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

Description: 判断两个点是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://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])

@overload

method self + other: Vector3 => Point3 ​

Source code or View on GitHub
python
@overload
-def __add__(self, other: 'Vector3') -> 'Point3':
-    ...

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

Description: P + V -> P P + P -> P

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([\`Vector3\`](./vector#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

Description: 判断两个点是否相等。

Arguments:

Return: bool: 是否相等

Source code or View on GitHub
python
def __eq__(self, other):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`bool\`](https://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 => Vector3 ​

Description: P - P -> V

P - V -> P 已在 Vector3 中实现

Arguments:

Return: Vector3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [\`Vector3\`](./vector#class-vector3) 中实现
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 新的向量
-        """
-    from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[e];function h(p,o,k,r,d,c){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_point.md.Dr2bDE6-.js b/assets/en_api_mp_math_point.md.Dr2bDE6-.js new file mode 100644 index 0000000..7a53d15 --- /dev/null +++ b/assets/en_api_mp_math_point.md.Dr2bDE6-.js @@ -0,0 +1 @@ +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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),e={name:"en/api/mp_math/point.md"},h=t('

Module mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

Description: 笛卡尔坐标系中的点。

Arguments:

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

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

Description: 判断两个点是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

@overload

method self + other: Vector3 => Point3 ​

Source code or View on GitHub
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Point3':\n    ...

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

Description: P + V -> P P + P -> P

Arguments:

Return: Point3: 新的点

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

method __eq__(self, other) ​

Description: 判断两个点是否相等。

Arguments:

Return: bool: 是否相等

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

method self - other: Point3 => Vector3 ​

Description: P - P -> V

P - V -> P 已在 Vector3 中实现

Arguments:

Return: Vector3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':\n    from .vector import Vector3\n    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
',39),n=[h];function l(p,o,r,k,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_point.md.Ba_i7dDC.lean.js b/assets/en_api_mp_math_point.md.Dr2bDE6-.lean.js similarity index 58% rename from assets/en_api_mp_math_point.md.Ba_i7dDC.lean.js rename to assets/en_api_mp_math_point.md.Dr2bDE6-.lean.js index 8047eb5..1f98d0d 100644 --- a/assets/en_api_mp_math_point.md.Ba_i7dDC.lean.js +++ b/assets/en_api_mp_math_point.md.Dr2bDE6-.lean.js @@ -1 +1 @@ -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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},e=t("",39),l=[e];function h(p,o,k,r,d,c){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; +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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),e={name:"en/api/mp_math/point.md"},h=t("",39),n=[h];function l(p,o,r,k,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{E as __pageData,y as default}; diff --git a/assets/en_api_mp_math_segment.md.BhIGb9yq.lean.js b/assets/en_api_mp_math_segment.md.BhIGb9yq.lean.js deleted file mode 100644 index cbf8c29..0000000 --- a/assets/en_api_mp_math_segment.md.BhIGb9yq.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 c=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},p=n("",8),h=[p];function e(l,k,r,d,o,E){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{c as __pageData,F as default}; diff --git a/assets/en_api_mp_math_segment.md.BhIGb9yq.js b/assets/en_api_mp_math_segment.md.D0wpX8Us.js similarity index 83% rename from assets/en_api_mp_math_segment.md.BhIGb9yq.js rename to assets/en_api_mp_math_segment.md.D0wpX8Us.js index 9594a7c..b253cd0 100644 --- a/assets/en_api_mp_math_segment.md.BhIGb9yq.js +++ b/assets/en_api_mp_math_segment.md.D0wpX8Us.js @@ -1,10 +1,4 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},p=n(`

Module mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

Description: 三维空间中的线段。

Arguments:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 线段的一个端点
-            p2 ([\`Point3\`](./point#class-point3)): 线段的另一个端点
-        """
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),n={name:"en/api/mp_math/segment.md"},h=t(`
Module mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。
Arguments:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -12,4 +6,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     '长度'
     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)
`,8),h=[p];function e(l,k,r,d,o,E){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{c as __pageData,F as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),e=[h];function p(l,k,r,d,o,E){return a(),i("div",null,e)}const c=s(n,[["render",p]]);export{m as __pageData,c as default}; diff --git a/assets/en_api_mp_math_segment.md.D0wpX8Us.lean.js b/assets/en_api_mp_math_segment.md.D0wpX8Us.lean.js new file mode 100644 index 0000000..2e00bc6 --- /dev/null +++ b/assets/en_api_mp_math_segment.md.D0wpX8Us.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),n={name:"en/api/mp_math/segment.md"},h=t("",8),e=[h];function p(l,k,r,d,o,E){return a(),i("div",null,e)}const c=s(n,[["render",p]]);export{m as __pageData,c as default}; diff --git a/assets/en_api_mp_math_utils.md.Bz-xJhl3.js b/assets/en_api_mp_math_utils.md.n9Hkxc_q.js similarity index 81% rename from assets/en_api_mp_math_utils.md.Bz-xJhl3.js rename to assets/en_api_mp_math_utils.md.n9Hkxc_q.js index 7f55306..4516905 100644 --- a/assets/en_api_mp_math_utils.md.Bz-xJhl3.js +++ b/assets/en_api_mp_math_utils.md.n9Hkxc_q.js @@ -1,20 +1,5 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),n={name:"en/api/mp_math/utils.md"},l=t(`

Module mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

Description: 区间限定函数

Arguments:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

Return: float: 限定在区间内的值

Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (\`float\`): 最小值
-        max_ (\`float\`): 最大值
-
-    Returns:
-        \`float\`: 限定在区间内的值
-    """
+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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),n={name:"en/api/mp_math/utils.md"},l=t(`
Module mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
Description: 区间限定函数
Arguments:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
Return: float: 限定在区间内的值
Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
     return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
Description: 用于近似比较对象
Arguments:
Source code or View on GitHub
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value
method __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -28,42 +13,16 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
             self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code or View on GitHub
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (\`float\`): 数2
-        epsilon (\`float\`): 误差
-    Returns:
-        [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{F as __pageData,c as default};
+        return ''
`,38),e=[l];function h(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(n,[["render",h]]);export{E as __pageData,c as default}; diff --git a/assets/en_api_mp_math_utils.md.Bz-xJhl3.lean.js b/assets/en_api_mp_math_utils.md.n9Hkxc_q.lean.js similarity index 58% rename from assets/en_api_mp_math_utils.md.Bz-xJhl3.lean.js rename to assets/en_api_mp_math_utils.md.n9Hkxc_q.lean.js index 292eb4c..266f09c 100644 --- a/assets/en_api_mp_math_utils.md.Bz-xJhl3.lean.js +++ b/assets/en_api_mp_math_utils.md.n9Hkxc_q.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),n={name:"en/api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{F as __pageData,c as default}; +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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),n={name:"en/api/mp_math/utils.md"},l=t("",38),e=[l];function h(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(n,[["render",h]]);export{E as __pageData,c as default}; diff --git a/assets/en_api_mp_math_vector.md.ARDQGWRk.js b/assets/en_api_mp_math_vector.md.ARDQGWRk.js new file mode 100644 index 0000000..6713d46 --- /dev/null +++ b/assets/en_api_mp_math_vector.md.ARDQGWRk.js @@ -0,0 +1 @@ +import{_ as e,c as t,j as s,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const z=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),l={name:"en/api/mp_math/vector.md"},n=a('

Module mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

Description: 3维向量

Arguments:

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

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

Description: 判断两个向量是否近似相等。

Arguments:

Return: bool: 是否近似相等

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

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

Description: 计算两个向量之间的夹角。

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Arguments:

Return: AnyAngle: 夹角

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

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

Description: 向量积 叉乘：v1 x v2 -> v3

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Arguments:

Return: Vector3: 叉乘结果

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

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

Description: 判断两个向量是否近似平行。

Arguments:

Return: bool: 是否近似平行

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

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

Description: 判断两个向量是否平行。

Arguments:

Return: bool: 是否平行

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

method normalize(self) ​

Description: 将向量归一化。

自体归一化，不返回值。

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

@property

method np_array(self) -> np.ndarray ​

Return: np.ndarray: numpy数组

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

@property

method length(self) -> float ​

Description: 向量的模。

Return: float: 模

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

@property

method unit(self) -> Vector3 ​

Description: 获取该向量的单位向量。

Return: Vector3: 单位向量

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

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

Description: V + P -> P

V + V -> V

Arguments:

Return: Vector3 | Point3: 新的向量或点

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

method __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):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

Description: P + V -> P

别去点那边实现了。

Arguments:

Return: Point3: 新的点

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

@overload

method self - other: Vector3 => Vector3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

method self - other ​

Description: V - P -> P

V - V -> V

Arguments:

Return: Vector3 | Point3: 新的向量

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

method self - other: Point3 ​

Description: P - V -> P

Arguments:

Return: Point3: 新的点

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

@overload

method self * other: Vector3 => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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

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

Arguments:

Return: Vector3: 数组运算结果

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

method self * other: RealNumber => Vector3 ​

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

method self @ other: Vector3 => RealNumber ​

Description: 点乘。

Arguments:

Return: float: 点乘结果

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

method self / other: RealNumber => Vector3 ​

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

method - self => Vector3 ​

Description: 取负。

Return: Vector3: 负向量

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

var zero_vector3 ​

  • Description: 零向量

  • Type: Vector3

  • Default: Vector3(0, 0, 0)

var x_axis ​

  • Description: x轴单位向量

  • Type: Vector3

  • Default: Vector3(1, 0, 0)

var y_axis ​

  • Description: y轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 1, 0)

var z_axis ​

  • Description: z轴单位向量

  • Type: Vector3

  • Default: Vector3(0, 0, 1)

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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)

`,115);function 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/en_api_presets_model_index.md.tRSLY10d.js b/assets/en_api_presets_model_index.md.CF6gWxhr.js similarity index 87% rename from assets/en_api_presets_model_index.md.tRSLY10d.js rename to assets/en_api_presets_model_index.md.CF6gWxhr.js index bd865a8..1de50dc 100644 --- a/assets/en_api_presets_model_index.md.tRSLY10d.js +++ b/assets/en_api_presets_model_index.md.CF6gWxhr.js @@ -1,13 +1,5 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n(`

Module mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

Description: 生成球体上的点集。

Arguments:

  • radius:
  • density:

Return: List[Point3]: 球体上的点集。

Source code or View on GitHub
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),h={name:"en/api/presets/model/index.md"},n=t(`
Module mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -15,4 +7,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     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)]
`,10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),e=[n];function l(p,k,r,d,E,o){return a(),i("div",null,e)}const c=s(h,[["render",l]]);export{y as __pageData,c as default}; diff --git a/assets/en_api_presets_model_index.md.tRSLY10d.lean.js b/assets/en_api_presets_model_index.md.CF6gWxhr.lean.js similarity index 50% rename from assets/en_api_presets_model_index.md.tRSLY10d.lean.js rename to assets/en_api_presets_model_index.md.CF6gWxhr.lean.js index d57d4c4..711aae3 100644 --- a/assets/en_api_presets_model_index.md.tRSLY10d.lean.js +++ b/assets/en_api_presets_model_index.md.CF6gWxhr.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n("",10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default}; +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),h={name:"en/api/presets/model/index.md"},n=t("",10),e=[n];function l(p,k,r,d,E,o){return a(),i("div",null,e)}const c=s(h,[["render",l]]);export{y as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_angle.md.BPpenAm_.js b/assets/ja_api_mp_math_angle.md.BPpenAm_.js deleted file mode 100644 index 0c9f1f5..0000000 --- a/assets/ja_api_mp_math_angle.md.BPpenAm_.js +++ /dev/null @@ -1,99 +0,0 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n(`

モジュール mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

説明: 任意角度。

引数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
-    if is_radian:
-        self.radian = value
-    else:
-        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

説明: 余角：两角的和为90°。

戻り値: 余角

ソースコード または GitHubで表示
python
@property
-def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

説明: 补角：两角的和为180°。

戻り値: 补角

ソースコード または GitHubで表示
python
@property
-def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

説明: 角度。

戻り値: 弧度

ソースコード または GitHubで表示
python
@property
-def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
-    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

説明: 最小正角。

戻り値: 最小正角度

ソースコード または GitHubで表示
python
@property
-def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
-    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

説明: 最大负角。

戻り値: 最大负角度

ソースコード または GitHubで表示
python
@property
-def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

説明: 正弦值。

戻り値: 正弦值

ソースコード または GitHubで表示
python
@property
-def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
-    return math.sin(self.radian)

@property

method cos(self) -> float ​

説明: 余弦值。

戻り値: 余弦值

ソースコード または GitHubで表示
python
@property
-def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
-    return math.cos(self.radian)

@property

method tan(self) -> float ​

説明: 正切值。

戻り値: 正切值

ソースコード または GitHubで表示
python
@property
-def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
-    return math.tan(self.radian)

@property

method cot(self) -> float ​

説明: 余切值。

戻り値: 余切值

ソースコード または GitHubで表示
python
@property
-def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
-    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

説明: 正割值。

戻り値: 正割值

ソースコード または GitHubで表示
python
@property
-def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
-    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

説明: 余割值。

戻り値: 余割值

ソースコード または GitHubで表示
python
@property
-def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
-    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

ソースコード または GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

ソースコード または GitHubで表示
python
def __truediv__(self, other):
-    if isinstance(other, AnyAngle):
-        return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/ja_api_mp_math_angle.md.BPpenAm_.lean.js b/assets/ja_api_mp_math_angle.md.BPpenAm_.lean.js deleted file mode 100644 index feff6a6..0000000 --- a/assets/ja_api_mp_math_angle.md.BPpenAm_.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/ja_api_mp_math_angle.md.DurFoqAy.js b/assets/ja_api_mp_math_angle.md.DurFoqAy.js new file mode 100644 index 0000000..9e3aafb --- /dev/null +++ b/assets/ja_api_mp_math_angle.md.DurFoqAy.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),e={name:"ja/api/mp_math/angle.md"},n=t('

モジュール mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

説明: 任意角度。

引数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):\n    if is_radian:\n        self.radian = value\n    else:\n        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

説明: 余角：两角的和为90°。

戻り値: 余角

ソースコード または GitHubで表示
python
@property\ndef complementary(self) -> 'AnyAngle':\n    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

説明: 补角：两角的和为180°。

戻り値: 补角

ソースコード または GitHubで表示
python
@property\ndef supplementary(self) -> 'AnyAngle':\n    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

説明: 角度。

戻り値: 弧度

ソースコード または GitHubで表示
python
@property\ndef degree(self) -> float:\n    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

説明: 最小正角。

戻り値: 最小正角度

ソースコード または GitHubで表示
python
@property\ndef minimum_positive(self) -> 'AnyAngle':\n    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

説明: 最大负角。

戻り値: 最大负角度

ソースコード または GitHubで表示
python
@property\ndef maximum_negative(self) -> 'AnyAngle':\n    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

説明: 正弦值。

戻り値: 正弦值

ソースコード または GitHubで表示
python
@property\ndef sin(self) -> float:\n    return math.sin(self.radian)

@property

method cos(self) -> float ​

説明: 余弦值。

戻り値: 余弦值

ソースコード または GitHubで表示
python
@property\ndef cos(self) -> float:\n    return math.cos(self.radian)

@property

method tan(self) -> float ​

説明: 正切值。

戻り値: 正切值

ソースコード または GitHubで表示
python
@property\ndef tan(self) -> float:\n    return math.tan(self.radian)

@property

method cot(self) -> float ​

説明: 余切值。

戻り値: 余切值

ソースコード または GitHubで表示
python
@property\ndef cot(self) -> float:\n    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

説明: 正割值。

戻り値: 正割值

ソースコード または GitHubで表示
python
@property\ndef sec(self) -> float:\n    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

説明: 余割值。

戻り値: 余割值

ソースコード または GitHubで表示
python
@property\ndef csc(self) -> float:\n    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

ソースコード または GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':\n    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

ソースコード または GitHubで表示
python
def __truediv__(self, other):\n    if isinstance(other, AnyAngle):\n        return self.radian / other.radian\n    return AnyAngle(self.radian / other, is_radian=True)
',80),h=[n];function l(p,k,r,o,d,g){return i(),a("div",null,h)}const c=s(e,[["render",l]]);export{m as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_angle.md.DurFoqAy.lean.js b/assets/ja_api_mp_math_angle.md.DurFoqAy.lean.js new file mode 100644 index 0000000..efbbb83 --- /dev/null +++ b/assets/ja_api_mp_math_angle.md.DurFoqAy.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),e={name:"ja/api/mp_math/angle.md"},n=t("",80),h=[n];function l(p,k,r,o,d,g){return i(),a("div",null,h)}const c=s(e,[["render",l]]);export{m as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_equation.md.Cxc2AyGq.js b/assets/ja_api_mp_math_equation.md.ClACMtEE.js similarity index 77% rename from assets/ja_api_mp_math_equation.md.Cxc2AyGq.js rename to assets/ja_api_mp_math_equation.md.ClACMtEE.js index dd9dc65..85a7105 100644 --- a/assets/ja_api_mp_math_equation.md.Cxc2AyGq.js +++ b/assets/ja_api_mp_math_equation.md.ClACMtEE.js @@ -1,44 +1,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n(`

モジュール mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

説明: 曲线方程。

引数:

ソースコード または GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

説明: 计算曲线上的点。

引数:

  • *t:
  • 参数:

戻り値: 目标点

ソースコード または GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

引数:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

戻り値: 偏导函数

例外:

  • ValueError 无效变量类型
ソースコード または GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -48,18 +18,10 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default}; + raise ValueError('Invalid var type')`,23),h=[l];function p(e,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",p]]);export{u as __pageData,o as default}; diff --git a/assets/ja_api_mp_math_equation.md.Cxc2AyGq.lean.js b/assets/ja_api_mp_math_equation.md.ClACMtEE.lean.js similarity index 66% rename from assets/ja_api_mp_math_equation.md.Cxc2AyGq.lean.js rename to assets/ja_api_mp_math_equation.md.ClACMtEE.lean.js index 3aac2d8..69fc77e 100644 --- a/assets/ja_api_mp_math_equation.md.Cxc2AyGq.lean.js +++ b/assets/ja_api_mp_math_equation.md.ClACMtEE.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default}; +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n("",23),h=[l];function p(e,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",p]]);export{u as __pageData,o as default}; diff --git a/assets/ja_api_mp_math_function.md.zcK7s9-C.js b/assets/ja_api_mp_math_function.md.pJM1NJ2m.js similarity index 82% rename from assets/ja_api_mp_math_function.md.zcK7s9-C.js rename to assets/ja_api_mp_math_function.md.pJM1NJ2m.js index 72836de..7b3d551 100644 --- a/assets/ja_api_mp_math_function.md.zcK7s9-C.js +++ b/assets/ja_api_mp_math_function.md.pJM1NJ2m.js @@ -1,16 +1,4 @@ -import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),e={name:"ja/api/mp_math/function.md"},Q=a('

モジュール mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

説明: 计算三元函数在某点的梯度向量。

',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`

引数:

戻り値: 梯度

ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
+import{_ as n,c as s,j as a,a as Q,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),T={name:"ja/api/mp_math/function.md"},e=t('
モジュール mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
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引数:
戻り値: 梯度
ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -18,25 +6,7 @@ import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1Zp
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
ソースコード または GitHubで表示
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
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+    return curried_func
`,13);function L(H,F,M,v,D,Z){return i(),s("div",null,[e,a("div",l,[h,a("p",null,[Q("已知一个函数"),a("mjx-container",r,[(i(),s("svg",d,o)),m]),Q("，则其在点"),a("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),a("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/ja_api_mp_math_function.md.pJM1NJ2m.lean.js b/assets/ja_api_mp_math_function.md.pJM1NJ2m.lean.js new file mode 100644 index 0000000..2b484d5 --- /dev/null +++ b/assets/ja_api_mp_math_function.md.pJM1NJ2m.lean.js @@ -0,0 +1 @@ +import{_ as n,c as s,j as a,a as Q,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),T={name:"ja/api/mp_math/function.md"},e=t("",4),l={class:"tip custom-block github-alert"},h=a("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=t("",1),o=[p],m=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",null,"f"),a("mo",{stretchy:"false"},"("),a("mi",null,"x"),a("mo",null,","),a("mi",null,"y"),a("mo",null,","),a("mi",null,"z"),a("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=t("",1),u=[g],y=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"x"),a("mn",null,"0")]),a("mo",null,","),a("msub",null,[a("mi",null,"y"),a("mn",null,"0")]),a("mo",null,","),a("msub",null,[a("mi",null,"z"),a("mn",null,"0")]),a("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=t("",1),w=[_],x=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("mi",{mathvariant:"normal"},"∇"),a("mi",null,"f"),a("mo",{stretchy:"false"},"("),a("msub",null,[a("mi",null,"x"),a("mn",null,"0")]),a("mo",null,","),a("msub",null,[a("mi",null,"y"),a("mn",null,"0")]),a("mo",null,","),a("msub",null,[a("mi",null,"z"),a("mn",null,"0")]),a("mo",{stretchy:"false"},")"),a("mo",null,"="),a("mrow",{"data-mjx-texclass":"INNER"},[a("mo",{"data-mjx-texclass":"OPEN"},"("),a("mfrac",null,[a("mrow",null,[a("mi",null,"∂"),a("mi",null,"f")]),a("mrow",null,[a("mi",null,"∂"),a("mi",null,"x")])]),a("mo",null,","),a("mfrac",null,[a("mrow",null,[a("mi",null,"∂"),a("mi",null,"f")]),a("mrow",null,[a("mi",null,"∂"),a("mi",null,"y")])]),a("mo",null,","),a("mfrac",null,[a("mrow",null,[a("mi",null,"∂"),a("mi",null,"f")]),a("mrow",null,[a("mi",null,"∂"),a("mi",null,"z")])]),a("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=t("",13);function L(H,F,M,v,D,Z){return i(),s("div",null,[e,a("div",l,[h,a("p",null,[Q("已知一个函数"),a("mjx-container",r,[(i(),s("svg",d,o)),m]),Q("，则其在点"),a("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),a("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; 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diff --git a/assets/ja_api_mp_math_line.md.BUEG7Qno.lean.js b/assets/ja_api_mp_math_line.md.BUEG7Qno.lean.js deleted file mode 100644 index 572538c..0000000 --- a/assets/ja_api_mp_math_line.md.BUEG7Qno.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 F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default}; diff --git a/assets/ja_api_mp_math_line.md.BUEG7Qno.js b/assets/ja_api_mp_math_line.md.BbbGydDH.js similarity index 75% rename from assets/ja_api_mp_math_line.md.BUEG7Qno.js rename to assets/ja_api_mp_math_line.md.BbbGydDH.js index 58e0c20..984e8d0 100644 --- a/assets/ja_api_mp_math_line.md.BUEG7Qno.js +++ b/assets/ja_api_mp_math_line.md.BbbGydDH.js @@ -1,38 +1,8 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n(`

モジュール mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

説明: 三维空间中的直线。由一个点和一个方向向量确定。

引数:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 直线上的一点
-            direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
-        """
+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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),n={name:"ja/api/mp_math/line.md"},e=t(`
モジュール mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     self.point = point
     self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
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: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other (Line3): 另一条直线
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: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
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: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -46,91 +16,19 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other (Line3): 另一条直线
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(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            \`ValueError\`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
戻り値: Line3: 垂线
ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Line3\`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
戻り値: Point3: 点
ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([\`RealNumber\`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [\`Point3\`](./point#class-point3): 点
-        """
     return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
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: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
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: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
戻り値: bool: 是否共线
ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
戻り値: bool: 是否在直线上
ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 点
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
戻り値: bool: 是否共面
ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード または GitHubで表示
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -139,36 +37,12 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.z == 0:
         self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
戻り値: Line3: 直线
ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 ([\`Point3\`](./point#class-point3)): 点2
-        Returns:
-            [\`Line3\`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other (Line3): 另一条直线
戻り値: Line3 | Point3 | None: 交集
ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other (Line3): 另一条直线
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`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)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_line.md.BbbGydDH.lean.js b/assets/ja_api_mp_math_line.md.BbbGydDH.lean.js new file mode 100644 index 0000000..e30db9d --- /dev/null +++ b/assets/ja_api_mp_math_line.md.BbbGydDH.lean.js @@ -0,0 +1 @@ +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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),n={name:"ja/api/mp_math/line.md"},e=t("",106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_plane.md.DmM6KUUe.js b/assets/ja_api_mp_math_plane.md.BvT51o_C.js similarity index 85% rename from assets/ja_api_mp_math_plane.md.DmM6KUUe.js rename to assets/ja_api_mp_math_plane.md.BvT51o_C.js index 2759a9d..17c8542 100644 --- a/assets/ja_api_mp_math_plane.md.DmM6KUUe.js +++ b/assets/ja_api_mp_math_plane.md.BvT51o_C.js @@ -1,23 +1,8 @@ -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
-        """
+import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=t(`
モジュール mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     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)
@@ -28,67 +13,19 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
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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
-        """
+        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':
     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
-        """
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
`,16),R={class:"tip custom-block"},J=s("p",{class:"custom-block-title"},"TIP",-1),O=s("p",null,"计算两平面交线的一般步骤:",-1),$=s("ol",null,[s("li",null,"求两平面的法向量的叉乘得到方向向量")],-1),U={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},K={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.186ex"},xmlns:"http://www.w3.org/2000/svg",width:"11.937ex",height:"1.756ex",role:"img",focusable:"false",viewBox:"0 -694 5276 776","aria-hidden":"true"},W=t('',1),X=[W],Y=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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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':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -106,106 +43,36 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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
@@ -216,12 +83,5 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},h=t(`

モジュール mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

説明: 笛卡尔坐标系中的点。

引数:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (\`float\`): y 坐标
-            z (\`float\`): z 坐标
-        """
-    self.x = x
-    self.y = y
-    self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

説明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://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])

@overload

method self + other: Vector3 => Point3 ​

ソースコード または GitHubで表示
python
@overload
-def __add__(self, other: 'Vector3') -> 'Point3':
-    ...

@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: P + V -> P P + P -> 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 __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([\`Vector3\`](./vector#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

説明: 判断两个点是否相等。

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):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`bool\`](https://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 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

引数:

戻り値: Vector3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [\`Vector3\`](./vector#class-vector3) 中实现
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 新的向量
-        """
-    from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_point.md.Bj_wyaCj.lean.js b/assets/ja_api_mp_math_point.md.Bj_wyaCj.lean.js deleted file mode 100644 index 891c12b..0000000 --- a/assets/ja_api_mp_math_point.md.Bj_wyaCj.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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},h=t("",39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_point.md.CevhXWsh.js b/assets/ja_api_mp_math_point.md.CevhXWsh.js new file mode 100644 index 0000000..242c659 --- /dev/null +++ b/assets/ja_api_mp_math_point.md.CevhXWsh.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),e={name:"ja/api/mp_math/point.md"},h=t('

モジュール mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

説明: 笛卡尔坐标系中的点。

引数:

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

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

説明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

@overload

method self + other: Vector3 => Point3 ​

ソースコード または GitHubで表示
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Point3':\n    ...

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

説明: P + V -> P P + P -> 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 __add__(self, other):\n    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

説明: 判断两个点是否相等。

引数:

戻り値: bool: 是否相等

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

method self - other: Point3 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

引数:

戻り値: Vector3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':\n    from .vector import Vector3\n    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
',39),n=[h];function l(p,o,k,r,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{c as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_point.md.CevhXWsh.lean.js b/assets/ja_api_mp_math_point.md.CevhXWsh.lean.js new file mode 100644 index 0000000..7d888f8 --- /dev/null +++ b/assets/ja_api_mp_math_point.md.CevhXWsh.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),e={name:"ja/api/mp_math/point.md"},h=t("",39),n=[h];function l(p,o,k,r,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{c as __pageData,y as default}; diff --git a/assets/ja_api_mp_math_segment.md.hBKUntDs.js b/assets/ja_api_mp_math_segment.md.DZAkmIjJ.js similarity index 83% rename from assets/ja_api_mp_math_segment.md.hBKUntDs.js rename to assets/ja_api_mp_math_segment.md.DZAkmIjJ.js index 38632aa..c290789 100644 --- a/assets/ja_api_mp_math_segment.md.hBKUntDs.js +++ b/assets/ja_api_mp_math_segment.md.DZAkmIjJ.js @@ -1,10 +1,4 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},p=n(`

モジュール mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

説明: 三维空间中的线段。

引数:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 线段的一个端点
-            p2 ([\`Point3\`](./point#class-point3)): 线段的另一个端点
-        """
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),n={name:"ja/api/mp_math/segment.md"},h=t(`
モジュール mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
引数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -12,4 +6,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     '长度'
     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)
`,8),h=[p];function l(e,k,r,d,o,E){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const c=s(n,[["render",e]]);export{m as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_segment.md.DZAkmIjJ.lean.js b/assets/ja_api_mp_math_segment.md.DZAkmIjJ.lean.js new file mode 100644 index 0000000..18bf63a --- /dev/null +++ b/assets/ja_api_mp_math_segment.md.DZAkmIjJ.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),n={name:"ja/api/mp_math/segment.md"},h=t("",8),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const c=s(n,[["render",e]]);export{m as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_segment.md.hBKUntDs.lean.js b/assets/ja_api_mp_math_segment.md.hBKUntDs.lean.js deleted file mode 100644 index cbe9481..0000000 --- a/assets/ja_api_mp_math_segment.md.hBKUntDs.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 F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,o,E){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_utils.md.DdrbPY-j.js b/assets/ja_api_mp_math_utils.md.Bk8MHgOd.js similarity index 81% rename from assets/ja_api_mp_math_utils.md.DdrbPY-j.js rename to assets/ja_api_mp_math_utils.md.Bk8MHgOd.js index 339fac2..6d437d7 100644 --- a/assets/ja_api_mp_math_utils.md.DdrbPY-j.js +++ b/assets/ja_api_mp_math_utils.md.Bk8MHgOd.js @@ -1,20 +1,5 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),n={name:"ja/api/mp_math/utils.md"},l=t(`

モジュール mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

説明: 区间限定函数

引数:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

戻り値: float: 限定在区间内的值

ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (\`float\`): 最小值
-        max_ (\`float\`): 最大值
-
-    Returns:
-        \`float\`: 限定在区间内的值
-    """
+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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},n=t(`
モジュール mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
引数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
戻り値: float: 限定在区间内的值
ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
     return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
引数:
ソースコード または GitHubで表示
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value
method __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -28,42 +13,16 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
             self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード または GitHubで表示
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード または GitHubで表示
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
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(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (\`float\`): 数2
-        epsilon (\`float\`): 误差
-    Returns:
-        [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[n];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{E as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_utils.md.Bk8MHgOd.lean.js b/assets/ja_api_mp_math_utils.md.Bk8MHgOd.lean.js new file mode 100644 index 0000000..d0a5feb --- /dev/null +++ b/assets/ja_api_mp_math_utils.md.Bk8MHgOd.lean.js @@ -0,0 +1 @@ +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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},n=t("",38),h=[n];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{E as __pageData,c as default}; diff --git a/assets/ja_api_mp_math_utils.md.DdrbPY-j.lean.js b/assets/ja_api_mp_math_utils.md.DdrbPY-j.lean.js deleted file mode 100644 index 935a7fb..0000000 --- a/assets/ja_api_mp_math_utils.md.DdrbPY-j.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 F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),n={name:"ja/api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default}; diff --git a/assets/ja_api_mp_math_vector.md.DuAJ8ZJo.js b/assets/ja_api_mp_math_vector.md.DuAJ8ZJo.js deleted file mode 100644 index f7cb615..0000000 --- a/assets/ja_api_mp_math_vector.md.DuAJ8ZJo.js +++ /dev/null @@ -1,176 +0,0 @@ -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":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),l={name:"ja/api/mp_math/vector.md"},e=a('

モジュール mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

説明: 3维向量

引数:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):\n    """\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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モジュール mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

説明: 3维向量

引数:

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

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

説明: 判断两个向量是否近似相等。

引数:

戻り値: bool: 是否近似相等

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

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

説明: 计算两个向量之间的夹角。

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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':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

説明: 向量积 叉乘：v1 x v2 -> v3

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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':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

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

説明: 判断两个向量是否近似平行。

引数:

戻り値: bool: 是否近似平行

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

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

説明: 判断两个向量是否平行。

引数:

戻り値: bool: 是否平行

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

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

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

@property

method np_array(self) -> np.ndarray ​

戻り値: np.ndarray: numpy数组

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

@property

method length(self) -> float ​

説明: 向量的模。

戻り値: float: 模

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

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

戻り値: Vector3: 单位向量

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

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

説明: V + P -> P

V + V -> V

引数:

戻り値: Vector3 | Point3: 新的向量或点

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

method __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):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

引数:

戻り値: Point3: 新的点

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

@overload

method self - other: Vector3 => Vector3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

method self - other ​

説明: V - P -> P

V - V -> V

引数:

戻り値: Vector3 | Point3: 新的向量

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

method self - other: Point3 ​

説明: P - V -> P

引数:

戻り値: Point3: 新的点

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

@overload

method self * other: Vector3 => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

引数:

戻り値: Vector3: 数组运算结果

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

method self * other: RealNumber => Vector3 ​

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

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

引数:

戻り値: float: 点乘结果

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

method self / other: RealNumber => Vector3 ​

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

method - self => Vector3 ​

説明: 取负。

戻り値: Vector3: 负向量

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

var zero_vector3 ​

  • 説明: 零向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • タイプ: Vector3

  • デフォルト: Vector3(0, 0, 1)

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y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),n={name:"ja/api/presets/model/index.md"},h=t(`

モジュール mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

説明: 生成球体上的点集。

引数:

  • radius:
  • density:

戻り値: List[Point3]: 球体上的点集。

ソースコード または GitHubで表示
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),h={name:"ja/api/presets/model/index.md"},n=t(`
モジュール mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -15,4 +7,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     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)]
`,10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[n];function e(p,k,r,d,E,o){return a(),i("div",null,l)}const c=s(h,[["render",e]]);export{y as __pageData,c as default}; diff --git a/assets/ja_api_presets_model_index.md.BqEjZ7IY.lean.js b/assets/ja_api_presets_model_index.md.wZZUhvvV.lean.js similarity index 63% rename from assets/ja_api_presets_model_index.md.BqEjZ7IY.lean.js rename to assets/ja_api_presets_model_index.md.wZZUhvvV.lean.js index 8d2ea37..35693d3 100644 --- a/assets/ja_api_presets_model_index.md.BqEjZ7IY.lean.js +++ b/assets/ja_api_presets_model_index.md.wZZUhvvV.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),n={name:"ja/api/presets/model/index.md"},h=t("",10),l=[h];function p(e,k,r,d,E,o){return 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var(--vp-c-yellow-1);--vp-c-warning-2: var(--vp-c-yellow-2);--vp-c-warning-3: var(--vp-c-yellow-3);--vp-c-warning-soft: var(--vp-c-yellow-soft);--vp-c-danger-1: var(--vp-c-red-1);--vp-c-danger-2: var(--vp-c-red-2);--vp-c-danger-3: var(--vp-c-red-3);--vp-c-danger-soft: var(--vp-c-red-soft);--vp-c-caution-1: var(--vp-c-red-1);--vp-c-caution-2: var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, "Menlo", "Monaco", "Consolas", "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root:where(:lang(zh)){--vp-font-family-base: "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: var(--vp-c-text-1);--vp-custom-block-warning-bg: var(--vp-c-warning-soft);--vp-custom-block-warning-code-bg: var(--vp-c-warning-soft);--vp-custom-block-danger-border: transparent;--vp-custom-block-danger-text: var(--vp-c-text-1);--vp-custom-block-danger-bg: var(--vp-c-danger-soft);--vp-custom-block-danger-code-bg: var(--vp-c-danger-soft);--vp-custom-block-caution-border: transparent;--vp-custom-block-caution-text: var(--vp-c-text-1);--vp-custom-block-caution-bg: var(--vp-c-caution-soft);--vp-custom-block-caution-code-bg: var(--vp-c-caution-soft);--vp-custom-block-details-border: var(--vp-custom-block-info-border);--vp-custom-block-details-text: var(--vp-custom-block-info-text);--vp-custom-block-details-bg: var(--vp-custom-block-info-bg);--vp-custom-block-details-code-bg: var(--vp-custom-block-info-code-bg)}:root{--vp-input-border-color: var(--vp-c-border);--vp-input-bg-color: var(--vp-c-bg-alt);--vp-input-switch-bg-color: var(--vp-c-default-soft)}:root{--vp-nav-height: 64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: var(--vp-c-bg);--vp-local-search-result-bg: var(--vp-c-bg);--vp-local-search-result-border: var(--vp-c-divider);--vp-local-search-result-selected-bg: 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transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: 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m=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),e={name:"zht/api/mp_math/angle.md"},n=t('

模組 mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

説明: 任意角度。

變數説明:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):\n    if is_radian:\n        self.radian = value\n    else:\n        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

説明: 余角：两角的和为90°。

返回: 余角

源碼 或 於GitHub上查看
python
@property\ndef complementary(self) -> 'AnyAngle':\n    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

説明: 补角：两角的和为180°。

返回: 补角

源碼 或 於GitHub上查看
python
@property\ndef supplementary(self) -> 'AnyAngle':\n    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

説明: 角度。

返回: 弧度

源碼 或 於GitHub上查看
python
@property\ndef degree(self) -> float:\n    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

説明: 最小正角。

返回: 最小正角度

源碼 或 於GitHub上查看
python
@property\ndef minimum_positive(self) -> 'AnyAngle':\n    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

説明: 最大负角。

返回: 最大负角度

源碼 或 於GitHub上查看
python
@property\ndef maximum_negative(self) -> 'AnyAngle':\n    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

説明: 正弦值。

返回: 正弦值

源碼 或 於GitHub上查看
python
@property\ndef sin(self) -> float:\n    return math.sin(self.radian)

@property

method cos(self) -> float ​

説明: 余弦值。

返回: 余弦值

源碼 或 於GitHub上查看
python
@property\ndef cos(self) -> float:\n    return math.cos(self.radian)

@property

method tan(self) -> float ​

説明: 正切值。

返回: 正切值

源碼 或 於GitHub上查看
python
@property\ndef tan(self) -> float:\n    return math.tan(self.radian)

@property

method cot(self) -> float ​

説明: 余切值。

返回: 余切值

源碼 或 於GitHub上查看
python
@property\ndef cot(self) -> float:\n    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

説明: 正割值。

返回: 正割值

源碼 或 於GitHub上查看
python
@property\ndef sec(self) -> float:\n    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

説明: 余割值。

返回: 余割值

源碼 或 於GitHub上查看
python
@property\ndef csc(self) -> float:\n    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':\n    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

源碼 或 於GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':\n    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

源碼 或 於GitHub上查看
python
def __truediv__(self, other):\n    if isinstance(other, AnyAngle):\n        return self.radian / other.radian\n    return AnyAngle(self.radian / other, is_radian=True)
',80),h=[n];function l(p,k,r,o,d,g){return i(),a("div",null,h)}const c=s(e,[["render",l]]);export{m as __pageData,c as default}; diff --git a/assets/zht_api_mp_math_angle.md.CBKEZciJ.lean.js b/assets/zht_api_mp_math_angle.md.CBKEZciJ.lean.js new file mode 100644 index 0000000..811c48a --- /dev/null +++ b/assets/zht_api_mp_math_angle.md.CBKEZciJ.lean.js @@ -0,0 +1 @@ +import{_ as s,c as a,o as i,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),e={name:"zht/api/mp_math/angle.md"},n=t("",80),h=[n];function l(p,k,r,o,d,g){return i(),a("div",null,h)}const c=s(e,[["render",l]]);export{m as __pageData,c as default}; diff --git a/assets/zht_api_mp_math_angle.md.mmecNIJM.js b/assets/zht_api_mp_math_angle.md.mmecNIJM.js deleted file mode 100644 index 51d85ef..0000000 --- a/assets/zht_api_mp_math_angle.md.mmecNIJM.js +++ /dev/null @@ -1,99 +0,0 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n(`

模組 mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

説明: 任意角度。

變數説明:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
-    if is_radian:
-        self.radian = value
-    else:
-        self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

説明: 余角：两角的和为90°。

返回: 余角

源碼 或 於GitHub上查看
python
@property
-def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

説明: 补角：两角的和为180°。

返回: 补角

源碼 或 於GitHub上查看
python
@property
-def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

説明: 角度。

返回: 弧度

源碼 或 於GitHub上查看
python
@property
-def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
-    return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

説明: 最小正角。

返回: 最小正角度

源碼 或 於GitHub上查看
python
@property
-def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
-    return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

説明: 最大负角。

返回: 最大负角度

源碼 或 於GitHub上查看
python
@property
-def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

説明: 正弦值。

返回: 正弦值

源碼 或 於GitHub上查看
python
@property
-def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
-    return math.sin(self.radian)

@property

method cos(self) -> float ​

説明: 余弦值。

返回: 余弦值

源碼 或 於GitHub上查看
python
@property
-def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
-    return math.cos(self.radian)

@property

method tan(self) -> float ​

説明: 正切值。

返回: 正切值

源碼 或 於GitHub上查看
python
@property
-def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
-    return math.tan(self.radian)

@property

method cot(self) -> float ​

説明: 余切值。

返回: 余切值

源碼 或 於GitHub上查看
python
@property
-def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
-    return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

説明: 正割值。

返回: 正割值

源碼 或 於GitHub上查看
python
@property
-def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
-    return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

説明: 余割值。

返回: 余割值

源碼 或 於GitHub上查看
python
@property
-def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
-    return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)

method self * other: float => AnyAngle ​

源碼 或 於GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)

@overload

method self / other: float => AnyAngle ​

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

@overload

method self / other: AnyAngle => float ​

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

method self / other ​

源碼 或 於GitHub上查看
python
def __truediv__(self, other):
-    if isinstance(other, AnyAngle):
-        return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/zht_api_mp_math_angle.md.mmecNIJM.lean.js b/assets/zht_api_mp_math_angle.md.mmecNIJM.lean.js deleted file mode 100644 index a629079..0000000 --- a/assets/zht_api_mp_math_angle.md.mmecNIJM.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default}; diff --git a/assets/zht_api_mp_math_equation.md.B00IWO_d.js b/assets/zht_api_mp_math_equation.md.DckV9F7F.js similarity index 77% rename from assets/zht_api_mp_math_equation.md.B00IWO_d.js rename to assets/zht_api_mp_math_equation.md.DckV9F7F.js index 3ea7d70..d15aec4 100644 --- a/assets/zht_api_mp_math_equation.md.B00IWO_d.js +++ b/assets/zht_api_mp_math_equation.md.DckV9F7F.js @@ -1,44 +1,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n(`

模組 mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

説明: 曲线方程。

變數説明:

源碼 或 於GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([\`OneVarFunc\`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

説明: 计算曲线上的点。

變數説明:

  • *t:
  • 参数:

返回: 目标点

源碼 或 於GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

變數説明:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

返回: 偏导函数

抛出:

  • ValueError 无效变量类型
源碼 或 於GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -48,18 +18,10 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default}; + raise ValueError('Invalid var type')`,23),h=[l];function p(e,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",p]]);export{u as __pageData,o as default}; diff --git a/assets/zht_api_mp_math_equation.md.B00IWO_d.lean.js b/assets/zht_api_mp_math_equation.md.DckV9F7F.lean.js similarity index 65% rename from assets/zht_api_mp_math_equation.md.B00IWO_d.lean.js rename to assets/zht_api_mp_math_equation.md.DckV9F7F.lean.js index b4dd5c1..981b6ea 100644 --- a/assets/zht_api_mp_math_equation.md.B00IWO_d.lean.js +++ b/assets/zht_api_mp_math_equation.md.DckV9F7F.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default}; +import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n("",23),h=[l];function p(e,k,r,E,d,c){return a(),i("div",null,h)}const o=s(t,[["render",p]]);export{u as __pageData,o as default}; diff --git a/assets/zht_api_mp_math_function.md.BnUerglv.js b/assets/zht_api_mp_math_function.md.3Rru8vfk.js similarity index 82% rename from assets/zht_api_mp_math_function.md.BnUerglv.js rename to assets/zht_api_mp_math_function.md.3Rru8vfk.js index dea7319..654e2b0 100644 --- a/assets/zht_api_mp_math_function.md.BnUerglv.js +++ b/assets/zht_api_mp_math_function.md.3Rru8vfk.js @@ -1,16 +1,4 @@ -import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),e={name:"zht/api/mp_math/function.md"},Q=a('

模組 mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

説明: 计算三元函数在某点的梯度向量。

',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`

變數説明:

返回: 梯度

源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
+import{_ as n,c as s,j as t,a as Q,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),T={name:"zht/api/mp_math/function.md"},e=a('
模組 mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),l={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=a('',1),u=[g],y=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=a('',1),w=[_],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=a(`
變數説明:
返回: 梯度
源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -18,25 +6,7 @@ import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1Zp
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
源碼 或 於GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
+    return curried_func
`,13);function L(H,F,M,v,D,Z){return i(),s("div",null,[e,t("div",l,[h,t("p",null,[Q("已知一个函数"),t("mjx-container",r,[(i(),s("svg",d,o)),m]),Q("，则其在点"),t("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),t("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/zht_api_mp_math_function.md.3Rru8vfk.lean.js b/assets/zht_api_mp_math_function.md.3Rru8vfk.lean.js new file mode 100644 index 0000000..de59fd7 --- /dev/null +++ b/assets/zht_api_mp_math_function.md.3Rru8vfk.lean.js @@ -0,0 +1 @@ +import{_ as n,c as s,j as t,a as Q,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),T={name:"zht/api/mp_math/function.md"},e=a("",4),l={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},c={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},g=a("",1),u=[g],y=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},f={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},_=a("",1),w=[_],x=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),b=a("",13);function L(H,F,M,v,D,Z){return i(),s("div",null,[e,t("div",l,[h,t("p",null,[Q("已知一个函数"),t("mjx-container",r,[(i(),s("svg",d,o)),m]),Q("，则其在点"),t("mjx-container",k,[(i(),s("svg",c,u)),y]),Q("处的梯度向量为: "),t("mjx-container",E,[(i(),s("svg",f,w)),x])])]),b])}const A=n(T,[["render",L]]);export{V as __pageData,A as default}; diff --git a/assets/zht_api_mp_math_function.md.BnUerglv.lean.js b/assets/zht_api_mp_math_function.md.BnUerglv.lean.js deleted file mode 100644 index 39dd29d..0000000 --- a/assets/zht_api_mp_math_function.md.BnUerglv.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),e={name:"zht/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default}; diff --git a/assets/zht_api_mp_math_line.md.Dg3ji_dG.lean.js b/assets/zht_api_mp_math_line.md.Dg3ji_dG.lean.js deleted file mode 100644 index 62d797b..0000000 --- a/assets/zht_api_mp_math_line.md.Dg3ji_dG.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 F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default}; diff --git a/assets/zht_api_mp_math_line.md.Dg3ji_dG.js b/assets/zht_api_mp_math_line.md.DopGqzVZ.js similarity index 74% rename from assets/zht_api_mp_math_line.md.Dg3ji_dG.js rename to assets/zht_api_mp_math_line.md.DopGqzVZ.js index a358a97..f52d208 100644 --- a/assets/zht_api_mp_math_line.md.Dg3ji_dG.js +++ b/assets/zht_api_mp_math_line.md.DopGqzVZ.js @@ -1,38 +1,8 @@ -import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n(`

模組 mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

説明: 三维空间中的直线。由一个点和一个方向向量确定。

變數説明:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 直线上的一点
-            direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
-        """
+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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),n={name:"zht/api/mp_math/line.md"},e=t(`
模組 mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     self.point = point
     self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`AnyAngle\`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
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: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -46,91 +16,19 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other (Line3): 另一条直线
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Point3\`](./point#class-point3): 交点
-        Raises:
-            [\`ValueError\`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            \`ValueError\`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
返回: Line3: 垂线
源碼 或 於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 指定点
-        Returns:
-            [\`Line3\`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
返回: Point3: 点
源碼 或 於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([\`RealNumber\`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [\`Point3\`](./point#class-point3): 点
-        """
     return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源碼 或 於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
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: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
返回: bool: 是否共线
源碼 或 於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
返回: bool: 是否在直线上
源碼 或 於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([\`Point3\`](./point#class-point3)): 点
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
返回: bool: 是否共面
源碼 或 於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一
-        Returns:
-            [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼 或 於GitHub上查看
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -139,36 +37,12 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.z == 0:
         self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
返回: Line3: 直线
源碼 或 於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 点1
-            p2 ([\`Point3\`](./point#class-point3)): 点2
-        Returns:
-            [\`Line3\`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`Line3\`](./line#class-line3) | [\`Point3\`](./point#class-point3) | [\`None\`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([\`Line3\`](./line#class-line3)): 另一条直线
-        Returns:
-            [\`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)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_line.md.DopGqzVZ.lean.js b/assets/zht_api_mp_math_line.md.DopGqzVZ.lean.js new file mode 100644 index 0000000..d282918 --- /dev/null +++ b/assets/zht_api_mp_math_line.md.DopGqzVZ.lean.js @@ -0,0 +1 @@ +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.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),n={name:"zht/api/mp_math/line.md"},e=t("",106),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_plane.md.DHKntbKb.js b/assets/zht_api_mp_math_plane.md.OnI32y0z.js similarity index 85% rename from assets/zht_api_mp_math_plane.md.DHKntbKb.js rename to assets/zht_api_mp_math_plane.md.OnI32y0z.js index 3a597e9..d113dd4 100644 --- a/assets/zht_api_mp_math_plane.md.DHKntbKb.js +++ b/assets/zht_api_mp_math_plane.md.OnI32y0z.js @@ -1,23 +1,8 @@ -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
-        """
+import{_ as n,c as a,j as s,a as e,a4 as t,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Zs=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=t(`
模組 mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     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)
@@ -28,67 +13,19 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},k=s("p",{class:"custom-block-title"},"TIP",-1),r=s("p",null,"平面间夹角计算公式:",-1),o={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),g=[Q],c=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"n"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"n"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"n"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),T={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},m={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.025ex"},xmlns:"http://www.w3.org/2000/svg",width:"2.489ex",height:"1.532ex",role:"img",focusable:"false",viewBox:"0 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0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"d")])],-1),N=t(`
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
-    """
-        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
-        """
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
`,16),p={class:"tip custom-block"},r=s("p",{class:"custom-block-title"},"TIP",-1),o=s("p",null,"平面间夹角计算公式:",-1),k={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"22.011ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9729 2301","aria-hidden":"true"},Q=t('',1),T=[Q],g=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 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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':
     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
-        """
+        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':
     if self.normal.is_parallel(other.normal):
         raise ValueError('Planes are parallel and have no intersection.')
     direction = self.normal.cross(other.normal)
@@ -106,106 +43,36 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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
@@ -216,12 +83,5 @@ import{_ as l,c as a,j as s,a as n,a4 as t,o as i}from"./chunks/framework.DpC1Zp
         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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c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),e={name:"zht/api/mp_math/point.md"},h=t('

模組 mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

説明: 笛卡尔坐标系中的点。

變數説明:

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

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

説明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:\n    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])

@overload

method self + other: Vector3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload\ndef __add__(self, other: 'Vector3') -> 'Point3':\n    ...

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

説明: P + V -> P P + P -> P

變數説明:

返回: Point3: 新的点

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

method __eq__(self, other) ​

説明: 判断两个点是否相等。

變數説明:

返回: bool: 是否相等

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

method self - other: Point3 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

變數説明:

返回: Vector3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':\n    from .vector import Vector3\n    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
',39),n=[h];function l(p,o,k,r,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{c as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_point.md.DoQ35q26.lean.js b/assets/zht_api_mp_math_point.md.DoQ35q26.lean.js new file mode 100644 index 0000000..3a9146a --- /dev/null +++ b/assets/zht_api_mp_math_point.md.DoQ35q26.lean.js @@ -0,0 +1 @@ +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),e={name:"zht/api/mp_math/point.md"},h=t("",39),n=[h];function l(p,o,k,r,d,g){return a(),i("div",null,n)}const y=s(e,[["render",l]]);export{c as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_point.md.vFMEEeVu.js b/assets/zht_api_mp_math_point.md.vFMEEeVu.js deleted file mode 100644 index 7051d19..0000000 --- a/assets/zht_api_mp_math_point.md.vFMEEeVu.js +++ /dev/null @@ -1,52 +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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},h=t(`

模組 mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

説明: 笛卡尔坐标系中的点。

變數説明:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (\`float\`): y 坐标
-            z (\`float\`): z 坐标
-        """
-    self.x = x
-    self.y = y
-    self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

説明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-            epsilon ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [\`bool\`](https://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])

@overload

method self + other: Vector3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload
-def __add__(self, other: 'Vector3') -> 'Point3':
-    ...

@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: P + V -> P P + P -> P

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([\`Vector3\`](./vector#class-vector3) | [\`Point3\`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [\`Point3\`](./point#class-point3): 新的点
-        """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

説明: 判断两个点是否相等。

變數説明:

返回: bool: 是否相等

源碼 或 於GitHub上查看
python
def __eq__(self, other):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`bool\`](https://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 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

變數説明:

返回: Vector3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [\`Vector3\`](./vector#class-vector3) 中实现
-        Args:
-            other ([\`Point3\`](./point#class-point3)): 另一个点
-        Returns:
-            [\`Vector3\`](./vector#class-vector3): 新的向量
-        """
-    from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_point.md.vFMEEeVu.lean.js b/assets/zht_api_mp_math_point.md.vFMEEeVu.lean.js deleted file mode 100644 index 8ede03c..0000000 --- a/assets/zht_api_mp_math_point.md.vFMEEeVu.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.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},h=t("",39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default}; diff --git a/assets/zht_api_mp_math_segment.md.BuDHbwYP.js b/assets/zht_api_mp_math_segment.md.CqQitARa.js similarity index 86% rename from assets/zht_api_mp_math_segment.md.BuDHbwYP.js rename to assets/zht_api_mp_math_segment.md.CqQitARa.js index 91014cf..6775791 100644 --- a/assets/zht_api_mp_math_segment.md.BuDHbwYP.js +++ b/assets/zht_api_mp_math_segment.md.CqQitARa.js @@ -1,10 +1,4 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),n={name:"zht/api/mp_math/segment.md"},h=t(`

模組 mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

説明: 三维空间中的线段。

變數説明:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([\`Point3\`](./point#class-point3)): 线段的一个端点
-            p2 ([\`Point3\`](./point#class-point3)): 线段的另一个端点
-        """
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),n={name:"zht/api/mp_math/segment.md"},h=t(`
模組 mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
變數説明:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -12,4 +6,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     '长度'
     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)
`,8),p=[h];function l(e,k,r,d,o,E){return a(),i("div",null,p)}const c=s(n,[["render",l]]);export{F as __pageData,c as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const c=s(n,[["render",e]]);export{m as __pageData,c as default}; diff --git a/assets/zht_api_mp_math_segment.md.BuDHbwYP.lean.js b/assets/zht_api_mp_math_segment.md.CqQitARa.lean.js similarity index 53% rename from assets/zht_api_mp_math_segment.md.BuDHbwYP.lean.js rename to assets/zht_api_mp_math_segment.md.CqQitARa.lean.js index b18ade0..ce5442c 100644 --- a/assets/zht_api_mp_math_segment.md.BuDHbwYP.lean.js +++ b/assets/zht_api_mp_math_segment.md.CqQitARa.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),n={name:"zht/api/mp_math/segment.md"},h=t("",8),p=[h];function l(e,k,r,d,o,E){return a(),i("div",null,p)}const c=s(n,[["render",l]]);export{F as __pageData,c as default}; +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const m=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),n={name:"zht/api/mp_math/segment.md"},h=t("",8),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const c=s(n,[["render",e]]);export{m as __pageData,c as default}; diff --git a/assets/zht_api_mp_math_utils.md.DvxTZy5j.lean.js b/assets/zht_api_mp_math_utils.md.DvxTZy5j.lean.js deleted file mode 100644 index 24b504f..0000000 --- a/assets/zht_api_mp_math_utils.md.DvxTZy5j.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 F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),n={name:"zht/api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default}; diff --git a/assets/zht_api_mp_math_utils.md.DvxTZy5j.js b/assets/zht_api_mp_math_utils.md.itNFG1x8.js similarity index 81% rename from assets/zht_api_mp_math_utils.md.DvxTZy5j.js rename to assets/zht_api_mp_math_utils.md.itNFG1x8.js index 3c130cb..96667d8 100644 --- a/assets/zht_api_mp_math_utils.md.DvxTZy5j.js +++ b/assets/zht_api_mp_math_utils.md.itNFG1x8.js @@ -1,20 +1,5 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),n={name:"zht/api/mp_math/utils.md"},l=t(`

模組 mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

説明: 区间限定函数

變數説明:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

返回: float: 限定在区间内的值

源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (\`float\`): 最小值
-        max_ (\`float\`): 最大值
-
-    Returns:
-        \`float\`: 限定在区间内的值
-    """
+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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},n=t(`
模組 mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
變數説明:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value
method __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -28,42 +13,16 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
             self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼 或 於GitHub上查看
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (\`float\`): 数2
-        epsilon (\`float\`): 误差
-    Returns:
-        [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([\`bool\`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [\`str\`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[n];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{E as __pageData,c as default}; diff --git a/assets/zht_api_mp_math_utils.md.itNFG1x8.lean.js b/assets/zht_api_mp_math_utils.md.itNFG1x8.lean.js new file mode 100644 index 0000000..330d56b --- /dev/null +++ b/assets/zht_api_mp_math_utils.md.itNFG1x8.lean.js @@ -0,0 +1 @@ +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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},n=t("",38),h=[n];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{E as __pageData,c as default}; diff --git a/assets/zht_api_mp_math_vector.md.DoP7bI-7.js b/assets/zht_api_mp_math_vector.md.DoP7bI-7.js deleted file mode 100644 index d442ae0..0000000 --- a/assets/zht_api_mp_math_vector.md.DoP7bI-7.js +++ /dev/null @@ -1,176 +0,0 @@ -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":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),l={name:"zht/api/mp_math/vector.md"},e=a('

模組 mbcp.mp_math.vector ​

本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

説明: 3维向量

變數説明:

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

',16),h={class:"tip custom-block"},p=s("p",{class:"custom-block-title"},"TIP",-1),r=s("p",null,"向量夹角计算公式:",-1),o={tabindex:"0",class:"MathJax",jax:"SVG",display:"true",style:{direction:"ltr",display:"block","text-align":"center",margin:"1em 0",position:"relative"}},k={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-2.17ex"},xmlns:"http://www.w3.org/2000/svg",width:"21.491ex",height:"5.206ex",role:"img",focusable:"false",viewBox:"0 -1342 9499 2301","aria-hidden":"true"},d=a('',1),T=[d],Q=s("mjx-assistive-mml",{unselectable:"on",display:"block",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",overflow:"hidden",width:"100%"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[s("mi",null,"θ"),s("mo",null,"="),s("mi",null,"arccos"),s("mo",{"data-mjx-texclass":"NONE"},"⁡"),s("mo",{stretchy:"false"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"v"),s("mn",null,"1"),s("mo",null,"⋅"),s("mi",null,"v"),s("mn",null,"2")]),s("mrow",null,[s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"1"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mo",null,"⋅"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|"),s("mi",null,"v"),s("mn",null,"2"),s("mo",{"data-mjx-texclass":"ORD",stretchy:"false"},"|")])]),s("mo",{stretchy:"false"},")")])],-1),g=a(`

變數説明:

返回: AnyAngle: 夹角

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
-    """
-        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):\n    self.x = x\n    self.y = y\n    self.z = z

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

説明: 判断两个向量是否近似相等。

變數説明:

返回: bool: 是否近似相等

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

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

説明: 计算两个向量之间的夹角。

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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':\n    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)

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

説明: 向量积 叉乘：v1 x v2 -> v3

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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':\n    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)

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

説明: 判断两个向量是否近似平行。

變數説明:

返回: bool: 是否近似平行

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

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

説明: 判断两个向量是否平行。

變數説明:

返回: bool: 是否平行

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

method normalize(self) ​

説明: 将向量归一化。

自体归一化，不返回值。

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

@property

method np_array(self) -> np.ndarray ​

返回: np.ndarray: numpy数组

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

@property

method length(self) -> float ​

説明: 向量的模。

返回: float: 模

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

@property

method unit(self) -> Vector3 ​

説明: 获取该向量的单位向量。

返回: Vector3: 单位向量

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

method __abs__(self) ​

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

@overload

method self + other: Vector3 => Vector3 ​

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

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

説明: V + P -> P

V + V -> V

變數説明:

返回: Vector3 | Point3: 新的向量或点

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

method __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):\n    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)

method self + other: Point3 => Point3 ​

説明: P + V -> P

别去点那边实现了。

變數説明:

返回: Point3: 新的点

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

@overload

method self - other: Vector3 => Vector3 ​

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

@overload

method self - other: Point3 => Point3 ​

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

method self - other ​

説明: V - P -> P

V - V -> V

變數説明:

返回: Vector3 | Point3: 新的向量

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

method self - other: Point3 ​

説明: P - V -> P

變數説明:

返回: Point3: 新的点

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

@overload

method self * other: Vector3 => Vector3 ​

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

@overload

method self * other: RealNumber => Vector3 ​

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

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

説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。

變數説明:

返回: Vector3: 数组运算结果

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

method self * other: RealNumber => Vector3 ​

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

method self @ other: Vector3 => RealNumber ​

説明: 点乘。

變數説明:

返回: float: 点乘结果

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

method self / other: RealNumber => Vector3 ​

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

method - self => Vector3 ​

説明: 取负。

返回: Vector3: 负向量

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

var zero_vector3 ​

  • 説明: 零向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 0)

var x_axis ​

  • 説明: x轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(1, 0, 0)

var y_axis ​

  • 説明: y轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 1, 0)

var z_axis ​

  • 説明: z轴单位向量

  • 類型: Vector3

  • 默認值: Vector3(0, 0, 1)

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B(w,A,L,M,Z,q){return i(),t("div",null,[h,s("div",n,[r,p,s("mjx-container",o,[(i(),t("svg",d,T)),Q])]),g,s("div",m,[c,y,s("mjx-container",E,[(i(),t("svg",u,f)),F]),C,s("mjx-container",_,[(i(),t("svg",v,H)),x])]),D])}const G=e(l,[["render",B]]);export{z as __pageData,G as default}; diff --git a/assets/zht_api_presets_model_index.md.CyrJscBT.js b/assets/zht_api_presets_model_index.md.BfmFWGa-.js similarity index 87% rename from assets/zht_api_presets_model_index.md.CyrJscBT.js rename to assets/zht_api_presets_model_index.md.BfmFWGa-.js index fd35ac1..d25fe44 100644 --- a/assets/zht_api_presets_model_index.md.CyrJscBT.js +++ b/assets/zht_api_presets_model_index.md.BfmFWGa-.js @@ -1,13 +1,5 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t(`

模組 mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

説明: 生成球体上的点集。

變數説明:

  • radius:
  • density:

返回: List[Point3]: 球体上的点集。

源碼 或 於GitHub上查看
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),h={name:"zht/api/presets/model/index.md"},n=t(`
模組 mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -15,4 +7,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     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)]
`,10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[n];function e(p,k,r,d,E,o){return a(),i("div",null,l)}const c=s(h,[["render",e]]);export{y as __pageData,c as default}; diff --git a/assets/zht_api_presets_model_index.md.CyrJscBT.lean.js b/assets/zht_api_presets_model_index.md.BfmFWGa-.lean.js similarity index 63% rename from assets/zht_api_presets_model_index.md.CyrJscBT.lean.js rename to assets/zht_api_presets_model_index.md.BfmFWGa-.lean.js index 443be63..cc75e16 100644 --- a/assets/zht_api_presets_model_index.md.CyrJscBT.lean.js +++ b/assets/zht_api_presets_model_index.md.BfmFWGa-.lean.js @@ -1 +1 @@ -import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t("",10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default}; +import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),h={name:"zht/api/presets/model/index.md"},n=t("",10),l=[n];function e(p,k,r,d,E,o){return a(),i("div",null,l)}const c=s(h,[["render",e]]);export{y as __pageData,c as default}; diff --git a/demo/best-practice.html b/demo/best-practice.html index d87dbd3..e8a675a 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 51356f2..c323ea1 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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English
日本語
繁體中文

Appearance

demo ​

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- + \ No newline at end of file diff --git a/en/api/index.html b/en/api/index.html index 98a8f2f..f62b6eb 100644 --- a/en/api/index.html +++ b/en/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

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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 9943c31..b8a677f 100644 --- a/en/api/mp_math/angle.html +++ b/en/api/mp_math/angle.html @@ -6,12 +6,12 @@ mbcp.mp_math.angle | MBCP docs - + - - + + - + @@ -19,92 +19,31 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

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日本語
繁體中文

Appearance

Module mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

Description: 任意角度。

Arguments:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
     if is_radian:
         self.radian = value
     else:
         self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

Description: 余角：两角的和为90°。

Return: 余角

Source code or View on GitHub
python
@property
 def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
     return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

Description: 补角：两角的和为180°。

Return: 补角

Source code or View on GitHub
python
@property
 def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
     return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

Description: 角度。

Return: 弧度

Source code or View on GitHub
python
@property
 def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
     return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

Description: 最小正角。

Return: 最小正角度

Source code or View on GitHub
python
@property
 def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
     return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

Description: 最大负角。

Return: 最大负角度

Source code or View on GitHub
python
@property
 def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
     return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

Description: 正弦值。

Return: 正弦值

Source code or View on GitHub
python
@property
 def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
     return math.sin(self.radian)

@property

method cos(self) -> float ​

Description: 余弦值。

Return: 余弦值

Source code or View on GitHub
python
@property
 def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
     return math.cos(self.radian)

@property

method tan(self) -> float ​

Description: 正切值。

Return: 正切值

Source code or View on GitHub
python
@property
 def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
     return math.tan(self.radian)

@property

method cot(self) -> float ​

Description: 余切值。

Return: 余切值

Source code or View on GitHub
python
@property
 def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
     return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

Description: 正割值。

Return: 正割值

Source code or View on GitHub
python
@property
 def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
     return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

Description: 余割值。

Return: 余割值

Source code or View on GitHub
python
@property
 def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
     return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
     return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
@@ -117,7 +56,7 @@
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

Documentation built with VitePress | API references generated by litedoc

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

- + \ No newline at end of file diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html index 2b528ed..e87e739 100644 --- a/en/api/mp_math/const.html +++ b/en/api/mp_math/const.html @@ -6,10 +6,10 @@ mbcp.mp_math.const | MBCP docs - + - - + + @@ -19,7 +19,7 @@
MBCP docs

English

简体中文
日本語
繁體中文

English

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繁體中文

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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 ab5a958..9bd0f4a 100644 --- a/en/api/mp_math/equation.html +++ b/en/api/mp_math/equation.html @@ -6,12 +6,12 @@ mbcp.mp_math.equation | MBCP docs - + - - + + - + @@ -19,46 +19,16 @@
MBCP docs

English

简体中文
日本語
繁體中文

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Module mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

Description: 曲线方程。

Arguments:

Source code or View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

Description: 计算曲线上的点。

Arguments:

  • *t:
  • 参数:

Return: 目标点

Source code or View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

Arguments:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

Return: 偏导函数

Raises:

  • ValueError 无效变量类型
Source code or View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -68,14 +38,6 @@
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
@@ -83,7 +45,7 @@
         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/en/api/mp_math/function.html b/en/api/mp_math/function.html index 9e82275..cf6df05 100644 --- a/en/api/mp_math/function.html +++ b/en/api/mp_math/function.html @@ -6,12 +6,12 @@ mbcp.mp_math.function | MBCP docs - + - - + + - + @@ -19,18 +19,6 @@
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Module mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

Description: 计算三元函数在某点的梯度向量。

TIP

已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)

Arguments:

Return: 梯度

Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\nabla f(x_0, y_0, z_0) = \\left(\\frac{\\partial f}{\\partial x}, \\frac{\\partial f}{\\partial y}, \\frac{\\partial f}{\\partial z}\\right)$
-    Args:
-        func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([`Point3`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -38,29 +26,11 @@
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
Source code or View on GitHub
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([`Var`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        ```python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        ```
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func

Documentation built with VitePress | API references generated by litedoc

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- + \ No newline at end of file diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html index 5ace721..acd0664 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 @@
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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 e959851..1eb64e2 100644 --- a/en/api/mp_math/line.html +++ b/en/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP docs - + - - + + - + @@ -19,40 +19,10 @@
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Module mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

Description: 三维空间中的直线。由一个点和一个方向向量确定。

Arguments:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([`Point3`](./point#class-point3)): 直线上的一点
-            direction ([`Vector3`](./vector#class-vector3)): 方向向量
-        """
     self.point = point
     self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​

Description: 判断两条直线是否近似相等。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

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

Description: 计算直线和直线之间的夹角。

Arguments:

  • other (Line3): 另一条直线

Return: AnyAngle: 夹角

Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`AnyAngle`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float ​

Description: 计算直线和直线或点之间的距离。

Arguments:

Return: float: 距离

Raises:

Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([`Line3`](./line#class-line3) | [`Point3`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -66,91 +36,19 @@
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')

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

Description: 计算两条直线的交点。

Arguments:

  • other (Line3): 另一条直线

Return: Point3: 交点

Raises:

Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Point3`](./point#class-point3): 交点
-        Raises:
-            [`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            `ValueError`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3 ​

Description: 计算直线经过指定点p的垂线。

Arguments:

Return: Line3: 垂线

Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([`Point3`](./point#class-point3)): 指定点
-        Returns:
-            [`Line3`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3 ​

Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。

Arguments:

Return: Point3: 点

Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([`RealNumber`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [`Point3`](./point#class-point3): 点
-        """
     return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​

Description: 获取直线的参数方程。

Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​

Description: 判断两条直线是否近似平行。

Arguments:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

Return: bool: 是否近似平行

Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool ​

Description: 判断两条直线是否平行。

Arguments:

Return: bool: 是否平行

Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool ​

Description: 判断两条直线是否共线。

Arguments:

Return: bool: 是否共线

Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool ​

Description: 判断点是否在直线上。

Arguments:

Return: bool: 是否在直线上

Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([`Point3`](./point#class-point3)): 点
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool ​

Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

Arguments:

Return: bool: 是否共面

Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self) ​

Description: 简化直线方程，等价相等。 自体简化，不返回值。

按照可行性一次对x y z 化 0 处理，并对向量单位化

Source code or View on GitHub
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -159,40 +57,16 @@
     if self.direction.z == 0:
         self.point.z = 0

@classmethod

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

Description: 工厂函数 由两点构造直线。

Arguments:

Return: Line3: 直线

Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 点1
-            p2 ([`Point3`](./point#class-point3)): 点2
-        Returns:
-            [`Line3`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)

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

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

Arguments:

  • other (Line3): 另一条直线

Return: Line3 | Point3 | None: 交集

Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

Description: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

Arguments:

  • other (Line3): 另一条直线

Return: bool: 是否等价

Source code or View on GitHub
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`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 a06c404..3652b19 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 @@
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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 2f8303e..b245a1d 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 - + - - + + - + @@ -19,25 +19,10 @@
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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)
@@ -49,66 +34,18 @@
         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。

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:
-            [`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。

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:
-            [`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)
@@ -126,106 +63,36 @@
         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
@@ -236,16 +103,9 @@
         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)

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 722dae2..7324d34 100644 --- a/en/api/mp_math/point.html +++ b/en/api/mp_math/point.html @@ -6,12 +6,12 @@ mbcp.mp_math.point | MBCP docs - + - - + + - + @@ -19,58 +19,19 @@
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Module mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

Description: 笛卡尔坐标系中的点。

Arguments:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([`float`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (`float`): y 坐标
-            z (`float`): z 坐标
-        """
     self.x = x
     self.y = y
     self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

Description: 判断两个点是否近似相等。

Arguments:

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://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])

@overload

method self + other: Vector3 => Point3 ​

Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
     ...

@overload

method self + other: Point3 => Point3 ​

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

method self + other ​

Description: P + V -> P P + P -> P

Arguments:

Return: Point3: 新的点

Source code or View on GitHub
python
def __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([`Vector3`](./vector#class-vector3) | [`Point3`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [`Point3`](./point#class-point3): 新的点
-        """
     return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

Description: 判断两个点是否相等。

Arguments:

Return: bool: 是否相等

Source code or View on GitHub
python
def __eq__(self, other):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`bool`](https://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 => Vector3 ​

Description: P - P -> V

P - V -> P 已在 Vector3 中实现

Arguments:

Return: Vector3: 新的向量

Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [`Vector3`](./vector#class-vector3) 中实现
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`Vector3`](./vector#class-vector3): 新的向量
-        """
     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 e8e7451..03a5d14 100644 --- a/en/api/mp_math/segment.html +++ b/en/api/mp_math/segment.html @@ -6,12 +6,12 @@ mbcp.mp_math.segment | MBCP docs - + - - + + - + @@ -19,12 +19,6 @@
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Module mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

Description: 三维空间中的线段。

Arguments:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 线段的一个端点
-            p2 ([`Point3`](./point#class-point3)): 线段的另一个端点
-        """
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -33,7 +27,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

Documentation built with VitePress | API references generated by litedoc

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

- + \ No newline at end of file diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html index c1c5bdb..ba3c5f6 100644 --- a/en/api/mp_math/utils.html +++ b/en/api/mp_math/utils.html @@ -6,12 +6,12 @@ mbcp.mp_math.utils | MBCP docs - + - - + + - + @@ -19,22 +19,7 @@
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Module mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

Description: 区间限定函数

Arguments:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

Return: float: 限定在区间内的值

Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (`float`): 最小值
-        max_ (`float`): 最大值
-
-    Returns:
-        `float`: 限定在区间内的值
-    """
     return max(min(x, max_), min_)

class Approx ​

method __init__(self, value: RealNumber) ​

Description: 用于近似比较对象

Arguments:

Source code or View on GitHub
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value

method __eq__(self, other) ​

Source code or View on GitHub
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -48,46 +33,20 @@
             self.raise_type_error(other)

method raise_type_error(self, other) ​

Source code or View on GitHub
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')

method __ne__(self, other) ​

Source code or View on GitHub
python
def __ne__(self, other):
     return not self.__eq__(other)

func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​

Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。

Arguments:

  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差

Return: bool: 是否近似相等

Source code or View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (`float`): 数2
-        epsilon (`float`): 误差
-    Returns:
-        [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon

func sign(x: float, only_neg: bool = False) -> str ​

Description: 获取数的符号。

Arguments:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

Return: str: 符号 + - ""

Source code or View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''

func sign_format(x: float, only_neg: bool = False) -> str ​

Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""

Arguments:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

Return: str: 符号 + - ""

Source code or View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         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 f742b9f..a61136e 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 - + - - + + - + @@ -19,164 +19,47 @@
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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。

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 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 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:
@@ -185,13 +68,6 @@
     ...

@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)):
@@ -199,22 +75,10 @@
     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)

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 b108c16..66f46d8 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 8d97d03..7f1ca14 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 d326eb5..adc9d63 100644 --- a/en/api/presets/model/index.html +++ b/en/api/presets/model/index.html @@ -6,12 +6,12 @@ mbcp.presets.model | MBCP docs - + - - + + - + @@ -20,14 +20,6 @@
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Module mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

Description: 生成球体上的点集。

Arguments:

  • radius:
  • density:

Return: List[Point3]: 球体上的点集。

Source code or View on GitHub
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -36,7 +28,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

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开始不了一点 ​

∫12x111

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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
MBCP logo
🛠️

Easy to use

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

📦

Integrated

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

🧊

Rich presets

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

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- + \ No newline at end of file diff --git a/en/refer/index.html b/en/refer/index.html index 5efc36c..f5fe29b 100644 --- a/en/refer/index.html +++ b/en/refer/index.html @@ -6,10 +6,10 @@ Reference | MBCP docs - + - - + + @@ -19,7 +19,7 @@
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Documentation built with VitePress | API references generated by litedoc

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

- + \ No newline at end of file diff --git a/guide/index.html b/guide/index.html index 30ea9ae..ea7f049 100644 --- a/guide/index.html +++ b/guide/index.html @@ -6,10 +6,10 @@ 快速开始 | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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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

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

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diff --git a/index.html b/index.html index 5c821a1..07fe391 100644 --- a/index.html +++ b/index.html @@ -6,10 +6,10 @@ MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

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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
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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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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 1a8e439..76c5140 100644 --- a/ja/api/mp_math/angle.html +++ b/ja/api/mp_math/angle.html @@ -6,12 +6,12 @@ mbcp.mp_math.angle | MBCP ドキュメント - + - - + + - + @@ -19,92 +19,31 @@
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モジュール mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

説明: 任意角度。

引数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
     if is_radian:
         self.radian = value
     else:
         self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

説明: 余角：两角的和为90°。

戻り値: 余角

ソースコード または GitHubで表示
python
@property
 def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
     return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

説明: 补角：两角的和为180°。

戻り値: 补角

ソースコード または GitHubで表示
python
@property
 def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
     return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

説明: 角度。

戻り値: 弧度

ソースコード または GitHubで表示
python
@property
 def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
     return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

説明: 最小正角。

戻り値: 最小正角度

ソースコード または GitHubで表示
python
@property
 def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
     return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

説明: 最大负角。

戻り値: 最大负角度

ソースコード または GitHubで表示
python
@property
 def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
     return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

説明: 正弦值。

戻り値: 正弦值

ソースコード または GitHubで表示
python
@property
 def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
     return math.sin(self.radian)

@property

method cos(self) -> float ​

説明: 余弦值。

戻り値: 余弦值

ソースコード または GitHubで表示
python
@property
 def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
     return math.cos(self.radian)

@property

method tan(self) -> float ​

説明: 正切值。

戻り値: 正切值

ソースコード または GitHubで表示
python
@property
 def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
     return math.tan(self.radian)

@property

method cot(self) -> float ​

説明: 余切值。

戻り値: 余切值

ソースコード または GitHubで表示
python
@property
 def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
     return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

説明: 正割值。

戻り値: 正割值

ソースコード または GitHubで表示
python
@property
 def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
     return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

説明: 余割值。

戻り値: 余割值

ソースコード または GitHubで表示
python
@property
 def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
     return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
     return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
@@ -117,7 +56,7 @@
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

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

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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 a5d82e7..be9bc04 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

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- + \ No newline at end of file diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html index 6011cf6..248d038 100644 --- a/ja/api/mp_math/equation.html +++ b/ja/api/mp_math/equation.html @@ -6,12 +6,12 @@ mbcp.mp_math.equation | MBCP ドキュメント - + - - + + - + @@ -19,46 +19,16 @@
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モジュール mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

説明: 曲线方程。

引数:

ソースコード または GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

説明: 计算曲线上的点。

引数:

  • *t:
  • 参数:

戻り値: 目标点

ソースコード または GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

引数:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

戻り値: 偏导函数

例外:

  • ValueError 无效变量类型
ソースコード または GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -68,14 +38,6 @@
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
@@ -83,7 +45,7 @@
         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/ja/api/mp_math/function.html b/ja/api/mp_math/function.html index 7a56cd1..f63ad62 100644 --- a/ja/api/mp_math/function.html +++ b/ja/api/mp_math/function.html @@ -6,12 +6,12 @@ mbcp.mp_math.function | MBCP ドキュメント - + - - + + - + @@ -19,18 +19,6 @@
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モジュール mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

説明: 计算三元函数在某点的梯度向量。

TIP

已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)

引数:

戻り値: 梯度

ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\nabla f(x_0, y_0, z_0) = \\left(\\frac{\\partial f}{\\partial x}, \\frac{\\partial f}{\\partial y}, \\frac{\\partial f}{\\partial z}\\right)$
-    Args:
-        func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([`Point3`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -38,29 +26,11 @@
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
ソースコード または GitHubで表示
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([`Var`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        ```python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        ```
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func

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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：

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- + \ No newline at end of file diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html index edaccea..aef19d6 100644 --- a/ja/api/mp_math/line.html +++ b/ja/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP ドキュメント - + - - + + - + @@ -19,40 +19,10 @@
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モジュール mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

説明: 三维空间中的直线。由一个点和一个方向向量确定。

引数:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([`Point3`](./point#class-point3)): 直线上的一点
-            direction ([`Vector3`](./vector#class-vector3)): 方向向量
-        """
     self.point = point
     self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​

説明: 判断两条直线是否近似相等。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

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: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

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

説明: 计算直线和直线之间的夹角。

引数:

  • other (Line3): 另一条直线

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: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`AnyAngle`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float ​

説明: 计算直线和直线或点之间的距离。

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: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([`Line3`](./line#class-line3) | [`Point3`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -66,91 +36,19 @@
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')

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

説明: 计算两条直线的交点。

引数:

  • other (Line3): 另一条直线

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(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Point3`](./point#class-point3): 交点
-        Raises:
-            [`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            `ValueError`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3 ​

説明: 计算直线经过指定点p的垂线。

引数:

戻り値: Line3: 垂线

ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([`Point3`](./point#class-point3)): 指定点
-        Returns:
-            [`Line3`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3 ​

説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。

引数:

戻り値: Point3: 点

ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([`RealNumber`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [`Point3`](./point#class-point3): 点
-        """
     return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​

説明: 获取直线的参数方程。

戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​

説明: 判断两条直线是否近似平行。

引数:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

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: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool ​

説明: 判断两条直线是否平行。

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: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool ​

説明: 判断两条直线是否共线。

引数:

戻り値: bool: 是否共线

ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool ​

説明: 判断点是否在直线上。

引数:

戻り値: bool: 是否在直线上

ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([`Point3`](./point#class-point3)): 点
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool ​

説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

引数:

戻り値: bool: 是否共面

ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self) ​

説明: 简化直线方程，等价相等。 自体简化，不返回值。

按照可行性一次对x y z 化 0 处理，并对向量单位化

ソースコード または GitHubで表示
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -159,40 +57,16 @@
     if self.direction.z == 0:
         self.point.z = 0

@classmethod

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

説明: 工厂函数 由两点构造直线。

引数:

戻り値: Line3: 直线

ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 点1
-            p2 ([`Point3`](./point#class-point3)): 点2
-        Returns:
-            [`Line3`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)

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

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

引数:

  • other (Line3): 另一条直线

戻り値: Line3 | Point3 | None: 交集

ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

引数:

  • other (Line3): 另一条直线

戻り値: bool: 是否等价

ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`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)

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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

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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 b7bfdf0..d2e6d94 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 - + - - + + - + @@ -19,25 +19,10 @@
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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)
@@ -49,66 +34,18 @@
         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。

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:
-            [`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。

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:
-            [`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)
@@ -126,106 +63,36 @@
         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
@@ -236,16 +103,9 @@
         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)

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 ac35501..d16ca2a 100644 --- a/ja/api/mp_math/point.html +++ b/ja/api/mp_math/point.html @@ -6,12 +6,12 @@ mbcp.mp_math.point | MBCP ドキュメント - + - - + + - + @@ -19,58 +19,19 @@
MBCP ドキュメント

日本語

简体中文
English
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日本語

简体中文
English
繁體中文

Appearance

モジュール mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

説明: 笛卡尔坐标系中的点。

引数:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([`float`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (`float`): y 坐标
-            z (`float`): z 坐标
-        """
     self.x = x
     self.y = y
     self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

説明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://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])

@overload

method self + other: Vector3 => Point3 ​

ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
     ...

@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: P + V -> P P + P -> 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 __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([`Vector3`](./vector#class-vector3) | [`Point3`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [`Point3`](./point#class-point3): 新的点
-        """
     return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

説明: 判断两个点是否相等。

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):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`bool`](https://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 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

引数:

戻り値: Vector3: 新的向量

ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [`Vector3`](./vector#class-vector3) 中实现
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`Vector3`](./vector#class-vector3): 新的向量
-        """
     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 f5702e4..1db5d68 100644 --- a/ja/api/mp_math/segment.html +++ b/ja/api/mp_math/segment.html @@ -6,12 +6,12 @@ mbcp.mp_math.segment | MBCP ドキュメント - + - - + + - + @@ -19,12 +19,6 @@
MBCP ドキュメント

日本語

简体中文
English
繁體中文

日本語

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モジュール mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

説明: 三维空间中的线段。

引数:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 线段的一个端点
-            p2 ([`Point3`](./point#class-point3)): 线段的另一个端点
-        """
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -33,7 +27,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

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- + \ No newline at end of file diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html index 7923271..fe95f1a 100644 --- a/ja/api/mp_math/utils.html +++ b/ja/api/mp_math/utils.html @@ -6,12 +6,12 @@ mbcp.mp_math.utils | MBCP ドキュメント - + - - + + - + @@ -19,22 +19,7 @@
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モジュール mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

説明: 区间限定函数

引数:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

戻り値: float: 限定在区间内的值

ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (`float`): 最小值
-        max_ (`float`): 最大值
-
-    Returns:
-        `float`: 限定在区间内的值
-    """
     return max(min(x, max_), min_)

class Approx ​

method __init__(self, value: RealNumber) ​

説明: 用于近似比较对象

引数:

ソースコード または GitHubで表示
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value

method __eq__(self, other) ​

ソースコード または GitHubで表示
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -48,46 +33,20 @@
             self.raise_type_error(other)

method raise_type_error(self, other) ​

ソースコード または GitHubで表示
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')

method __ne__(self, other) ​

ソースコード または GitHubで表示
python
def __ne__(self, other):
     return not self.__eq__(other)

func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​

説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。

引数:

  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差

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(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (`float`): 数2
-        epsilon (`float`): 误差
-    Returns:
-        [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon

func sign(x: float, only_neg: bool = False) -> str ​

説明: 获取数的符号。

引数:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

戻り値: str: 符号 + - ""

ソースコード または GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''

func sign_format(x: float, only_neg: bool = False) -> str ​

説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""

引数:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

戻り値: str: 符号 + - ""

ソースコード または GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         return f'-{abs(x)}'
     else:
         return ''

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- + \ No newline at end of file diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html index 3f30e2e..89dc6a9 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 - + - - + + - + @@ -19,164 +19,47 @@
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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):
-    """
-        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。

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 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 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:
@@ -185,13 +68,6 @@
     ...

@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)):
@@ -199,22 +75,10 @@
     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)

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

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

- + \ No newline at end of file diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html index 1cd588f..8cb950d 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 fcc894c..aaa70af 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 21dc400..7814bde 100644 --- a/ja/api/presets/model/index.html +++ b/ja/api/presets/model/index.html @@ -6,12 +6,12 @@ mbcp.presets.model | MBCP ドキュメント - + - - + + - + @@ -20,14 +20,6 @@
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モジュール mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

説明: 生成球体上的点集。

引数:

  • radius:
  • density:

戻り値: List[Point3]: 球体上的点集。

ソースコード または GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -36,7 +28,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

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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
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🛠️

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

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Reference ​

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微分方程 ​

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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

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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 c436e7a..a5d60e7 100644 --- a/zht/api/mp_math/angle.html +++ b/zht/api/mp_math/angle.html @@ -6,12 +6,12 @@ mbcp.mp_math.angle | MBCP 文檔 - + - - + + - + @@ -19,92 +19,31 @@
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模組 mbcp.mp_math.angle ​

本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

method __init__(self, value: float, is_radian: bool = False) ​

説明: 任意角度。

變數説明:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
-    """
-        任意角度。
-        Args:
-            value: 角度或弧度值
-            is_radian: 是否为弧度，默认为否
-        """
     if is_radian:
         self.radian = value
     else:
         self.radian = value * PI / 180

@property

method complementary(self) -> AnyAngle ​

説明: 余角：两角的和为90°。

返回: 余角

源碼 或 於GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
-    """
-        余角：两角的和为90°。
-        Returns:
-            余角
-        """
     return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)

@property

method supplementary(self) -> AnyAngle ​

説明: 补角：两角的和为180°。

返回: 补角

源碼 或 於GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
-    """
-        补角：两角的和为180°。
-        Returns:
-            补角
-        """
     return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)

@property

method degree(self) -> float ​

説明: 角度。

返回: 弧度

源碼 或 於GitHub上查看
python
@property
 def degree(self) -> float:
-    """
-        角度。
-        Returns:
-            弧度
-        """
     return self.radian * 180 / PI

@property

method minimum_positive(self) -> AnyAngle ​

説明: 最小正角。

返回: 最小正角度

源碼 或 於GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
-    """
-        最小正角。
-        Returns:
-            最小正角度
-        """
     return AnyAngle(self.radian % (2 * PI))

@property

method maximum_negative(self) -> AnyAngle ​

説明: 最大负角。

返回: 最大负角度

源碼 或 於GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
-    """
-        最大负角。
-        Returns:
-            最大负角度
-        """
     return AnyAngle(-self.radian % (2 * PI), is_radian=True)

@property

method sin(self) -> float ​

説明: 正弦值。

返回: 正弦值

源碼 或 於GitHub上查看
python
@property
 def sin(self) -> float:
-    """
-        正弦值。
-        Returns:
-            正弦值
-        """
     return math.sin(self.radian)

@property

method cos(self) -> float ​

説明: 余弦值。

返回: 余弦值

源碼 或 於GitHub上查看
python
@property
 def cos(self) -> float:
-    """
-        余弦值。
-        Returns:
-            余弦值
-        """
     return math.cos(self.radian)

@property

method tan(self) -> float ​

説明: 正切值。

返回: 正切值

源碼 或 於GitHub上查看
python
@property
 def tan(self) -> float:
-    """
-        正切值。
-        Returns:
-            正切值
-        """
     return math.tan(self.radian)

@property

method cot(self) -> float ​

説明: 余切值。

返回: 余切值

源碼 或 於GitHub上查看
python
@property
 def cot(self) -> float:
-    """
-        余切值。
-        Returns:
-            余切值
-        """
     return 1 / math.tan(self.radian)

@property

method sec(self) -> float ​

説明: 正割值。

返回: 正割值

源碼 或 於GitHub上查看
python
@property
 def sec(self) -> float:
-    """
-        正割值。
-        Returns:
-            正割值
-        """
     return 1 / math.cos(self.radian)

@property

method csc(self) -> float ​

説明: 余割值。

返回: 余割值

源碼 或 於GitHub上查看
python
@property
 def csc(self) -> float:
-    """
-        余割值。
-        Returns:
-            余割值
-        """
     return 1 / math.sin(self.radian)

method self + other: AnyAngle => AnyAngle ​

源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
     return AnyAngle(self.radian + other.radian, is_radian=True)

method __eq__(self, other) ​

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

method self - other: AnyAngle => AnyAngle ​

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
@@ -117,7 +56,7 @@
     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 4732eab..2a48918 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 e9c93e3..1ff298d 100644 --- a/zht/api/mp_math/equation.html +++ b/zht/api/mp_math/equation.html @@ -6,12 +6,12 @@ mbcp.mp_math.equation | MBCP 文檔 - + - - + + - + @@ -19,46 +19,16 @@
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模組 mbcp.mp_math.equation ​

本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​

説明: 曲线方程。

變數説明:

源碼 或 於GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
-    """
-        曲线方程。
-        Args:
-            x_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): x函数
-            y_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): y函数
-            z_func ([`OneVarFunc`](./mp_math_typing#var-onevarfunc)): z函数
-        """
     self.x_func = x_func
     self.y_func = y_func
     self.z_func = z_func

method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​

説明: 计算曲线上的点。

變數説明:

  • *t:
  • 参数:

返回: 目标点

源碼 或 於GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
-    """
-        计算曲线上的点。
-        Args:
-            *t:
-                参数
-        Returns:
-            目标点
-        """
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
         return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])

func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​

説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。

WARNING

目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升

變數説明:

  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量

返回: 偏导函数

抛出:

  • ValueError 无效变量类型
源碼 或 於GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
-    """
-    求N元函数一阶偏导函数。这玩意不太稳定，慎用。
-    > [!warning]
-    > 目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
-
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): N元函数
-        var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
-        epsilon: 偏移量
-    Returns:
-        偏导函数
-    Raises:
-        ValueError: 无效变量类型
-    """
     if isinstance(var, int):
 
         def partial_derivative_func(*args: Var) -> Var:
-            """@litedoc-hide"""
             args_list_plus = list(args)
             args_list_plus[var] += epsilon
             args_list_minus = list(args)
@@ -68,14 +38,6 @@
     elif isinstance(var, tuple):
 
         def high_order_partial_derivative_func(*args: Var) -> Var:
-            """
-            @litedoc-hide
-            求高阶偏导函数
-            Args:
-                *args: 参数
-            Returns:
-                高阶偏导数值
-            """
             result_func = func
             for v in var:
                 result_func = get_partial_derivative_func(result_func, v, epsilon)
@@ -83,7 +45,7 @@
         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 d00474c..80e665d 100644 --- a/zht/api/mp_math/function.html +++ b/zht/api/mp_math/function.html @@ -6,12 +6,12 @@ mbcp.mp_math.function | MBCP 文檔 - + - - + + - + @@ -19,18 +19,6 @@
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模組 mbcp.mp_math.function ​

AAA

func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​

説明: 计算三元函数在某点的梯度向量。

TIP

已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)

變數説明:

返回: 梯度

源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\nabla f(x_0, y_0, z_0) = \\left(\\frac{\\partial f}{\\partial x}, \\frac{\\partial f}{\\partial y}, \\frac{\\partial f}{\\partial z}\\right)$
-    Args:
-        func ([`ThreeSingleVarsFunc`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([`Point3`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
     dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
     dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
     dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
@@ -38,29 +26,11 @@
     return a + b + c
 add_curried = curry(add, 1, 2)
 add_curried(3)  # 6
源碼 或 於GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([`MultiVarsFunc`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([`Var`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        ```python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        ```
-    """
 
     def curried_func(*args2: Var) -> Var:
-        """@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 5a69c65..7eb9dc0 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 98f28ba..fa4b3e1 100644 --- a/zht/api/mp_math/line.html +++ b/zht/api/mp_math/line.html @@ -6,12 +6,12 @@ mbcp.mp_math.line | MBCP 文檔 - + - - + + - + @@ -19,40 +19,10 @@
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模組 mbcp.mp_math.line ​

本模块定义了三维空间中的直线类

class Line3 ​

method __init__(self, point: Point3, direction: Vector3) ​

説明: 三维空间中的直线。由一个点和一个方向向量确定。

變數説明:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
-    """
-        三维空间中的直线。由一个点和一个方向向量确定。
-        Args:
-            point ([`Point3`](./point#class-point3)): 直线上的一点
-            direction ([`Vector3`](./vector#class-vector3)): 方向向量
-        """
     self.point = point
     self.direction = direction

method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​

説明: 判断两条直线是否近似相等。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
-    """
-        判断两条直线是否近似相等。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-        """
     return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)

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

説明: 计算直线和直线之间的夹角。

變數説明:

  • other (Line3): 另一条直线

返回: AnyAngle: 夹角

源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
-    """
-        计算直线和直线之间的夹角。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`AnyAngle`](./angle#class-anyangle): 夹角
-        """
     return self.direction.cal_angle(other.direction)

method cal_distance(self, other: Line3 | Point3) -> float ​

説明: 计算直线和直线或点之间的距离。

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: 'Line3 | Point3') -> float:
-    """
-        计算直线和直线或点之间的距离。
-        Args:
-            other ([`Line3`](./line#class-line3) | [`Point3`](./point#class-point3)): 另一条直线或点
-        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, Line3):
         if self == other:
             return 0
@@ -66,91 +36,19 @@
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
         raise TypeError('Unsupported type.')

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

説明: 计算两条直线的交点。

變數説明:

  • other (Line3): 另一条直线

返回: Point3: 交点

抛出:

源碼 或 於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
-    """
-        计算两条直线的交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Point3`](./point#class-point3): 交点
-        Raises:
-            [`ValueError`](https%3A//docs.python.org/3/library/exceptions.html#TypeError): 直线平行
-            `ValueError`: 直线不共面
-        """
     if self.is_parallel(other):
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
     return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction

method cal_perpendicular(self, point: Point3) -> Line3 ​

説明: 计算直线经过指定点p的垂线。

變數説明:

返回: Line3: 垂线

源碼 或 於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
-    """
-        计算直线经过指定点p的垂线。
-        Args:
-            point ([`Point3`](./point#class-point3)): 指定点
-        Returns:
-            [`Line3`](./line#class-line3): 垂线
-        """
     return Line3(point, self.direction.cross(point - self.point))

method get_point(self, t: RealNumber) -> Point3 ​

説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。

變數説明:

返回: Point3: 点

源碼 或 於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
-    """
-        获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
-        Args:
-            t ([`RealNumber`](./mp_math_typing#var-realnumber)): 参数t
-        Returns:
-            [`Point3`](./point#class-point3): 点
-        """
     return self.point + t * self.direction

method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​

説明: 获取直线的参数方程。

返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程

源碼 或 於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
-    """
-        获取直线的参数方程。
-        Returns:
-            [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
-        """
     return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)

method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​

説明: 判断两条直线是否近似平行。

變數説明:

  • other (Line3): 另一条直线
  • epsilon (float): 误差

返回: bool: 是否近似平行

源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
-    """
-        判断两条直线是否近似平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-            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.direction.is_approx_parallel(other.direction, epsilon)

method is_parallel(self, other: Line3) -> bool ​

説明: 判断两条直线是否平行。

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: 'Line3') -> bool:
-    """
-        判断两条直线是否平行。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
-        """
     return self.direction.is_parallel(other.direction)

method is_collinear(self, other: Line3) -> bool ​

説明: 判断两条直线是否共线。

變數説明:

返回: bool: 是否共线

源碼 或 於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共线。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
-        """
     return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)

method is_point_on(self, point: Point3) -> bool ​

説明: 判断点是否在直线上。

變數説明:

返回: bool: 是否在直线上

源碼 或 於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
-    """
-        判断点是否在直线上。
-        Args:
-            point ([`Point3`](./point#class-point3)): 点
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
-        """
     return (point - self.point).is_parallel(self.direction)

method is_coplanar(self, other: Line3) -> bool ​

説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。

變數説明:

返回: bool: 是否共面

源碼 或 於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
-    """
-        判断两条直线是否共面。
-        充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一
-        Returns:
-            [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
-        """
     return self.direction.cross(other.direction) @ (self.point - other.point) == 0

method simplify(self) ​

説明: 简化直线方程，等价相等。 自体简化，不返回值。

按照可行性一次对x y z 化 0 处理，并对向量单位化

源碼 或 於GitHub上查看
python
def simplify(self):
-    """
-        简化直线方程，等价相等。
-        自体简化，不返回值。
-
-        按照可行性一次对x y z 化 0 处理，并对向量单位化
-        """
     self.direction.normalize()
     if self.direction.x == 0:
         self.point.x = 0
@@ -159,40 +57,16 @@
     if self.direction.z == 0:
         self.point.z = 0

@classmethod

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

説明: 工厂函数 由两点构造直线。

變數説明:

返回: Line3: 直线

源碼 或 於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
-    """
-        工厂函数 由两点构造直线。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 点1
-            p2 ([`Point3`](./point#class-point3)): 点2
-        Returns:
-            [`Line3`](./line#class-line3): 直线
-        """
     direction = p2 - p1
     return cls(p1, direction)

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

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

變數説明:

  • other (Line3): 另一条直线

返回: Line3 | Point3 | None: 交集

源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
-    """
-        计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`Line3`](./line#class-line3) | [`Point3`](./point#class-point3) | [`None`](https://docs.python.org/3/library/constants.html#None): 交集
-        """
     if self.is_collinear(other):
         return self
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
         return self.cal_intersection(other)

method __eq__(self, other) -> bool ​

説明: 判断两条直线是否等价。

v1 // v2 ∧ (p1 - p2) // v1

變數説明:

  • other (Line3): 另一条直线

返回: bool: 是否等价

源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
-    """
-        判断两条直线是否等价。
-
-        v1 // v2 ∧ (p1 - p2) // v1
-        Args:
-            other ([`Line3`](./line#class-line3)): 另一条直线
-        Returns:
-            [`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 0124ece..ce1a5c7 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 @@
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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 e55ed3c..3fae06a 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 - + - - + + - + @@ -19,25 +19,10 @@
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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)
@@ -49,66 +34,18 @@
         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。

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:
-            [`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。

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:
-            [`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)
@@ -126,106 +63,36 @@
         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
@@ -236,16 +103,9 @@
         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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- + \ No newline at end of file diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html index 1f4b4cc..d9e16f9 100644 --- a/zht/api/mp_math/point.html +++ b/zht/api/mp_math/point.html @@ -6,12 +6,12 @@ mbcp.mp_math.point | MBCP 文檔 - + - - + + - + @@ -19,58 +19,19 @@
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模組 mbcp.mp_math.point ​

本模块定义了三维空间中点的类。

class Point3 ​

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

説明: 笛卡尔坐标系中的点。

變數説明:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
-    """
-        笛卡尔坐标系中的点。
-        Args:
-            x ([`float`](https://docs.python.org/3/library/functions.html#float)): x 坐标
-            y (`float`): y 坐标
-            z (`float`): z 坐标
-        """
     self.x = x
     self.y = y
     self.z = z

method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​

説明: 判断两个点是否近似相等。

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: 'Point3', epsilon: float=APPROX) -> bool:
-    """
-        判断两个点是否近似相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-            epsilon ([`float`](https://docs.python.org/3/library/functions.html#float)): 误差
-        Returns:
-            [`bool`](https://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])

@overload

method self + other: Vector3 => Point3 ​

源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
     ...

@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: P + V -> P P + P -> P

變數説明:

返回: Point3: 新的点

源碼 或 於GitHub上查看
python
def __add__(self, other):
-    """
-        P + V -> P
-        P + P -> P
-        Args:
-            other ([`Vector3`](./vector#class-vector3) | [`Point3`](./point#class-point3)): 另一个点或向量
-        Returns:
-            [`Point3`](./point#class-point3): 新的点
-        """
     return Point3(self.x + other.x, self.y + other.y, self.z + other.z)

method __eq__(self, other) ​

説明: 判断两个点是否相等。

變數説明:

返回: bool: 是否相等

源碼 或 於GitHub上查看
python
def __eq__(self, other):
-    """
-        判断两个点是否相等。
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`bool`](https://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 => Vector3 ​

説明: P - P -> V

P - V -> P 已在 Vector3 中实现

變數説明:

返回: Vector3: 新的向量

源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
-    """
-        P - P -> V
-
-        P - V -> P  已在 [`Vector3`](./vector#class-vector3) 中实现
-        Args:
-            other ([`Point3`](./point#class-point3)): 另一个点
-        Returns:
-            [`Vector3`](./vector#class-vector3): 新的向量
-        """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

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模組 mbcp.mp_math.segment ​

本模块定义了三维空间中的线段类

class Segment3 ​

method __init__(self, p1: Point3, p2: Point3) ​

説明: 三维空间中的线段。

變數説明:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
-    """
-        三维空间中的线段。
-        Args:
-            p1 ([`Point3`](./point#class-point3)): 线段的一个端点
-            p2 ([`Point3`](./point#class-point3)): 线段的另一个端点
-        """
     self.p1 = p1
     self.p2 = p2
     '方向向量'
@@ -33,7 +27,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

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模組 mbcp.mp_math.utils ​

本模块定义了一些常用的工具函数

func clamp(x: float, min_: float, max_: float) -> float ​

説明: 区间限定函数

變數説明:

  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值

返回: float: 限定在区间内的值

源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
-    """
-    区间限定函数
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 值
-        min_ (`float`): 最小值
-        max_ (`float`): 最大值
-
-    Returns:
-        `float`: 限定在区间内的值
-    """
     return max(min(x, max_), min_)

class Approx ​

method __init__(self, value: RealNumber) ​

説明: 用于近似比较对象

變數説明:

源碼 或 於GitHub上查看
python
def __init__(self, value: RealNumber):
-    """
-        用于近似比较对象
-        Args:
-            value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
-        """
     self.value = value

method __eq__(self, other) ​

源碼 或 於GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
@@ -48,46 +33,20 @@
             self.raise_type_error(other)

method raise_type_error(self, other) ​

源碼 或 於GitHub上查看
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')

method __ne__(self, other) ​

源碼 或 於GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)

func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​

説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。

變數説明:

  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差

返回: bool: 是否近似相等

源碼 或 於GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
-    """
-    判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数1
-        y (`float`): 数2
-        epsilon (`float`): 误差
-    Returns:
-        [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
-    """
     return abs(x - y) < epsilon

func sign(x: float, only_neg: bool = False) -> str ​

説明: 获取数的符号。

變數説明:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

返回: str: 符号 + - ""

源碼 或 於GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
-    """获取数的符号。
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return '+' if not only_neg else ''
     elif x < 0:
         return '-'
     else:
         return ''

func sign_format(x: float, only_neg: bool = False) -> str ​

説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""

變數説明:

  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号

返回: str: 符号 + - ""

源碼 或 於GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
-    """格式化符号数
-    -1 -> -1
-    1 -> +1
-    0 -> ""
-    Args:
-        x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
-        only_neg ([`bool`](https://docs.python.org/3/library/functions.html#bool)): 是否只返回负数的符号
-    Returns:
-        [`str`](https://docs.python.org/3/library/functions.html#str): 符号 + - ""
-    """
     if x > 0:
         return f'+{x}' if not only_neg else f'{x}'
     elif x < 0:
         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 93a7007..96c3bf2 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 - + - - + + - + @@ -19,164 +19,47 @@
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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。

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 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 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:
@@ -185,13 +68,6 @@
     ...

@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)):
@@ -199,22 +75,10 @@
     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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- + \ No newline at end of file diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html index a54c0ee..a69cd42 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 4fa6fe4..13beff4 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 2b53da5..f7b52d6 100644 --- a/zht/api/presets/model/index.html +++ b/zht/api/presets/model/index.html @@ -6,12 +6,12 @@ mbcp.presets.model | MBCP 文檔 - + - - + + - + @@ -20,14 +20,6 @@
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模組 mbcp.presets.model ​

几何模型点集

class GeometricModels ​

@staticmethod

method sphere(radius: float, density: float) ​

説明: 生成球体上的点集。

變數説明:

  • radius:
  • density:

返回: List[Point3]: 球体上的点集。

源碼 或 於GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
     area = 4 * np.pi * radius ** 2
     num = int(area * density)
     phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
@@ -36,7 +28,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

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开始不了一点 ​

∫12x111

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