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Page Frontmatter ​

{
   "outline": "deep"
 }

More ​

Check out the documentation for the full list of runtime APIs.

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class Angle ​

class AnyAngle(Angle) ​

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

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
python
def __init__(self, value: float, is_radian: bool=False):
+    
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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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
返回:
  • 余角
源代码
python
@property
+        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
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 ​
补角：两角的和为180°。
返回:
  • 补角
源代码
python
@property
+    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
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 ​
角度。
返回:
  • 弧度
源代码
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
返回:
  • 最小正角度
源代码
python
@property
+    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
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 ​
最大负角。
返回:
  • 最大负角度
源代码
python
@property
+    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
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 ​
正弦值。
返回:
  • 正弦值
源代码
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
返回:
  • 余弦值
源代码
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
返回:
  • 正切值
源代码
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
返回:
  • 余切值
源代码
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
返回:
  • 正割值
源代码
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
返回:
  • 余割值
源代码
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
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
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源代码
python
def __truediv__(self, other):
+    ...
method self / other ​
源代码
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
参数:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
返回: 偏导函数
参数:
  • func: 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
引发:
  • ValueError 无效变量类型
源代码
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。
     Args:
@@ -47,16 +47,16 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源代码
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源代码
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源代码
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源代码
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +66,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +79,7 @@
         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))])

-    
+    
     
   
 
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+++ b/api/mp_math/index.html
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diff --git a/api/mp_math/line.html b/api/mp_math/line.html
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+++ b/api/mp_math/line.html
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class Line3 ​
method __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。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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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: 直线上的一点
  • direction: 直线的方向向量
源代码
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:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
参数:
  • other: 另一条直线
  • epsilon: 误差
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             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 ​
计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回:
  • 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
返回: 夹角弧度
参数:
  • other: 另一条直线
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回:
  • 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
返回: 距离
参数:
  • other: 平行直线或点
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
参数:
  • other: 另一条直线
返回:
  • 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
返回: 交点
参数:
  • other: 另一条直线
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         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 ​
计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回:
  • 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
返回: 垂线
参数:
  • point: 指定点
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
参数:
  • t: 参数t
返回:
  • 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
返回: 点
参数:
  • t: 参数t
源代码
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:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
返回:
  • x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
返回: 是否近似平行
参数:
  • other: 另一条直线
  • epsilon: 误差
源代码
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:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
参数:
  • other: 另一条直线
返回:
  • 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
返回: 是否平行
参数:
  • other: 另一条直线
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
参数:
  • other: 另一条直线
返回:
  • 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
返回: 是否共线
参数:
  • other: 另一条直线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             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 ​
判断点是否在直线上。
参数:
  • point: 点
返回:
  • 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
返回: 是否在直线上
参数:
  • point: 点
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
参数:
  • other: 另一条直线
返回:
  • 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
返回: 是否共面
参数:
  • other: 另一条直线
源代码
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。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
源代码
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
参数:
  • p1: 点1
  • p2: 点2
返回:
  • 直线
源代码
python
@classmethod
+        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。
返回: 直线
参数:
  • p1: 点1
  • p2: 点2
源代码
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
参数:
  • other: 另一条直线
返回:
  • 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
返回: 交点
参数:
  • other: 另一条直线
源代码
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:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
+        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:
源代码
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html
index 94a3adc..1939efc 100644
--- a/api/mp_math/mp_math_typing.html
+++ b/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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
var RealNumber = int | float ​
  • 类型: TypeAlias
var Number = RealNumber | complex ​
  • 类型: TypeAlias
var Var = SingleVar | ArrayVar ​
  • 类型: TypeAlias
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • 类型: TypeAlias
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • 类型: TypeAlias
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • 类型: TypeAlias
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • 类型: TypeAlias
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • 类型: TypeAlias
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • 类型: TypeAlias
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • 类型: TypeAlias
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • 类型: TypeAlias
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • 类型: TypeAlias

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html
index d917112..a4b963b 100644
--- a/api/mp_math/plane.html
+++ b/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
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繁體中文
Appearance
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
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
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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
返回: 是否近似相等
参数:
  • other: 另一个平面
源代码
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         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 ​
计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回:
  • 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
返回: 夹角弧度
参数:
  • other: 另一个平面
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回:
  • 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
返回: 距离
参数:
  • other: 另一个平面或点
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     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 ​
计算两平面的交线。
参数:
  • other: 另一个平面
返回:
  • 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
返回: 两平面的交线
参数:
  • other: 另一个平面
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回:
  • 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
返回: 交点
参数:
  • other: 不与平面平行或在平面上的直线
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回:
  • 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
返回: 所求平面
参数:
  • point: 指定点
源代码
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:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
参数:
  • other: 另一个平面
返回:
  • 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
返回: 是否平行
参数:
  • other: 另一个平面
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
返回:
  • 法向量
源代码
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
参数:
  • point: 平面上的一点
  • normal: 法向量
返回:
  • 平面
源代码
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
返回: 平面
参数:
  • point: 平面上的一点
  • normal: 法向量
源代码
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)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回:
  • 平面
源代码
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
返回: 平面
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
源代码
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。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回:
  • 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
返回: 平面
参数:
  • l1: 直线1
  • l2: 直线2
源代码
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回:
  • 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
返回: 平面
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
源代码
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。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
参数:
  • other:
返回:
  • 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
返回: 不平行平面的交线，平面平行返回None
参数:
  • other:
源代码
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
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diff --git a/api/mp_math/point.html b/api/mp_math/point.html
index 600bf8b..4c4b94c 100644
--- a/api/mp_math/point.html
+++ b/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
+    
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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: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
参数:
  • other:
  • epsilon:
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
+    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:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html
index 9d9ffb2..0cbae2d 100644
--- a/api/mp_math/segment.html
+++ b/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html
index 7ba994e..2e355da 100644
--- a/api/mp_math/utils.html
+++ b/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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func clamp() -> float ​
区间限定函数
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回:
  • 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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func clamp() -> float ​
说明: 区间限定函数
返回: 限制后的值
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回:
  • 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
返回: 是否近似相等
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
源代码
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:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
说明: 获取数的符号。
返回: 符号 + - ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
返回: 符号 + - ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
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
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
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
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html
index 4b965b4..0d8bd54 100644
--- a/api/mp_math/vector.html
+++ b/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
参数:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
参数:
  • other:
  • epsilon:
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             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 ​
计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回:
  • 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
返回: 夹角
参数:
  • other: 另一个向量
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • other:
返回:
  • 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
返回: 行列式的结果
参数:
  • other:
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回:
  • 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
返回: 是否近似平行
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
源代码
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:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
参数:
  • other: 另一个向量
返回:
  • 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
返回: 是否平行
参数:
  • other: 另一个向量
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
返回:
  • 模
源代码
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
返回:
  • 单位向量
源代码
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
判断两个向量是否相等。
参数:
  • other:
返回:
  • 是否相等
源代码
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
返回: 是否相等
参数:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
+    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
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:
@@ -193,18 +193,18 @@
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/particle/index.html b/api/particle/index.html
index 68b1671..eba8ff2 100644
--- a/api/particle/index.html
+++ b/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/index.html b/api/presets/index.html
index c9e3bf5..1382c01 100644
--- a/api/presets/index.html
+++ b/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/model/index.html b/api/presets/model/index.html
index 6f4d6a2..687e011 100644
--- a/api/presets/model/index.html
+++ b/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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
python
@staticmethod
+    
MBCP docs
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
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
返回: List[Point3]: 球体上的点集。
参数:
  • radius:
  • density:
源代码
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file
diff --git a/assets/api_mp_math_angle.md.HvtyV1VE.js b/assets/api_mp_math_angle.md.B8w0LP6o.js
similarity index 82%
rename from assets/api_mp_math_angle.md.HvtyV1VE.js
rename to assets/api_mp_math_angle.md.B8w0LP6o.js
index 481299c..7b43490 100644
--- a/assets/api_mp_math_angle.md.HvtyV1VE.js
+++ b/assets/api_mp_math_angle.md.B8w0LP6o.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
返回:
  • 余角
源代码
python
@property
+        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
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 ​
补角：两角的和为180°。
返回:
  • 补角
源代码
python
@property
+    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
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 ​
角度。
返回:
  • 弧度
源代码
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
返回:
  • 最小正角度
源代码
python
@property
+    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
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 ​
最大负角。
返回:
  • 最大负角度
源代码
python
@property
+    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
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 ​
正弦值。
返回:
  • 正弦值
源代码
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
返回:
  • 余弦值
源代码
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
返回:
  • 正切值
源代码
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
返回:
  • 余切值
源代码
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
返回:
  • 正割值
源代码
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
返回:
  • 余割值
源代码
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
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
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源代码
python
def __truediv__(self, other):
+    ...
method self / other ​
源代码
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,89),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/api_mp_math_angle.md.HvtyV1VE.lean.js b/assets/api_mp_math_angle.md.B8w0LP6o.lean.js
similarity index 58%
rename from assets/api_mp_math_angle.md.HvtyV1VE.lean.js
rename to assets/api_mp_math_angle.md.B8w0LP6o.lean.js
index 3589a07..ca34d60 100644
--- a/assets/api_mp_math_angle.md.HvtyV1VE.lean.js
+++ b/assets/api_mp_math_angle.md.B8w0LP6o.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n("",89),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n("",78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/api_mp_math_equation.md.C2RSv9WY.js b/assets/api_mp_math_equation.md.Bx4yJe6o.js
similarity index 83%
rename from assets/api_mp_math_equation.md.C2RSv9WY.js
rename to assets/api_mp_math_equation.md.Bx4yJe6o.js
index 1f306b3..a1170c8 100644
--- a/assets/api_mp_math_equation.md.C2RSv9WY.js
+++ b/assets/api_mp_math_equation.md.Bx4yJe6o.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
参数:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
返回: 偏导函数
参数:
  • func: 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
引发:
  • ValueError 无效变量类型
源代码
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。
     Args:
@@ -28,16 +28,16 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源代码
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源代码
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源代码
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源代码
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +47,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +59,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
     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))])
`,24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
diff --git a/assets/api_mp_math_equation.md.C2RSv9WY.lean.js b/assets/api_mp_math_equation.md.Bx4yJe6o.lean.js
similarity index 85%
rename from assets/api_mp_math_equation.md.C2RSv9WY.lean.js
rename to assets/api_mp_math_equation.md.Bx4yJe6o.lean.js
index 72ef7c6..c988365 100644
--- a/assets/api_mp_math_equation.md.C2RSv9WY.lean.js
+++ b/assets/api_mp_math_equation.md.Bx4yJe6o.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n("",24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=n("",23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
diff --git a/assets/api_mp_math_line.md.BPnyTp_q.js b/assets/api_mp_math_line.md.B1s7_FXM.js
similarity index 73%
rename from assets/api_mp_math_line.md.BPnyTp_q.js
rename to assets/api_mp_math_line.md.B1s7_FXM.js
index b6fcabc..c69e848 100644
--- a/assets/api_mp_math_line.md.BPnyTp_q.js
+++ b/assets/api_mp_math_line.md.B1s7_FXM.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n(`
class Line3 ​
method __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。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n(`
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: 直线上的一点
  • direction: 直线的方向向量
源代码
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:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
参数:
  • other: 另一条直线
  • epsilon: 误差
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回:
  • 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
返回: 夹角弧度
参数:
  • other: 另一条直线
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回:
  • 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
返回: 距离
参数:
  • other: 平行直线或点
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
参数:
  • other: 另一条直线
返回:
  • 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
返回: 交点
参数:
  • other: 另一条直线
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         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 ​
计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回:
  • 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
返回: 垂线
参数:
  • point: 指定点
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
参数:
  • t: 参数t
返回:
  • 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
返回: 点
参数:
  • t: 参数t
源代码
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:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
返回:
  • x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
返回: 是否近似平行
参数:
  • other: 另一条直线
  • epsilon: 误差
源代码
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:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
参数:
  • other: 另一条直线
返回:
  • 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
返回: 是否平行
参数:
  • other: 另一条直线
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
参数:
  • other: 另一条直线
返回:
  • 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
返回: 是否共线
参数:
  • other: 另一条直线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
判断点是否在直线上。
参数:
  • point: 点
返回:
  • 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
返回: 是否在直线上
参数:
  • point: 点
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
参数:
  • other: 另一条直线
返回:
  • 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
返回: 是否共面
参数:
  • other: 另一条直线
源代码
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。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
源代码
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
参数:
  • p1: 点1
  • p2: 点2
返回:
  • 直线
源代码
python
@classmethod
+        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。
返回: 直线
参数:
  • p1: 点1
  • p2: 点2
源代码
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
参数:
  • other: 另一条直线
返回:
  • 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
返回: 交点
参数:
  • other: 另一条直线
源代码
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:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
+        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:
源代码
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,119),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_line.md.BPnyTp_q.lean.js b/assets/api_mp_math_line.md.B1s7_FXM.lean.js
similarity index 85%
rename from assets/api_mp_math_line.md.BPnyTp_q.lean.js
rename to assets/api_mp_math_line.md.B1s7_FXM.lean.js
index cc6392a..e425cef 100644
--- a/assets/api_mp_math_line.md.BPnyTp_q.lean.js
+++ b/assets/api_mp_math_line.md.B1s7_FXM.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n("",119),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n("",105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DLhf2OdI.js b/assets/api_mp_math_plane.md.BiW2-xb_.js
similarity index 83%
rename from assets/api_mp_math_plane.md.DLhf2OdI.js
rename to assets/api_mp_math_plane.md.BiW2-xb_.js
index 2678270..cc67880 100644
--- a/assets/api_mp_math_plane.md.DLhf2OdI.js
+++ b/assets/api_mp_math_plane.md.BiW2-xb_.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n(`
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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
返回: 是否近似相等
参数:
  • other: 另一个平面
源代码
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回:
  • 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
返回: 夹角弧度
参数:
  • other: 另一个平面
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回:
  • 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
返回: 距离
参数:
  • other: 另一个平面或点
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算两平面的交线。
参数:
  • other: 另一个平面
返回:
  • 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
返回: 两平面的交线
参数:
  • other: 另一个平面
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回:
  • 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
返回: 交点
参数:
  • other: 不与平面平行或在平面上的直线
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回:
  • 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
返回: 所求平面
参数:
  • point: 指定点
源代码
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:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
参数:
  • other: 另一个平面
返回:
  • 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
返回: 是否平行
参数:
  • other: 另一个平面
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
返回:
  • 法向量
源代码
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
参数:
  • point: 平面上的一点
  • normal: 法向量
返回:
  • 平面
源代码
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
返回: 平面
参数:
  • point: 平面上的一点
  • normal: 法向量
源代码
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)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     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 ​
工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回:
  • 平面
源代码
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
返回: 平面
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
源代码
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。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回:
  • 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
返回: 平面
参数:
  • l1: 直线1
  • l2: 直线2
源代码
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回:
  • 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
返回: 平面
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
源代码
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。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
参数:
  • other:
返回:
  • 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
返回: 不平行平面的交线，平面平行返回None
参数:
  • other:
源代码
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,116),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DLhf2OdI.lean.js b/assets/api_mp_math_plane.md.BiW2-xb_.lean.js
similarity index 85%
rename from assets/api_mp_math_plane.md.DLhf2OdI.lean.js
rename to assets/api_mp_math_plane.md.BiW2-xb_.lean.js
index f2f27fd..434353e 100644
--- a/assets/api_mp_math_plane.md.DLhf2OdI.lean.js
+++ b/assets/api_mp_math_plane.md.BiW2-xb_.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n("",116),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n("",103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/api_mp_math_point.md.0dOKpGzi.js b/assets/api_mp_math_point.md.Cl5vX84g.js
similarity index 74%
rename from assets/api_mp_math_point.md.0dOKpGzi.js
rename to assets/api_mp_math_point.md.Cl5vX84g.js
index 12ce1d5..163f362 100644
--- a/assets/api_mp_math_point.md.0dOKpGzi.js
+++ b/assets/api_mp_math_point.md.Cl5vX84g.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t(`
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: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
参数:
  • other:
  • epsilon:
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
+    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:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_point.md.0dOKpGzi.lean.js b/assets/api_mp_math_point.md.Cl5vX84g.lean.js
similarity index 70%
rename from assets/api_mp_math_point.md.0dOKpGzi.lean.js
rename to assets/api_mp_math_point.md.Cl5vX84g.lean.js
index 2052d03..0d932bd 100644
--- a/assets/api_mp_math_point.md.0dOKpGzi.lean.js
+++ b/assets/api_mp_math_point.md.Cl5vX84g.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t("",35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t("",34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_segment.md.9QWXtPbn.js b/assets/api_mp_math_segment.md.C6i78ST1.js
similarity index 82%
rename from assets/api_mp_math_segment.md.9QWXtPbn.js
rename to assets/api_mp_math_segment.md.C6i78ST1.js
index 4eab4c2..8e16b56 100644
--- a/assets/api_mp_math_segment.md.9QWXtPbn.js
+++ b/assets/api_mp_math_segment.md.C6i78ST1.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
     '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)
`,4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const o=s(t,[["render",l]]);export{y as __pageData,o 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)
`,4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/api_mp_math_segment.md.9QWXtPbn.lean.js b/assets/api_mp_math_segment.md.C6i78ST1.lean.js
similarity index 57%
rename from assets/api_mp_math_segment.md.9QWXtPbn.lean.js
rename to assets/api_mp_math_segment.md.C6i78ST1.lean.js
index d7a0a0b..5f0b88a 100644
--- a/assets/api_mp_math_segment.md.9QWXtPbn.lean.js
+++ b/assets/api_mp_math_segment.md.C6i78ST1.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const o=s(t,[["render",l]]);export{y as __pageData,o as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/api_mp_math_utils.md.DdkUph5B.js b/assets/api_mp_math_utils.md.B902hNw4.js
similarity index 77%
rename from assets/api_mp_math_utils.md.DdkUph5B.js
rename to assets/api_mp_math_utils.md.B902hNw4.js
index fe3378f..2503b47 100644
--- a/assets/api_mp_math_utils.md.DdkUph5B.js
+++ b/assets/api_mp_math_utils.md.B902hNw4.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
区间限定函数
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回:
  • 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
说明: 区间限定函数
返回: 限制后的值
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回:
  • 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
返回: 是否近似相等
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
源代码
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:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
说明: 获取数的符号。
返回: 符号 + - ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
返回: 符号 + - ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
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
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,37),h=[t];function p(k,e,r,d,g,F){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
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
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_utils.md.DdkUph5B.lean.js b/assets/api_mp_math_utils.md.B902hNw4.lean.js
similarity index 70%
rename from assets/api_mp_math_utils.md.DdkUph5B.lean.js
rename to assets/api_mp_math_utils.md.B902hNw4.lean.js
index 8559b88..01c767a 100644
--- a/assets/api_mp_math_utils.md.DdkUph5B.lean.js
+++ b/assets/api_mp_math_utils.md.B902hNw4.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n("",37),h=[t];function p(k,e,r,d,g,F){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n("",33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_vector.md.Bodba8jG.js b/assets/api_mp_math_vector.md.CoooOTww.js
similarity index 81%
rename from assets/api_mp_math_vector.md.Bodba8jG.js
rename to assets/api_mp_math_vector.md.CoooOTww.js
index 0428b35..976c252 100644
--- a/assets/api_mp_math_vector.md.Bodba8jG.js
+++ b/assets/api_mp_math_vector.md.CoooOTww.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
参数:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
参数:
  • other:
  • epsilon:
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回:
  • 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
返回: 夹角
参数:
  • other: 另一个向量
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • other:
返回:
  • 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
返回: 行列式的结果
参数:
  • other:
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回:
  • 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
返回: 是否近似平行
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
源代码
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:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
参数:
  • other: 另一个向量
返回:
  • 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
返回: 是否平行
参数:
  • other: 另一个向量
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
返回:
  • 模
源代码
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
返回:
  • 单位向量
源代码
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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) ​
判断两个向量是否相等。
参数:
  • other:
返回:
  • 是否相等
源代码
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
返回: 是否相等
参数:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
+    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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 ​
P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
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:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
`,133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_vector.md.Bodba8jG.lean.js b/assets/api_mp_math_vector.md.CoooOTww.lean.js
similarity index 85%
rename from assets/api_mp_math_vector.md.Bodba8jG.lean.js
rename to assets/api_mp_math_vector.md.CoooOTww.lean.js
index 43c5e0a..b68d55a 100644
--- a/assets/api_mp_math_vector.md.Bodba8jG.lean.js
+++ b/assets/api_mp_math_vector.md.CoooOTww.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t("",133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_presets_model_index.md.YrmtLmca.js b/assets/api_presets_model_index.md.kSDvd14X.js
similarity index 90%
rename from assets/api_presets_model_index.md.YrmtLmca.js
rename to assets/api_presets_model_index.md.kSDvd14X.js
index d66832e..6efed50 100644
--- a/assets/api_presets_model_index.md.YrmtLmca.js
+++ b/assets/api_presets_model_index.md.kSDvd14X.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
返回: List[Point3]: 球体上的点集。
参数:
  • radius:
  • density:
源代码
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     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)]
`,9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/api_presets_model_index.md.YrmtLmca.lean.js b/assets/api_presets_model_index.md.kSDvd14X.lean.js
similarity index 71%
rename from assets/api_presets_model_index.md.YrmtLmca.lean.js
rename to assets/api_presets_model_index.md.kSDvd14X.lean.js
index adc84e0..433fffa 100644
--- a/assets/api_presets_model_index.md.YrmtLmca.lean.js
+++ b/assets/api_presets_model_index.md.kSDvd14X.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.fmci6qlC.js b/assets/en_api_mp_math_angle.md.DmK_A9xI.js
similarity index 84%
rename from assets/en_api_mp_math_angle.md.fmci6qlC.js
rename to assets/en_api_mp_math_angle.md.DmK_A9xI.js
index f47c3d4..46d588d 100644
--- a/assets/en_api_mp_math_angle.md.fmci6qlC.js
+++ b/assets/en_api_mp_math_angle.md.DmK_A9xI.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n(`
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
Return:
  • 余角
Source code
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
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 ​
补角：两角的和为180°。
Return:
  • 补角
Source code
python
@property
+    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
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 ​
角度。
Return:
  • 弧度
Source code
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
Return:
  • 最小正角度
Source code
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
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 ​
最大负角。
Return:
  • 最大负角度
Source code
python
@property
+    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
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 ​
正弦值。
Return:
  • 正弦值
Source code
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
Return:
  • 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
Return:
  • 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
Return:
  • 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
Return:
  • 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
Return:
  • 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
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
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
Source code
python
def __truediv__(self, other):
+    ...
method self / other ​
Source code
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,89),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.fmci6qlC.lean.js b/assets/en_api_mp_math_angle.md.DmK_A9xI.lean.js
similarity index 85%
rename from assets/en_api_mp_math_angle.md.fmci6qlC.lean.js
rename to assets/en_api_mp_math_angle.md.DmK_A9xI.lean.js
index 3b6207d..789df0d 100644
--- a/assets/en_api_mp_math_angle.md.fmci6qlC.lean.js
+++ b/assets/en_api_mp_math_angle.md.DmK_A9xI.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n("",89),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n("",78),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_equation.md.BwRlBW4s.js b/assets/en_api_mp_math_equation.md.BHF2EYD-.js
similarity index 83%
rename from assets/en_api_mp_math_equation.md.BwRlBW4s.js
rename to assets/en_api_mp_math_equation.md.BHF2EYD-.js
index e693d2a..73b09ec 100644
--- a/assets/en_api_mp_math_equation.md.BwRlBW4s.js
+++ b/assets/en_api_mp_math_equation.md.BHF2EYD-.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Arguments:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Return: 偏导函数
Arguments:
  • func: 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
Raises:
  • ValueError 无效变量类型
Source code
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。
     Args:
@@ -28,16 +28,16 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
Source code
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
Source code
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
Source code
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
Source code
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +47,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +59,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u
     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))])
`,24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{u as __pageData,y as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{u as __pageData,y as default};
diff --git a/assets/en_api_mp_math_equation.md.BwRlBW4s.lean.js b/assets/en_api_mp_math_equation.md.BHF2EYD-.lean.js
similarity index 86%
rename from assets/en_api_mp_math_equation.md.BwRlBW4s.lean.js
rename to assets/en_api_mp_math_equation.md.BHF2EYD-.lean.js
index 4c7a6bf..78e1a43 100644
--- a/assets/en_api_mp_math_equation.md.BwRlBW4s.lean.js
+++ b/assets/en_api_mp_math_equation.md.BHF2EYD-.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n("",24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{u as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n("",23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{u as __pageData,y as default};
diff --git a/assets/en_api_mp_math_line.md.B1oAhkHS.js b/assets/en_api_mp_math_line.md.B9L-UwK8.js
similarity index 74%
rename from assets/en_api_mp_math_line.md.B1oAhkHS.js
rename to assets/en_api_mp_math_line.md.B9L-UwK8.js
index ed13bff..0e78282 100644
--- a/assets/en_api_mp_math_line.md.B1oAhkHS.js
+++ b/assets/en_api_mp_math_line.md.B9L-UwK8.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),l={name:"en/api/mp_math/line.md"},t=n(`
class Line3 ​
method __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。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"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(`
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: 直线上的一点
  • direction: 直线的方向向量
Source code
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:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
Return: 是否近似相等
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return:
  • 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
Return: 夹角弧度
Arguments:
  • other: 另一条直线
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return:
  • 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
Return: 距离
Arguments:
  • other: 平行直线或点
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return:
  • 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Return: 交点
Arguments:
  • other: 另一条直线
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         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 ​
计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return:
  • 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
Return: 垂线
Arguments:
  • point: 指定点
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
Arguments:
  • t: 参数t
Return:
  • 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
Return: 点
Arguments:
  • t: 参数t
Source code
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:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
Return:
  • x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return:
  • 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
Return: 是否近似平行
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Source code
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:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return:
  • 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
Return: 是否平行
Arguments:
  • other: 另一条直线
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return:
  • 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
Return: 是否共线
Arguments:
  • other: 另一条直线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
判断点是否在直线上。
Arguments:
  • point: 点
Return:
  • 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
Return: 是否在直线上
Arguments:
  • point: 点
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
Arguments:
  • other: 另一条直线
Return:
  • 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
Return: 是否共面
Arguments:
  • other: 另一条直线
Source code
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。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
Source code
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return:
  • 直线
Source code
python
@classmethod
+        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。
Return: 直线
Arguments:
  • p1: 点1
  • p2: 点2
Source code
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
Arguments:
  • other: 另一条直线
Return:
  • 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
Return: 交点
Arguments:
  • other: 另一条直线
Source code
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:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
+        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:
Source code
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,119),h=[t];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),e=[l];function h(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",h]]);export{E as __pageData,c as default};
diff --git a/assets/en_api_mp_math_line.md.B1oAhkHS.lean.js b/assets/en_api_mp_math_line.md.B9L-UwK8.lean.js
similarity index 57%
rename from assets/en_api_mp_math_line.md.B1oAhkHS.lean.js
rename to assets/en_api_mp_math_line.md.B9L-UwK8.lean.js
index bd73715..7e81d3b 100644
--- a/assets/en_api_mp_math_line.md.B1oAhkHS.lean.js
+++ b/assets/en_api_mp_math_line.md.B9L-UwK8.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),l={name:"en/api/mp_math/line.md"},t=n("",119),h=[t];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"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("",105),e=[l];function h(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",h]]);export{E as __pageData,c as default};
diff --git a/assets/en_api_mp_math_plane.md.D3xHJy8e.js b/assets/en_api_mp_math_plane.md.BkRMq93h.js
similarity index 83%
rename from assets/en_api_mp_math_plane.md.D3xHJy8e.js
rename to assets/en_api_mp_math_plane.md.BkRMq93h.js
index 38887e1..6317eec 100644
--- a/assets/en_api_mp_math_plane.md.D3xHJy8e.js
+++ b/assets/en_api_mp_math_plane.md.BkRMq93h.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n(`
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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Return: 是否近似相等
Arguments:
  • other: 另一个平面
Source code
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return:
  • 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Return: 夹角弧度
Arguments:
  • other: 另一个平面
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return:
  • 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Return: 距离
Arguments:
  • other: 另一个平面或点
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算两平面的交线。
Arguments:
  • other: 另一个平面
Return:
  • 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Return: 两平面的交线
Arguments:
  • other: 另一个平面
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return:
  • 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Return: 交点
Arguments:
  • other: 不与平面平行或在平面上的直线
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return:
  • 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Return: 所求平面
Arguments:
  • point: 指定点
Source code
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:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return:
  • 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Return: 是否平行
Arguments:
  • other: 另一个平面
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
Return:
  • 法向量
Source code
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Return:
  • 平面
Source code
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Return: 平面
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Source code
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)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     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 ​
工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return:
  • 平面
Source code
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Return: 平面
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Source code
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。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return:
  • 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Return: 平面
Arguments:
  • l1: 直线1
  • l2: 直线2
Source code
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return:
  • 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Return: 平面
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Source code
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。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
Arguments:
  • other:
Return:
  • 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Return: 不平行平面的交线，平面平行返回None
Arguments:
  • other:
Source code
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,116),t=[h];function p(e,k,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,103),t=[h];function p(e,k,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_plane.md.D3xHJy8e.lean.js b/assets/en_api_mp_math_plane.md.BkRMq93h.lean.js
similarity index 85%
rename from assets/en_api_mp_math_plane.md.D3xHJy8e.lean.js
rename to assets/en_api_mp_math_plane.md.BkRMq93h.lean.js
index b1f0e83..e48f76b 100644
--- a/assets/en_api_mp_math_plane.md.D3xHJy8e.lean.js
+++ b/assets/en_api_mp_math_plane.md.BkRMq93h.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n("",116),t=[h];function p(e,k,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},h=n("",103),t=[h];function p(e,k,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_point.md.P1GRdc2H.js b/assets/en_api_mp_math_point.md.S7QlcMfS.js
similarity index 77%
rename from assets/en_api_mp_math_point.md.P1GRdc2H.js
rename to assets/en_api_mp_math_point.md.S7QlcMfS.js
index dfd3fc3..2e3a6ff 100644
--- a/assets/en_api_mp_math_point.md.P1GRdc2H.js
+++ b/assets/en_api_mp_math_point.md.S7QlcMfS.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},h=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},l=t(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Return: 是否近似相等
Arguments:
  • other:
  • epsilon:
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
+    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:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_point.md.P1GRdc2H.lean.js b/assets/en_api_mp_math_point.md.S7QlcMfS.lean.js
similarity index 71%
rename from assets/en_api_mp_math_point.md.P1GRdc2H.lean.js
rename to assets/en_api_mp_math_point.md.S7QlcMfS.lean.js
index 90dba7c..f995429 100644
--- a/assets/en_api_mp_math_point.md.P1GRdc2H.lean.js
+++ b/assets/en_api_mp_math_point.md.S7QlcMfS.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},h=t("",35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},l=t("",34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_segment.md.DqDvJpQR.js b/assets/en_api_mp_math_segment.md.CxreVgqR.js
similarity index 84%
rename from assets/en_api_mp_math_segment.md.DqDvJpQR.js
rename to assets/en_api_mp_math_segment.md.CxreVgqR.js
index eb3dad5..f462604 100644
--- a/assets/en_api_mp_math_segment.md.DqDvJpQR.js
+++ b/assets/en_api_mp_math_segment.md.CxreVgqR.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     '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)
`,4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y 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)
`,4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/en_api_mp_math_segment.md.DqDvJpQR.lean.js b/assets/en_api_mp_math_segment.md.CxreVgqR.lean.js
similarity index 85%
rename from assets/en_api_mp_math_segment.md.DqDvJpQR.lean.js
rename to assets/en_api_mp_math_segment.md.CxreVgqR.lean.js
index 10ebc2f..31daebf 100644
--- a/assets/en_api_mp_math_segment.md.DqDvJpQR.lean.js
+++ b/assets/en_api_mp_math_segment.md.CxreVgqR.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/en_api_mp_math_utils.md.B0nejTCy.js b/assets/en_api_mp_math_utils.md.B7bkEcyv.js
similarity index 76%
rename from assets/en_api_mp_math_utils.md.B0nejTCy.js
rename to assets/en_api_mp_math_utils.md.B7bkEcyv.js
index 641859c..5c84b87 100644
--- a/assets/en_api_mp_math_utils.md.B0nejTCy.js
+++ b/assets/en_api_mp_math_utils.md.B7bkEcyv.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),l={name:"en/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
区间限定函数
Arguments:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return:
  • 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),t={name:"en/api/mp_math/utils.md"},l=n(`
func clamp() -> float ​
Description: 区间限定函数
Return: 限制后的值
Arguments:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Return:
  • 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
Return: 是否近似相等
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Source code
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:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return:
  • 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
Description: 获取数的符号。
Return: 符号 + - ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return:
  • 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Return: 符号 + - ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,37),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[l];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_utils.md.B0nejTCy.lean.js b/assets/en_api_mp_math_utils.md.B7bkEcyv.lean.js
similarity index 57%
rename from assets/en_api_mp_math_utils.md.B0nejTCy.lean.js
rename to assets/en_api_mp_math_utils.md.B7bkEcyv.lean.js
index f3abe36..f7f1f3a 100644
--- a/assets/en_api_mp_math_utils.md.B0nejTCy.lean.js
+++ b/assets/en_api_mp_math_utils.md.B7bkEcyv.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),l={name:"en/api/mp_math/utils.md"},t=n("",37),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),t={name:"en/api/mp_math/utils.md"},l=n("",33),h=[l];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_vector.md.BpRKRIGw.js b/assets/en_api_mp_math_vector.md.BLUu1BnW.js
similarity index 81%
rename from assets/en_api_mp_math_vector.md.BpRKRIGw.js
rename to assets/en_api_mp_math_vector.md.BLUu1BnW.js
index a1687d7..383381b 100644
--- a/assets/en_api_mp_math_vector.md.BpRKRIGw.js
+++ b/assets/en_api_mp_math_vector.md.BLUu1BnW.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
Return: 是否近似相等
Arguments:
  • other:
  • epsilon:
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return:
  • 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Return: 夹角
Arguments:
  • other: 另一个向量
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • other:
Return:
  • 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Return: 行列式的结果
Arguments:
  • other:
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return:
  • 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Return: 是否近似平行
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Source code
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:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return:
  • 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Return: 是否平行
Arguments:
  • other: 另一个向量
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
Return:
  • 模
Source code
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
Return:
  • 单位向量
Source code
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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) ​
判断两个向量是否相等。
Arguments:
  • other:
Return:
  • 是否相等
Source code
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Return: 是否相等
Arguments:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
+    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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 ​
P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
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:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
`,133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
`,125),e=[h];function l(p,k,r,o,d,E){return a(),i("div",null,e)}const F=s(n,[["render",l]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_vector.md.BpRKRIGw.lean.js b/assets/en_api_mp_math_vector.md.BLUu1BnW.lean.js
similarity index 71%
rename from assets/en_api_mp_math_vector.md.BpRKRIGw.lean.js
rename to assets/en_api_mp_math_vector.md.BLUu1BnW.lean.js
index d177c3f..0c06b93 100644
--- a/assets/en_api_mp_math_vector.md.BpRKRIGw.lean.js
+++ b/assets/en_api_mp_math_vector.md.BLUu1BnW.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t("",133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t("",125),e=[h];function l(p,k,r,o,d,E){return a(),i("div",null,e)}const F=s(n,[["render",l]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_presets_model_index.md.j5zmPSwU.js b/assets/en_api_presets_model_index.md.Bd091b7b.js
similarity index 90%
rename from assets/en_api_presets_model_index.md.j5zmPSwU.js
rename to assets/en_api_presets_model_index.md.Bd091b7b.js
index 205228e..0cc6b7a 100644
--- a/assets/en_api_presets_model_index.md.j5zmPSwU.js
+++ b/assets/en_api_presets_model_index.md.Bd091b7b.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"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(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
生成球体上的点集。
Arguments:
  • radius:
  • density:
Return:
  • List[Point3]: 球体上的点集。
Source code
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"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(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Return: List[Point3]: 球体上的点集。
Arguments:
  • radius:
  • density:
Source code
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     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)]
`,9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/en_api_presets_model_index.md.j5zmPSwU.lean.js b/assets/en_api_presets_model_index.md.Bd091b7b.lean.js
similarity index 72%
rename from assets/en_api_presets_model_index.md.j5zmPSwU.lean.js
rename to assets/en_api_presets_model_index.md.Bd091b7b.lean.js
index 69c8af9..28f9d3a 100644
--- a/assets/en_api_presets_model_index.md.j5zmPSwU.lean.js
+++ b/assets/en_api_presets_model_index.md.Bd091b7b.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"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("",9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"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("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_angle.md.D2dStPZh.js b/assets/ja_api_mp_math_angle.md.DxBe_g0o.js
similarity index 82%
rename from assets/ja_api_mp_math_angle.md.D2dStPZh.js
rename to assets/ja_api_mp_math_angle.md.DxBe_g0o.js
index 01d7a73..cb5c395 100644
--- a/assets/ja_api_mp_math_angle.md.D2dStPZh.js
+++ b/assets/ja_api_mp_math_angle.md.DxBe_g0o.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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(`
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
戻り値:
  • 余角
ソースコード
python
@property
+        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
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 ​
补角：两角的和为180°。
戻り値:
  • 补角
ソースコード
python
@property
+    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
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 ​
角度。
戻り値:
  • 弧度
ソースコード
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
戻り値:
  • 最小正角度
ソースコード
python
@property
+    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
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 ​
最大负角。
戻り値:
  • 最大负角度
ソースコード
python
@property
+    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
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 ​
正弦值。
戻り値:
  • 正弦值
ソースコード
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
戻り値:
  • 余弦值
ソースコード
python
@property
+    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
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
戻り値:
  • 正切值
ソースコード
python
@property
+    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
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
戻り値:
  • 余切值
ソースコード
python
@property
+    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
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
戻り値:
  • 正割值
ソースコード
python
@property
+    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
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
戻り値:
  • 余割值
ソースコード
python
@property
+    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
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
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
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
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
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
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
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
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
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
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
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,89),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_angle.md.D2dStPZh.lean.js b/assets/ja_api_mp_math_angle.md.DxBe_g0o.lean.js
similarity index 71%
rename from assets/ja_api_mp_math_angle.md.D2dStPZh.lean.js
rename to assets/ja_api_mp_math_angle.md.DxBe_g0o.lean.js
index 48dff8f..0985b57 100644
--- a/assets/ja_api_mp_math_angle.md.D2dStPZh.lean.js
+++ b/assets/ja_api_mp_math_angle.md.DxBe_g0o.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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("",89),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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("",78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_equation.md.Cj8tgo_3.js b/assets/ja_api_mp_math_equation.md.CCgJ-L2G.js
similarity index 83%
rename from assets/ja_api_mp_math_equation.md.Cj8tgo_3.js
rename to assets/ja_api_mp_math_equation.md.CCgJ-L2G.js
index dc6213e..028c7f0 100644
--- a/assets/ja_api_mp_math_equation.md.Cj8tgo_3.js
+++ b/assets/ja_api_mp_math_equation.md.CCgJ-L2G.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
引数:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
戻り値: 偏导函数
引数:
  • func: 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
例外:
  • ValueError 无效变量类型
ソースコード
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。
     Args:
@@ -28,16 +28,16 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
ソースコード
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
ソースコード
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
ソースコード
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
ソースコード
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +47,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +59,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
     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))])
`,24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_equation.md.Cj8tgo_3.lean.js b/assets/ja_api_mp_math_equation.md.CCgJ-L2G.lean.js
similarity index 86%
rename from assets/ja_api_mp_math_equation.md.Cj8tgo_3.lean.js
rename to assets/ja_api_mp_math_equation.md.CCgJ-L2G.lean.js
index e34836e..83b725c 100644
--- a/assets/ja_api_mp_math_equation.md.Cj8tgo_3.lean.js
+++ b/assets/ja_api_mp_math_equation.md.CCgJ-L2G.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n("",24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n("",23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_line.md.Dg8duKLw.js b/assets/ja_api_mp_math_line.md.CxvAbM2L.js
similarity index 73%
rename from assets/ja_api_mp_math_line.md.Dg8duKLw.js
rename to assets/ja_api_mp_math_line.md.CxvAbM2L.js
index 2b18144..90c6f83 100644
--- a/assets/ja_api_mp_math_line.md.Dg8duKLw.js
+++ b/assets/ja_api_mp_math_line.md.CxvAbM2L.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n(`
class Line3 ​
method __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。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n(`
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: 直线上的一点
  • direction: 直线的方向向量
ソースコード
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:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
戻り値: 是否近似相等
引数:
  • other: 另一条直线
  • epsilon: 误差
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値:
  • 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
戻り値: 夹角弧度
引数:
  • other: 另一条直线
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値:
  • 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
戻り値: 距离
引数:
  • other: 平行直线或点
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値:
  • 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
戻り値: 交点
引数:
  • other: 另一条直线
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         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 ​
计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値:
  • 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
戻り値: 垂线
引数:
  • point: 指定点
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
引数:
  • t: 参数t
戻り値:
  • 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
戻り値: 点
引数:
  • t: 参数t
ソースコード
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:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
戻り値:
  • x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値:
  • 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
戻り値: 是否近似平行
引数:
  • other: 另一条直线
  • epsilon: 误差
ソースコード
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:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値:
  • 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
戻り値: 是否平行
引数:
  • other: 另一条直线
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値:
  • 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
戻り値: 是否共线
引数:
  • other: 另一条直线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
判断点是否在直线上。
引数:
  • point: 点
戻り値:
  • 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
戻り値: 是否在直线上
引数:
  • point: 点
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
引数:
  • other: 另一条直线
戻り値:
  • 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
戻り値: 是否共面
引数:
  • other: 另一条直线
ソースコード
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。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
ソースコード
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
引数:
  • p1: 点1
  • p2: 点2
戻り値:
  • 直线
ソースコード
python
@classmethod
+        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。
戻り値: 直线
引数:
  • p1: 点1
  • p2: 点2
ソースコード
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
引数:
  • other: 另一条直线
戻り値:
  • 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
戻り値: 交点
引数:
  • other: 另一条直线
ソースコード
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:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
+        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:
ソースコード
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,119),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_line.md.Dg8duKLw.lean.js b/assets/ja_api_mp_math_line.md.CxvAbM2L.lean.js
similarity index 85%
rename from assets/ja_api_mp_math_line.md.Dg8duKLw.lean.js
rename to assets/ja_api_mp_math_line.md.CxvAbM2L.lean.js
index d3a0964..8842389 100644
--- a/assets/ja_api_mp_math_line.md.Dg8duKLw.lean.js
+++ b/assets/ja_api_mp_math_line.md.CxvAbM2L.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n("",119),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n("",105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_plane.md.CTOkqSft.js b/assets/ja_api_mp_math_plane.md.DGnOnQrW.js
similarity index 82%
rename from assets/ja_api_mp_math_plane.md.CTOkqSft.js
rename to assets/ja_api_mp_math_plane.md.DGnOnQrW.js
index 75198d9..a9c992c 100644
--- a/assets/ja_api_mp_math_plane.md.CTOkqSft.js
+++ b/assets/ja_api_mp_math_plane.md.DGnOnQrW.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n(`
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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
戻り値: 是否近似相等
引数:
  • other: 另一个平面
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値:
  • 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
戻り値: 夹角弧度
引数:
  • other: 另一个平面
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値:
  • 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
戻り値: 距离
引数:
  • other: 另一个平面或点
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算两平面的交线。
引数:
  • other: 另一个平面
戻り値:
  • 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
戻り値: 两平面的交线
引数:
  • other: 另一个平面
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値:
  • 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
戻り値: 交点
引数:
  • other: 不与平面平行或在平面上的直线
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値:
  • 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
戻り値: 所求平面
引数:
  • point: 指定点
ソースコード
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:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値:
  • 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
戻り値: 是否平行
引数:
  • other: 另一个平面
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
戻り値:
  • 法向量
ソースコード
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
引数:
  • point: 平面上的一点
  • normal: 法向量
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
戻り値: 平面
引数:
  • point: 平面上的一点
  • normal: 法向量
ソースコード
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)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     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 ​
工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
戻り値: 平面
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
ソースコード
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。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
戻り値: 平面
引数:
  • l1: 直线1
  • l2: 直线2
ソースコード
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
戻り値: 平面
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
ソースコード
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。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
引数:
  • other:
戻り値:
  • 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
戻り値: 不平行平面的交线，平面平行返回None
引数:
  • other:
ソースコード
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,116),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_plane.md.CTOkqSft.lean.js b/assets/ja_api_mp_math_plane.md.DGnOnQrW.lean.js
similarity index 85%
rename from assets/ja_api_mp_math_plane.md.CTOkqSft.lean.js
rename to assets/ja_api_mp_math_plane.md.DGnOnQrW.lean.js
index f7f0be9..f33e85f 100644
--- a/assets/ja_api_mp_math_plane.md.CTOkqSft.lean.js
+++ b/assets/ja_api_mp_math_plane.md.DGnOnQrW.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n("",116),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n("",103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_point.md.ZsmRVuaC.js b/assets/ja_api_mp_math_point.md.0J5Y2wYa.js
similarity index 74%
rename from assets/ja_api_mp_math_point.md.ZsmRVuaC.js
rename to assets/ja_api_mp_math_point.md.0J5Y2wYa.js
index f953953..892ca50 100644
--- a/assets/ja_api_mp_math_point.md.ZsmRVuaC.js
+++ b/assets/ja_api_mp_math_point.md.0J5Y2wYa.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"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(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},l=t(`
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: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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。
戻り値: 是否近似相等
引数:
  • other:
  • epsilon:
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
引数:
  • other:
ソースコード
python
def __eq__(self, other):
+    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:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_point.md.ZsmRVuaC.lean.js b/assets/ja_api_mp_math_point.md.0J5Y2wYa.lean.js
similarity index 71%
rename from assets/ja_api_mp_math_point.md.ZsmRVuaC.lean.js
rename to assets/ja_api_mp_math_point.md.0J5Y2wYa.lean.js
index 3466d9a..735a512 100644
--- a/assets/ja_api_mp_math_point.md.ZsmRVuaC.lean.js
+++ b/assets/ja_api_mp_math_point.md.0J5Y2wYa.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"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("",35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},l=t("",34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_segment.md.D5ZKDDr_.js b/assets/ja_api_mp_math_segment.md.D0U5bMSu.js
similarity index 82%
rename from assets/ja_api_mp_math_segment.md.D5ZKDDr_.js
rename to assets/ja_api_mp_math_segment.md.D0U5bMSu.js
index afc42da..522a58c 100644
--- a/assets/ja_api_mp_math_segment.md.D5ZKDDr_.js
+++ b/assets/ja_api_mp_math_segment.md.D0U5bMSu.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
     '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)
`,4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const o=s(t,[["render",l]]);export{y as __pageData,o 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)
`,4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_segment.md.D5ZKDDr_.lean.js b/assets/ja_api_mp_math_segment.md.D0U5bMSu.lean.js
similarity index 57%
rename from assets/ja_api_mp_math_segment.md.D5ZKDDr_.lean.js
rename to assets/ja_api_mp_math_segment.md.D0U5bMSu.lean.js
index 91c8dde..72f6bf5 100644
--- a/assets/ja_api_mp_math_segment.md.D5ZKDDr_.lean.js
+++ b/assets/ja_api_mp_math_segment.md.D0U5bMSu.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const o=s(t,[["render",l]]);export{y as __pageData,o as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_utils.md.jeRmCp2Q.js b/assets/ja_api_mp_math_utils.md.zOjWX1mJ.js
similarity index 77%
rename from assets/ja_api_mp_math_utils.md.jeRmCp2Q.js
rename to assets/ja_api_mp_math_utils.md.zOjWX1mJ.js
index 0c0c990..4a0fc8f 100644
--- a/assets/ja_api_mp_math_utils.md.jeRmCp2Q.js
+++ b/assets/ja_api_mp_math_utils.md.zOjWX1mJ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
区间限定函数
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値:
  • 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
説明: 区间限定函数
戻り値: 限制后的值
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
戻り値:
  • 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
戻り値: 是否近似相等
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
ソースコード
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:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値:
  • 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
説明: 获取数的符号。
戻り値: 符号 + - ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値:
  • 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
戻り値: 符号 + - ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
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
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,37),h=[t];function p(k,e,r,d,g,F){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
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
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_utils.md.jeRmCp2Q.lean.js b/assets/ja_api_mp_math_utils.md.zOjWX1mJ.lean.js
similarity index 85%
rename from assets/ja_api_mp_math_utils.md.jeRmCp2Q.lean.js
rename to assets/ja_api_mp_math_utils.md.zOjWX1mJ.lean.js
index 627f47a..33263b4 100644
--- a/assets/ja_api_mp_math_utils.md.jeRmCp2Q.lean.js
+++ b/assets/ja_api_mp_math_utils.md.zOjWX1mJ.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n("",37),h=[t];function p(k,e,r,d,g,F){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n("",33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_vector.md.DAXdHSjp.js b/assets/ja_api_mp_math_vector.md.DiKIzhuY.js
similarity index 81%
rename from assets/ja_api_mp_math_vector.md.DAXdHSjp.js
rename to assets/ja_api_mp_math_vector.md.DiKIzhuY.js
index 71d30c1..5f7c6dd 100644
--- a/assets/ja_api_mp_math_vector.md.DAXdHSjp.js
+++ b/assets/ja_api_mp_math_vector.md.DiKIzhuY.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
引数:
  • other:
  • epsilon:
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
戻り値: 是否近似相等
引数:
  • other:
  • epsilon:
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値:
  • 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
戻り値: 夹角
引数:
  • other: 另一个向量
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • other:
戻り値:
  • 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
戻り値: 行列式的结果
引数:
  • other:
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値:
  • 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
戻り値: 是否近似平行
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
ソースコード
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:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値:
  • 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
戻り値: 是否平行
引数:
  • other: 另一个向量
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
戻り値:
  • 模
ソースコード
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
戻り値:
  • 单位向量
ソースコード
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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) ​
判断两个向量是否相等。
引数:
  • other:
戻り値:
  • 是否相等
ソースコード
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
戻り値: 是否相等
引数:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    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
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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 ​
P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
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:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
`,133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_vector.md.DAXdHSjp.lean.js b/assets/ja_api_mp_math_vector.md.DiKIzhuY.lean.js
similarity index 85%
rename from assets/ja_api_mp_math_vector.md.DAXdHSjp.lean.js
rename to assets/ja_api_mp_math_vector.md.DiKIzhuY.lean.js
index f6ef7be..a9174df 100644
--- a/assets/ja_api_mp_math_vector.md.DAXdHSjp.lean.js
+++ b/assets/ja_api_mp_math_vector.md.DiKIzhuY.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t("",133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_presets_model_index.md.CleEI4sj.js b/assets/ja_api_presets_model_index.md.Be7yN1vu.js
similarity index 90%
rename from assets/ja_api_presets_model_index.md.CleEI4sj.js
rename to assets/ja_api_presets_model_index.md.Be7yN1vu.js
index 699e103..21cecbb 100644
--- a/assets/ja_api_presets_model_index.md.CleEI4sj.js
+++ b/assets/ja_api_presets_model_index.md.Be7yN1vu.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
戻り値: List[Point3]: 球体上的点集。
引数:
  • radius:
  • density:
ソースコード
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     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)]
`,9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/ja_api_presets_model_index.md.CleEI4sj.lean.js b/assets/ja_api_presets_model_index.md.Be7yN1vu.lean.js
similarity index 72%
rename from assets/ja_api_presets_model_index.md.CleEI4sj.lean.js
rename to assets/ja_api_presets_model_index.md.Be7yN1vu.lean.js
index 9f1e55f..8f9992c 100644
--- a/assets/ja_api_presets_model_index.md.CleEI4sj.lean.js
+++ b/assets/ja_api_presets_model_index.md.Be7yN1vu.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_angle.md.CMQhsVJf.js b/assets/zht_api_mp_math_angle.md._4N19GGe.js
similarity index 82%
rename from assets/zht_api_mp_math_angle.md.CMQhsVJf.js
rename to assets/zht_api_mp_math_angle.md._4N19GGe.js
index b29a4c0..7c2b91f 100644
--- a/assets/zht_api_mp_math_angle.md.CMQhsVJf.js
+++ b/assets/zht_api_mp_math_angle.md._4N19GGe.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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(`
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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(`
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
返回:
  • 余角
源碼
python
@property
+        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
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 ​
补角：两角的和为180°。
返回:
  • 补角
源碼
python
@property
+    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
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 ​
角度。
返回:
  • 弧度
源碼
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
返回:
  • 最小正角度
源碼
python
@property
+    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
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 ​
最大负角。
返回:
  • 最大负角度
源碼
python
@property
+    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
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 ​
正弦值。
返回:
  • 正弦值
源碼
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
返回:
  • 余弦值
源碼
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
返回:
  • 正切值
源碼
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
返回:
  • 余切值
源碼
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
返回:
  • 正割值
源碼
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
返回:
  • 余割值
源碼
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
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
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源碼
python
def __truediv__(self, other):
+    ...
method self / other ​
源碼
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,89),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_angle.md.CMQhsVJf.lean.js b/assets/zht_api_mp_math_angle.md._4N19GGe.lean.js
similarity index 71%
rename from assets/zht_api_mp_math_angle.md.CMQhsVJf.lean.js
rename to assets/zht_api_mp_math_angle.md._4N19GGe.lean.js
index 32e4911..d02fff3 100644
--- a/assets/zht_api_mp_math_angle.md.CMQhsVJf.lean.js
+++ b/assets/zht_api_mp_math_angle.md._4N19GGe.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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("",89),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle"},"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("",78),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_equation.md.BwlIZxDL.js b/assets/zht_api_mp_math_equation.md.C9cWPaC8.js
similarity index 83%
rename from assets/zht_api_mp_math_equation.md.BwlIZxDL.js
rename to assets/zht_api_mp_math_equation.md.C9cWPaC8.js
index 0a0da10..72f0338 100644
--- a/assets/zht_api_mp_math_equation.md.BwlIZxDL.js
+++ b/assets/zht_api_mp_math_equation.md.C9cWPaC8.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
變數説明:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n(`
func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
返回: 偏导函数
變數説明:
  • func: 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
抛出:
  • ValueError 无效变量类型
源碼
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。
     Args:
@@ -28,16 +28,16 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源碼
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源碼
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源碼
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源碼
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -47,7 +47,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -59,4 +59,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
     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))])
`,24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
`,23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_equation.md.BwlIZxDL.lean.js b/assets/zht_api_mp_math_equation.md.C9cWPaC8.lean.js
similarity index 86%
rename from assets/zht_api_mp_math_equation.md.BwlIZxDL.lean.js
rename to assets/zht_api_mp_math_equation.md.C9cWPaC8.lean.js
index e2e34f2..7a9c189 100644
--- a/assets/zht_api_mp_math_equation.md.BwlIZxDL.lean.js
+++ b/assets/zht_api_mp_math_equation.md.C9cWPaC8.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n("",24),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation"},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n("",23),h=[t];function p(k,e,r,E,d,g){return a(),i("div",null,h)}const u=s(l,[["render",p]]);export{y as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_line.md.Czel-DYb.js b/assets/zht_api_mp_math_line.md.CG1Yioz9.js
similarity index 72%
rename from assets/zht_api_mp_math_line.md.Czel-DYb.js
rename to assets/zht_api_mp_math_line.md.CG1Yioz9.js
index db37b00..32405ce 100644
--- a/assets/zht_api_mp_math_line.md.Czel-DYb.js
+++ b/assets/zht_api_mp_math_line.md.CG1Yioz9.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n(`
class Line3 ​
method __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。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n(`
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: 直线上的一点
  • direction: 直线的方向向量
源碼
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:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
變數説明:
  • other: 另一条直线
  • epsilon: 误差
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回:
  • 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
返回: 夹角弧度
變數説明:
  • other: 另一条直线
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回:
  • 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
返回: 距离
變數説明:
  • other: 平行直线或点
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回:
  • 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
返回: 交点
變數説明:
  • other: 另一条直线
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         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 ​
计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回:
  • 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
返回: 垂线
變數説明:
  • point: 指定点
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
變數説明:
  • t: 参数t
返回:
  • 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
返回: 点
變數説明:
  • t: 参数t
源碼
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:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
返回:
  • x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
返回: 是否近似平行
變數説明:
  • other: 另一条直线
  • epsilon: 误差
源碼
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:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回:
  • 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
返回: 是否平行
變數説明:
  • other: 另一条直线
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回:
  • 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
返回: 是否共线
變數説明:
  • other: 另一条直线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             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 ​
判断点是否在直线上。
變數説明:
  • point: 点
返回:
  • 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
返回: 是否在直线上
變數説明:
  • point: 点
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
變數説明:
  • other: 另一条直线
返回:
  • 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
返回: 是否共面
變數説明:
  • other: 另一条直线
源碼
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。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
源碼
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
變數説明:
  • p1: 点1
  • p2: 点2
返回:
  • 直线
源碼
python
@classmethod
+        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。
返回: 直线
變數説明:
  • p1: 点1
  • p2: 点2
源碼
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
變數説明:
  • other: 另一条直线
返回:
  • 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
返回: 交点
變數説明:
  • other: 另一条直线
源碼
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:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
+        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:
源碼
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,119),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_line.md.Czel-DYb.lean.js b/assets/zht_api_mp_math_line.md.CG1Yioz9.lean.js
similarity index 85%
rename from assets/zht_api_mp_math_line.md.Czel-DYb.lean.js
rename to assets/zht_api_mp_math_line.md.CG1Yioz9.lean.js
index 1502b9d..8d2d9e6 100644
--- a/assets/zht_api_mp_math_line.md.Czel-DYb.lean.js
+++ b/assets/zht_api_mp_math_line.md.CG1Yioz9.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n("",119),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line"},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n("",105),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.CxUaQCvU.js b/assets/zht_api_mp_math_plane.md.jJjMMFlO.js
similarity index 83%
rename from assets/zht_api_mp_math_plane.md.CxUaQCvU.js
rename to assets/zht_api_mp_math_plane.md.jJjMMFlO.js
index f626c3f..4e555ae 100644
--- a/assets/zht_api_mp_math_plane.md.CxUaQCvU.js
+++ b/assets/zht_api_mp_math_plane.md.jJjMMFlO.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n(`
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n(`
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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
變數説明:
  • other: 另一个平面
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
返回: 是否近似相等
變數説明:
  • other: 另一个平面
源碼
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回:
  • 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
返回: 夹角弧度
變數説明:
  • other: 另一个平面
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回:
  • 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
返回: 距离
變數説明:
  • other: 另一个平面或点
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
计算两平面的交线。
變數説明:
  • other: 另一个平面
返回:
  • 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
返回: 两平面的交线
變數説明:
  • other: 另一个平面
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回:
  • 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
返回: 交点
變數説明:
  • other: 不与平面平行或在平面上的直线
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         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 ​
计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回:
  • 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
返回: 所求平面
變數説明:
  • point: 指定点
源碼
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:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回:
  • 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
返回: 是否平行
變數説明:
  • other: 另一个平面
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
返回:
  • 法向量
源碼
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
變數説明:
  • point: 平面上的一点
  • normal: 法向量
返回:
  • 平面
源碼
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
返回: 平面
變數説明:
  • point: 平面上的一点
  • normal: 法向量
源碼
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)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         """
     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 ​
工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回:
  • 平面
源碼
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
返回: 平面
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
源碼
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。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回:
  • 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
返回: 平面
變數説明:
  • l1: 直线1
  • l2: 直线2
源碼
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
     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 ​
工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回:
  • 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
返回: 平面
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
源碼
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。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
變數説明:
  • other:
返回:
  • 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
返回: 不平行平面的交线，平面平行返回None
變數説明:
  • other:
源碼
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,116),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.CxUaQCvU.lean.js b/assets/zht_api_mp_math_plane.md.jJjMMFlO.lean.js
similarity index 85%
rename from assets/zht_api_mp_math_plane.md.CxUaQCvU.lean.js
rename to assets/zht_api_mp_math_plane.md.jJjMMFlO.lean.js
index 8482a1d..9765112 100644
--- a/assets/zht_api_mp_math_plane.md.CxUaQCvU.lean.js
+++ b/assets/zht_api_mp_math_plane.md.jJjMMFlO.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n("",116),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane"},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n("",103),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_point.md.BmRy6Xj6.js b/assets/zht_api_mp_math_point.md.CRxiJq-m.js
similarity index 74%
rename from assets/zht_api_mp_math_point.md.BmRy6Xj6.js
rename to assets/zht_api_mp_math_point.md.CRxiJq-m.js
index 09fd819..a5044ce 100644
--- a/assets/zht_api_mp_math_point.md.BmRy6Xj6.js
+++ b/assets/zht_api_mp_math_point.md.CRxiJq-m.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"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(`
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},l=t(`
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: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
變數説明:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
變數説明:
  • other:
  • epsilon:
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
+    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:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_point.md.BmRy6Xj6.lean.js b/assets/zht_api_mp_math_point.md.CRxiJq-m.lean.js
similarity index 71%
rename from assets/zht_api_mp_math_point.md.BmRy6Xj6.lean.js
rename to assets/zht_api_mp_math_point.md.CRxiJq-m.lean.js
index 71132cb..606cff7 100644
--- a/assets/zht_api_mp_math_point.md.BmRy6Xj6.lean.js
+++ b/assets/zht_api_mp_math_point.md.CRxiJq-m.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"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("",35),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point"},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},l=t("",34),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_segment.md.Bn34DhAl.js b/assets/zht_api_mp_math_segment.md.U_lS4vUA.js
similarity index 83%
rename from assets/zht_api_mp_math_segment.md.Bn34DhAl.js
rename to assets/zht_api_mp_math_segment.md.U_lS4vUA.js
index d30797a..4e078d7 100644
--- a/assets/zht_api_mp_math_segment.md.Bn34DhAl.js
+++ b/assets/zht_api_mp_math_segment.md.U_lS4vUA.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n(`
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y
     '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)
`,4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const o=s(t,[["render",l]]);export{y as __pageData,o 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)
`,4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_segment.md.Bn34DhAl.lean.js b/assets/zht_api_mp_math_segment.md.U_lS4vUA.lean.js
similarity index 58%
rename from assets/zht_api_mp_math_segment.md.Bn34DhAl.lean.js
rename to assets/zht_api_mp_math_segment.md.U_lS4vUA.lean.js
index 7b7a204..8f983aa 100644
--- a/assets/zht_api_mp_math_segment.md.Bn34DhAl.lean.js
+++ b/assets/zht_api_mp_math_segment.md.U_lS4vUA.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,d,r,E,g){return a(),i("div",null,p)}const o=s(t,[["render",l]]);export{y as __pageData,o as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment"},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n("",4),p=[h];function l(k,e,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_utils.md.BtiDgiKf.js b/assets/zht_api_mp_math_utils.md.wrAVKQq5.js
similarity index 77%
rename from assets/zht_api_mp_math_utils.md.BtiDgiKf.js
rename to assets/zht_api_mp_math_utils.md.wrAVKQq5.js
index 6ee4438..1cd5d1b 100644
--- a/assets/zht_api_mp_math_utils.md.BtiDgiKf.js
+++ b/assets/zht_api_mp_math_utils.md.wrAVKQq5.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
区间限定函数
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回:
  • 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n(`
func clamp() -> float ​
説明: 区间限定函数
返回: 限制后的值
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,7 +9,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
變數説明:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回:
  • 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
返回: 是否近似相等
變數説明:
  • x: 数1
  • y: 数2
  • epsilon: 误差
源碼
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:
@@ -19,7 +19,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
説明: 获取数的符号。
返回: 符号 + - ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
返回: 符号 + - ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -48,8 +48,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -59,6 +59,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
-    return not self.__eq__(other)
`,37),h=[t];function p(k,e,r,d,g,F){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
+    return not self.__eq__(other)
`,33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_utils.md.BtiDgiKf.lean.js b/assets/zht_api_mp_math_utils.md.wrAVKQq5.lean.js
similarity index 85%
rename from assets/zht_api_mp_math_utils.md.BtiDgiKf.lean.js
rename to assets/zht_api_mp_math_utils.md.wrAVKQq5.lean.js
index c055d01..32646d9 100644
--- a/assets/zht_api_mp_math_utils.md.BtiDgiKf.lean.js
+++ b/assets/zht_api_mp_math_utils.md.wrAVKQq5.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n("",37),h=[t];function p(k,e,r,d,g,F){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils"},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n("",33),h=[t];function p(k,e,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_vector.md.DmxfMXiN.js b/assets/zht_api_mp_math_vector.md.B2jIk2y0.js
similarity index 81%
rename from assets/zht_api_mp_math_vector.md.DmxfMXiN.js
rename to assets/zht_api_mp_math_vector.md.B2jIk2y0.js
index f0bba58..db64f2e 100644
--- a/assets/zht_api_mp_math_vector.md.DmxfMXiN.js
+++ b/assets/zht_api_mp_math_vector.md.B2jIk2y0.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t(`
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
變數説明:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
變數説明:
  • other:
  • epsilon:
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回:
  • 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
返回: 夹角
變數説明:
  • other: 另一个向量
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • other:
返回:
  • 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
返回: 行列式的结果
變數説明:
  • other:
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回:
  • 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
返回: 是否近似平行
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
源碼
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:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回:
  • 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
返回: 是否平行
變數説明:
  • other: 另一个向量
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
返回:
  • 模
源碼
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
返回:
  • 单位向量
源碼
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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) ​
判断两个向量是否相等。
變數説明:
  • other:
返回:
  • 是否相等
源碼
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
返回: 是否相等
變數説明:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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 ​
P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
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:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
`,133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
`,125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_vector.md.DmxfMXiN.lean.js b/assets/zht_api_mp_math_vector.md.B2jIk2y0.lean.js
similarity index 85%
rename from assets/zht_api_mp_math_vector.md.DmxfMXiN.lean.js
rename to assets/zht_api_mp_math_vector.md.B2jIk2y0.lean.js
index 5bbc640..38a3194 100644
--- a/assets/zht_api_mp_math_vector.md.DmxfMXiN.lean.js
+++ b/assets/zht_api_mp_math_vector.md.B2jIk2y0.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",133),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.BV61Qrc0.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector"},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",125),l=[h];function e(p,k,r,o,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.DDom2SLG.js b/assets/zht_api_presets_model_index.md.CPzp1vmU.js
similarity index 90%
rename from assets/zht_api_presets_model_index.md.DDom2SLG.js
rename to assets/zht_api_presets_model_index.md.CPzp1vmU.js
index b44f611..bbf87b3 100644
--- a/assets/zht_api_presets_model_index.md.DDom2SLG.js
+++ b/assets/zht_api_presets_model_index.md.CPzp1vmU.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n(`
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
返回: List[Point3]: 球体上的点集。
變數説明:
  • radius:
  • density:
源碼
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o
     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)]
`,9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.DDom2SLG.lean.js b/assets/zht_api_presets_model_index.md.CPzp1vmU.lean.js
similarity index 72%
rename from assets/zht_api_presets_model_index.md.DDom2SLG.lean.js
rename to assets/zht_api_presets_model_index.md.CPzp1vmU.lean.js
index 2fc38dc..8e76554 100644
--- a/assets/zht_api_presets_model_index.md.DDom2SLG.lean.js
+++ b/assets/zht_api_presets_model_index.md.CPzp1vmU.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n("",9),l=[h];function p(k,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.BV61Qrc0.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model"},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n("",8),l=[h];function k(p,e,r,d,E,y){return a(),i("div",null,l)}const F=s(t,[["render",k]]);export{o as __pageData,F as default};
diff --git a/en/api/index.html b/en/api/index.html
index d2c8ab1..b12632d 100644
--- a/en/api/index.html
+++ b/en/api/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index 5a259b8..821ef28 100644
--- a/en/api/mp_math/angle.html
+++ b/en/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
Return:
  • 余角
Source code
python
@property
+        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
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 ​
补角：两角的和为180°。
Return:
  • 补角
Source code
python
@property
+    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
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 ​
角度。
Return:
  • 弧度
Source code
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
Return:
  • 最小正角度
Source code
python
@property
+    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
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 ​
最大负角。
Return:
  • 最大负角度
Source code
python
@property
+    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
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 ​
正弦值。
Return:
  • 正弦值
Source code
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
Return:
  • 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
Return:
  • 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
Return:
  • 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
Return:
  • 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
Return:
  • 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
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
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
Source code
python
def __truediv__(self, other):
+    ...
method self / other ​
Source code
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html
index 3bb0d7b..3f5fba2 100644
--- a/en/api/mp_math/const.html
+++ b/en/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html
index 2b78516..51aa6bf 100644
--- a/en/api/mp_math/equation.html
+++ b/en/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Arguments:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
Return: 偏导函数
Arguments:
  • func: 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
Raises:
  • ValueError 无效变量类型
Source code
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。
     Args:
@@ -47,16 +47,16 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
Source code
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
Source code
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
Source code
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
Source code
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +66,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +79,7 @@
         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))])

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html
index b544708..78ab216 100644
--- a/en/api/mp_math/index.html
+++ b/en/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html
index 106c9ea..580c008 100644
--- a/en/api/mp_math/line.html
+++ b/en/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Line3 ​
method __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。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
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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: 直线上的一点
  • direction: 直线的方向向量
Source code
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:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
Return: 是否近似相等
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             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 ​
计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return:
  • 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
Return: 夹角弧度
Arguments:
  • other: 另一条直线
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return:
  • 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
Return: 距离
Arguments:
  • other: 平行直线或点
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return:
  • 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Return: 交点
Arguments:
  • other: 另一条直线
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         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 ​
计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return:
  • 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
Return: 垂线
Arguments:
  • point: 指定点
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
Arguments:
  • t: 参数t
Return:
  • 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
Return: 点
Arguments:
  • t: 参数t
Source code
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:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
Return:
  • x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return:
  • 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
Return: 是否近似平行
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Source code
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:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return:
  • 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
Return: 是否平行
Arguments:
  • other: 另一条直线
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return:
  • 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
Return: 是否共线
Arguments:
  • other: 另一条直线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             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 ​
判断点是否在直线上。
Arguments:
  • point: 点
Return:
  • 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
Return: 是否在直线上
Arguments:
  • point: 点
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
Arguments:
  • other: 另一条直线
Return:
  • 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
Return: 是否共面
Arguments:
  • other: 另一条直线
Source code
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。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
Source code
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return:
  • 直线
Source code
python
@classmethod
+        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。
Return: 直线
Arguments:
  • p1: 点1
  • p2: 点2
Source code
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
Arguments:
  • other: 另一条直线
Return:
  • 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
Return: 交点
Arguments:
  • other: 另一条直线
Source code
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:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
+        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:
Source code
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
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diff --git a/en/api/mp_math/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html
index 2cc94d0..0410dfd 100644
--- a/en/api/mp_math/mp_math_typing.html
+++ b/en/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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var RealNumber = int | float ​
  • Type: TypeAlias
var Number = RealNumber | complex ​
  • Type: TypeAlias
var Var = SingleVar | ArrayVar ​
  • Type: TypeAlias
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • Type: TypeAlias
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • Type: TypeAlias
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • Type: TypeAlias
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • Type: TypeAlias
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • Type: TypeAlias
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • Type: TypeAlias
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • Type: TypeAlias
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • Type: TypeAlias
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • Type: TypeAlias
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • Type: TypeAlias
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • Type: TypeAlias
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • Type: TypeAlias

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html
index 1f363da..0d23a51 100644
--- a/en/api/mp_math/plane.html
+++ b/en/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
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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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Return: 是否近似相等
Arguments:
  • other: 另一个平面
Source code
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         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 ​
计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return:
  • 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Return: 夹角弧度
Arguments:
  • other: 另一个平面
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return:
  • 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Return: 距离
Arguments:
  • other: 另一个平面或点
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     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 ​
计算两平面的交线。
Arguments:
  • other: 另一个平面
Return:
  • 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Return: 两平面的交线
Arguments:
  • other: 另一个平面
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return:
  • 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Return: 交点
Arguments:
  • other: 不与平面平行或在平面上的直线
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return:
  • 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Return: 所求平面
Arguments:
  • point: 指定点
Source code
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:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return:
  • 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Return: 是否平行
Arguments:
  • other: 另一个平面
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
Return:
  • 法向量
Source code
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Return:
  • 平面
Source code
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Return: 平面
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Source code
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)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return:
  • 平面
Source code
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Return: 平面
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Source code
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。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return:
  • 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Return: 平面
Arguments:
  • l1: 直线1
  • l2: 直线2
Source code
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return:
  • 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Return: 平面
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Source code
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。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
Arguments:
  • other:
Return:
  • 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Return: 不平行平面的交线，平面平行返回None
Arguments:
  • other:
Source code
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html
index 91314cb..d04df87 100644
--- a/en/api/mp_math/point.html
+++ b/en/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Return: 是否近似相等
Arguments:
  • other:
  • epsilon:
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
+    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:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html
index f46d684..e2290d2 100644
--- a/en/api/mp_math/segment.html
+++ b/en/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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English
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html
index d206132..050a02a 100644
--- a/en/api/mp_math/utils.html
+++ b/en/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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func clamp() -> float ​
区间限定函数
Arguments:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return:
  • 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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func clamp() -> float ​
Description: 区间限定函数
Return: 限制后的值
Arguments:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Return:
  • 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
Return: 是否近似相等
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Source code
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:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return:
  • 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
Description: 获取数的符号。
Return: 符号 + - ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return:
  • 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Return: 符号 + - ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html
index 2bd78d6..d97d0bb 100644
--- a/en/api/mp_math/vector.html
+++ b/en/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
+    
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return:
  • 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
Return: 是否近似相等
Arguments:
  • other:
  • epsilon:
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             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 ​
计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return:
  • 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Return: 夹角
Arguments:
  • other: 另一个向量
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • other:
Return:
  • 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Return: 行列式的结果
Arguments:
  • other:
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return:
  • 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Return: 是否近似平行
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Source code
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:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return:
  • 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Return: 是否平行
Arguments:
  • other: 另一个向量
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
Return:
  • 模
Source code
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
Return:
  • 单位向量
Source code
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
判断两个向量是否相等。
Arguments:
  • other:
Return:
  • 是否相等
Source code
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Return: 是否相等
Arguments:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
+    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
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:
@@ -193,18 +193,18 @@
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/particle/index.html b/en/api/particle/index.html
index 26cf445..df4e322 100644
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+++ b/en/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
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diff --git a/en/api/presets/index.html b/en/api/presets/index.html
index 3d4f738..32da63f 100644
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diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html
index 4057700..192420f 100644
--- a/en/api/presets/model/index.html
+++ b/en/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
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-    
MBCP docs
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class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
生成球体上的点集。
Arguments:
  • radius:
  • density:
Return:
  • List[Point3]: 球体上的点集。
Source code
python
@staticmethod
+    
MBCP docs
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class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Return: List[Point3]: 球体上的点集。
Arguments:
  • radius:
  • density:
Source code
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     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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+    
     
   
 
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diff --git a/guide/index.html b/guide/index.html
index 484e0c0..1a5b54e 100644
--- a/guide/index.html
+++ b/guide/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
简体中文
English
日本語
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简体中文
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开始不了一点 ​

-    
+    
     
   
 
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diff --git a/hashmap.json b/hashmap.json
index 004e0f2..47693e4 100644
--- a/hashmap.json
+++ b/hashmap.json
@@ -1 +1 @@
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+{"api-ex.md":"DOsKaL8H","api_index.md":"BvazTqTB","api_mp_math_angle.md":"B8w0LP6o","api_mp_math_const.md":"BzOZuyZq","api_mp_math_equation.md":"Bx4yJe6o","api_mp_math_index.md":"4P0hk6gb","api_mp_math_line.md":"B1s7_FXM","api_mp_math_mp_math_typing.md":"B0OaWJmF","api_mp_math_plane.md":"BiW2-xb_","api_mp_math_point.md":"Cl5vX84g","api_mp_math_segment.md":"C6i78ST1","api_mp_math_utils.md":"B902hNw4","api_mp_math_vector.md":"CoooOTww","api_particle_index.md":"BRCSxC3e","api_presets_index.md":"Dl6Ss91J","api_presets_model_index.md":"kSDvd14X","en_api_index.md":"Bgu-LD1B","en_api_mp_math_angle.md":"DmK_A9xI","en_api_mp_math_const.md":"6yNmEodn","en_api_mp_math_equation.md":"BHF2EYD-","en_api_mp_math_index.md":"DrjDUYBY","en_api_mp_math_line.md":"B9L-UwK8","en_api_mp_math_mp_math_typing.md":"Ba9aYPR2","en_api_mp_math_plane.md":"BkRMq93h","en_api_mp_math_point.md":"S7QlcMfS","en_api_mp_math_segment.md":"CxreVgqR","en_api_mp_math_utils.md":"B7bkEcyv","en_api_mp_math_vector.md":"BLUu1BnW","en_api_particle_index.md":"CmC1QX5o","en_api_presets_index.md":"CZ5hl_7D","en_api_presets_model_index.md":"Bd091b7b","guide_index.md":"BE2yloik","index.md":"BE1qChTt","ja_api_index.md":"4BnflFIm","ja_api_mp_math_angle.md":"DxBe_g0o","ja_api_mp_math_const.md":"CflutYeA","ja_api_mp_math_equation.md":"CCgJ-L2G","ja_api_mp_math_index.md":"CSAMHYsB","ja_api_mp_math_line.md":"CxvAbM2L","ja_api_mp_math_mp_math_typing.md":"Bhy6h0r0","ja_api_mp_math_plane.md":"DGnOnQrW","ja_api_mp_math_point.md":"0J5Y2wYa","ja_api_mp_math_segment.md":"D0U5bMSu","ja_api_mp_math_utils.md":"zOjWX1mJ","ja_api_mp_math_vector.md":"DiKIzhuY","ja_api_particle_index.md":"E2YnH7EN","ja_api_presets_index.md":"ATGcHt9d","ja_api_presets_model_index.md":"Be7yN1vu","md-ex.md":"BX0WqOqv","zh-hant_api_index.md":"D-iBkJb-","zh-hant_api_mp_math_angle.md":"eKQSpiMX","zh-hant_api_mp_math_const.md":"B_tZ9wL7","zh-hant_api_mp_math_equation.md":"DPinrp8_","zh-hant_api_mp_math_index.md":"B8NLV8Cf","zh-hant_api_mp_math_line.md":"B-s8aLxY","zh-hant_api_mp_math_mp_math_typing.md":"DOwDUOu8","zh-hant_api_mp_math_plane.md":"B60Bzq3i","zh-hant_api_mp_math_point.md":"BEsHV_8G","zh-hant_api_mp_math_segment.md":"C-4eJk-Y","zh-hant_api_mp_math_utils.md":"z2lMMpnT","zh-hant_api_mp_math_vector.md":"n5Efae6D","zh-hant_api_particle_index.md":"BlduIPtw","zh-hant_api_presets_index.md":"CDyg87e9","zh-hant_api_presets_model_index.md":"DCHpjjZ_","zht_api_index.md":"Dq4XPUKZ","zht_api_mp_math_angle.md":"_4N19GGe","zht_api_mp_math_const.md":"CIhADrI2","zht_api_mp_math_equation.md":"C9cWPaC8","zht_api_mp_math_index.md":"D09y2ubg","zht_api_mp_math_line.md":"CG1Yioz9","zht_api_mp_math_mp_math_typing.md":"DlxSozR9","zht_api_mp_math_plane.md":"jJjMMFlO","zht_api_mp_math_point.md":"CRxiJq-m","zht_api_mp_math_segment.md":"U_lS4vUA","zht_api_mp_math_utils.md":"wrAVKQq5","zht_api_mp_math_vector.md":"B2jIk2y0","zht_api_particle_index.md":"kAm9VAEw","zht_api_presets_index.md":"BmouaEaT","zht_api_presets_model_index.md":"CPzp1vmU"}
diff --git a/index.html b/index.html
index 6e39a3c..f867032 100644
--- a/index.html
+++ b/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
简体中文
English
日本語
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简体中文
English
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Appearance
MBCP docs
More basic change particle
用于几何运算和粒子制作的库
快速开始
API文档
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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diff --git a/ja/api/index.html b/ja/api/index.html
index e268c1e..0e08d28 100644
--- a/ja/api/index.html
+++ b/ja/api/index.html
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diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html
index 02aaee1..e8247da 100644
--- a/ja/api/mp_math/angle.html
+++ b/ja/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
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class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
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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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
戻り値:
  • 余角
ソースコード
python
@property
+        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
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 ​
补角：两角的和为180°。
戻り値:
  • 补角
ソースコード
python
@property
+    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
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 ​
角度。
戻り値:
  • 弧度
ソースコード
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
戻り値:
  • 最小正角度
ソースコード
python
@property
+    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
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 ​
最大负角。
戻り値:
  • 最大负角度
ソースコード
python
@property
+    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
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 ​
正弦值。
戻り値:
  • 正弦值
ソースコード
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
戻り値:
  • 余弦值
ソースコード
python
@property
+    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
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
戻り値:
  • 正切值
ソースコード
python
@property
+    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
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
戻り値:
  • 余切值
ソースコード
python
@property
+    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
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
戻り値:
  • 正割值
ソースコード
python
@property
+    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
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
戻り値:
  • 余割值
ソースコード
python
@property
+    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
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
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
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
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
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
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
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
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
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
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
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html
index c6f66df..2279d26 100644
--- a/ja/api/mp_math/const.html
+++ b/ja/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
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diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html
index a376aa1..7735b3a 100644
--- a/ja/api/mp_math/equation.html
+++ b/ja/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
引数:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
戻り値: 偏导函数
引数:
  • func: 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
例外:
  • ValueError 无效变量类型
ソースコード
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。
     Args:
@@ -47,16 +47,16 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
ソースコード
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
ソースコード
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
ソースコード
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
ソースコード
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +66,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +79,7 @@
         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))])

-    
+    
     
   
 
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diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html
index 1e289d5..4fd1c33 100644
--- a/ja/api/mp_math/index.html
+++ b/ja/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
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diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html
index 7aa3dcf..382d7d9 100644
--- a/ja/api/mp_math/line.html
+++ b/ja/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Line3 ​
method __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。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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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: 直线上的一点
  • direction: 直线的方向向量
ソースコード
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:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
戻り値: 是否近似相等
引数:
  • other: 另一条直线
  • epsilon: 误差
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             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 ​
计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値:
  • 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
戻り値: 夹角弧度
引数:
  • other: 另一条直线
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値:
  • 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
戻り値: 距离
引数:
  • other: 平行直线或点
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値:
  • 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
戻り値: 交点
引数:
  • other: 另一条直线
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         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 ​
计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値:
  • 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
戻り値: 垂线
引数:
  • point: 指定点
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
引数:
  • t: 参数t
戻り値:
  • 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
戻り値: 点
引数:
  • t: 参数t
ソースコード
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:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
戻り値:
  • x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値:
  • 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
戻り値: 是否近似平行
引数:
  • other: 另一条直线
  • epsilon: 误差
ソースコード
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:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値:
  • 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
戻り値: 是否平行
引数:
  • other: 另一条直线
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値:
  • 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
戻り値: 是否共线
引数:
  • other: 另一条直线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             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 ​
判断点是否在直线上。
引数:
  • point: 点
戻り値:
  • 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
戻り値: 是否在直线上
引数:
  • point: 点
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
引数:
  • other: 另一条直线
戻り値:
  • 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
戻り値: 是否共面
引数:
  • other: 另一条直线
ソースコード
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。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
ソースコード
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
引数:
  • p1: 点1
  • p2: 点2
戻り値:
  • 直线
ソースコード
python
@classmethod
+        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。
戻り値: 直线
引数:
  • p1: 点1
  • p2: 点2
ソースコード
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
引数:
  • other: 另一条直线
戻り値:
  • 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
戻り値: 交点
引数:
  • other: 另一条直线
ソースコード
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:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
+        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:
ソースコード
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html
index 6da90b3..a358872 100644
--- a/ja/api/mp_math/mp_math_typing.html
+++ b/ja/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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var RealNumber = int | float ​
  • タイプ: TypeAlias
var Number = RealNumber | complex ​
  • タイプ: TypeAlias
var Var = SingleVar | ArrayVar ​
  • タイプ: TypeAlias
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • タイプ: TypeAlias
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • タイプ: TypeAlias
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • タイプ: TypeAlias
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • タイプ: TypeAlias
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • タイプ: TypeAlias
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • タイプ: TypeAlias
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • タイプ: TypeAlias
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • タイプ: TypeAlias
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • タイプ: TypeAlias

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html
index c777024..02e3093 100644
--- a/ja/api/mp_math/plane.html
+++ b/ja/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
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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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
戻り値: 是否近似相等
引数:
  • other: 另一个平面
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         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 ​
计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値:
  • 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
戻り値: 夹角弧度
引数:
  • other: 另一个平面
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値:
  • 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
戻り値: 距离
引数:
  • other: 另一个平面或点
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     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 ​
计算两平面的交线。
引数:
  • other: 另一个平面
戻り値:
  • 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
戻り値: 两平面的交线
引数:
  • other: 另一个平面
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値:
  • 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
戻り値: 交点
引数:
  • other: 不与平面平行或在平面上的直线
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値:
  • 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
戻り値: 所求平面
引数:
  • point: 指定点
ソースコード
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:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値:
  • 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
戻り値: 是否平行
引数:
  • other: 另一个平面
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
戻り値:
  • 法向量
ソースコード
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
引数:
  • point: 平面上的一点
  • normal: 法向量
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
戻り値: 平面
引数:
  • point: 平面上的一点
  • normal: 法向量
ソースコード
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)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
戻り値: 平面
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
ソースコード
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。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
戻り値: 平面
引数:
  • l1: 直线1
  • l2: 直线2
ソースコード
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値:
  • 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
戻り値: 平面
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
ソースコード
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。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
引数:
  • other:
戻り値:
  • 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
戻り値: 不平行平面的交线，平面平行返回None
引数:
  • other:
ソースコード
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html
index 6623310..0c8834a 100644
--- a/ja/api/mp_math/point.html
+++ b/ja/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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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: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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。
戻り値: 是否近似相等
引数:
  • other:
  • epsilon:
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
引数:
  • other:
ソースコード
python
def __eq__(self, other):
+    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:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html
index bfecb8f..dbced17 100644
--- a/ja/api/mp_math/segment.html
+++ b/ja/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html
index 212c332..b8761df 100644
--- a/ja/api/mp_math/utils.html
+++ b/ja/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func clamp() -> float ​
区间限定函数
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値:
  • 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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func clamp() -> float ​
説明: 区间限定函数
戻り値: 限制后的值
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
戻り値:
  • 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
戻り値: 是否近似相等
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
ソースコード
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:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値:
  • 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
説明: 获取数的符号。
戻り値: 符号 + - ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値:
  • 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
戻り値: 符号 + - ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
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
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
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
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html
index 024ea01..f171270 100644
--- a/ja/api/mp_math/vector.html
+++ b/ja/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
引数:
  • other:
  • epsilon:
戻り値:
  • 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
戻り値: 是否近似相等
引数:
  • other:
  • epsilon:
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             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 ​
计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値:
  • 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
戻り値: 夹角
引数:
  • other: 另一个向量
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • other:
戻り値:
  • 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
戻り値: 行列式的结果
引数:
  • other:
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値:
  • 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
戻り値: 是否近似平行
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
ソースコード
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:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値:
  • 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
戻り値: 是否平行
引数:
  • other: 另一个向量
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
戻り値:
  • 模
ソースコード
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
戻り値:
  • 单位向量
ソースコード
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
判断两个向量是否相等。
引数:
  • other:
戻り値:
  • 是否相等
ソースコード
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
戻り値: 是否相等
引数:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    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
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
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:
@@ -193,18 +193,18 @@
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量

-    
+    
     
   
 
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diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html
index 1ccc710..bfe8294 100644
--- a/ja/api/particle/index.html
+++ b/ja/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html
index 39d763d..7ddb3b8 100644
--- a/ja/api/presets/index.html
+++ b/ja/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html
index 9a97d0a..d75e608 100644
--- a/ja/api/presets/model/index.html
+++ b/ja/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
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Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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
python
@staticmethod
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
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class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
戻り値: List[Point3]: 球体上的点集。
引数:
  • radius:
  • density:
ソースコード
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file
diff --git a/md-ex.html b/md-ex.html
index 65e8351..8be09d2 100644
--- a/md-ex.html
+++ b/md-ex.html
@@ -50,7 +50,7 @@
 ::: details
 This is a details block.
 :::
Output
INFO
This is an info box.
TIP
This is a tip.
WARNING
This is a warning.
DANGER
This is a dangerous warning.
Details
This is a details block.
More ​
Check out the documentation for the full list of markdown extensions.

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/index.html b/zh-Hant/api/index.html
index 2709bfa..23ffea6 100644
--- a/zh-Hant/api/index.html
+++ b/zh-Hant/api/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/angle.html b/zh-Hant/api/mp_math/angle.html
index 4397cd0..e1bc606 100644
--- a/zh-Hant/api/mp_math/angle.html
+++ b/zh-Hant/api/mp_math/angle.html
@@ -118,7 +118,7 @@
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/const.html b/zh-Hant/api/mp_math/const.html
index a72bbdc..bf33071 100644
--- a/zh-Hant/api/mp_math/const.html
+++ b/zh-Hant/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/equation.html b/zh-Hant/api/mp_math/equation.html
index 3f83ff5..f1a547d 100644
--- a/zh-Hant/api/mp_math/equation.html
+++ b/zh-Hant/api/mp_math/equation.html
@@ -80,7 +80,7 @@
     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))])
def __str__(self) ​
源碼
python
def __str__(self):
     return 'CurveEquation()'
var result_func = get_partial_derivative_func(result_func, v, epsilon) ​

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/index.html b/zh-Hant/api/mp_math/index.html
index dc83dd5..2521ef7 100644
--- a/zh-Hant/api/mp_math/index.html
+++ b/zh-Hant/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/line.html b/zh-Hant/api/mp_math/line.html
index fa12d69..57951d0 100644
--- a/zh-Hant/api/mp_math/line.html
+++ b/zh-Hant/api/mp_math/line.html
@@ -209,7 +209,7 @@
         s += f' = (z{sign_format(-self.point.z)})/{self.direction.z}'
     return s
def __repr__(self) ​
源碼
python
def __repr__(self):
     return f'Line3({self.point}, {self.direction})'

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/mp_math_typing.html b/zh-Hant/api/mp_math/mp_math_typing.html
index 8074cf5..3d482c4 100644
--- a/zh-Hant/api/mp_math/mp_math_typing.html
+++ b/zh-Hant/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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
var RealNumber: TypeAlias = int | float ​
var Number: TypeAlias = RealNumber | complex ​
var SingleVar = TypeVar('SingleVar', bound=Number) ​
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
var Var: TypeAlias = SingleVar | ArrayVar ​
var OneSingleVarFunc: TypeAlias = Callable[[SingleVar], SingleVar] ​
var OneArrayFunc: TypeAlias = Callable[[ArrayVar], ArrayVar] ​
var OneVarFunc: TypeAlias = OneSingleVarFunc | OneArrayFunc ​
var TwoSingleVarsFunc: TypeAlias = Callable[[SingleVar, SingleVar], SingleVar] ​
var TwoArraysFunc: TypeAlias = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
var TwoVarsFunc: TypeAlias = TwoSingleVarsFunc | TwoArraysFunc ​
var ThreeSingleVarsFunc: TypeAlias = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
var ThreeArraysFunc: TypeAlias = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
var ThreeVarsFunc: TypeAlias = ThreeSingleVarsFunc | ThreeArraysFunc ​
var MultiSingleVarsFunc: TypeAlias = Callable[..., SingleVar] ​
var MultiArraysFunc: TypeAlias = Callable[..., ArrayVar] ​
var MultiVarsFunc: TypeAlias = MultiSingleVarsFunc | MultiArraysFunc ​

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/plane.html b/zh-Hant/api/mp_math/plane.html
index 3641700..8122e5a 100644
--- a/zh-Hant/api/mp_math/plane.html
+++ b/zh-Hant/api/mp_math/plane.html
@@ -226,7 +226,7 @@
         raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
     return self.approx(other)
def __rand__(self, other: 'Line3') -> 'Point3' ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
var k = other.a / self.a ​
var A = np.array([[self.b, self.c], [other.b, other.c]]) ​
var B = np.array([-self.d, -other.d]) ​
var v2 = l2.get_point(1) - l1.point ​
var k = other.b / self.b ​
var A = np.array([[self.a, self.c], [other.a, other.c]]) ​
var B = np.array([-self.d, -other.d]) ​
var k = other.c / self.c ​
var A = np.array([[self.a, self.b], [other.a, other.b]]) ​
var B = np.array([-self.d, -other.d]) ​

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/point.html b/zh-Hant/api/mp_math/point.html
index c060a77..29ff08f 100644
--- a/zh-Hant/api/mp_math/point.html
+++ b/zh-Hant/api/mp_math/point.html
@@ -69,7 +69,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/segment.html b/zh-Hant/api/mp_math/segment.html
index facfb00..4f27020 100644
--- a/zh-Hant/api/mp_math/segment.html
+++ b/zh-Hant/api/mp_math/segment.html
@@ -33,7 +33,7 @@
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
def __repr__(self) ​
源碼
python
def __repr__(self):
     return f'Segment3({self.p1}, {self.p2})'
def __str__(self) ​
源碼
python
def __str__(self):
     return f'Segment3({self.p1} -> {self.p2})'

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/utils.html b/zh-Hant/api/mp_math/utils.html
index 3310dd6..638f213 100644
--- a/zh-Hant/api/mp_math/utils.html
+++ b/zh-Hant/api/mp_math/utils.html
@@ -82,7 +82,7 @@
             self.raise_type_error(other)
def raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
     raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源碼
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/mp_math/vector.html b/zh-Hant/api/mp_math/vector.html
index 4a7cf71..6ca3cea 100644
--- a/zh-Hant/api/mp_math/vector.html
+++ b/zh-Hant/api/mp_math/vector.html
@@ -206,7 +206,7 @@
     return Vector3(-self.x, -self.y, -self.z)
def __repr__(self) ​
源碼
python
def __repr__(self):
     return f'Vector3({self.x}, {self.y}, {self.z})'
def __str__(self) ​
源碼
python
def __str__(self):
     return f'Vector3({self.x}, {self.y}, {self.z})'
var zero_vector3 = Vector3(0, 0, 0) ​
var x_axis = Vector3(1, 0, 0) ​
var y_axis = Vector3(0, 1, 0) ​
var z_axis = Vector3(0, 0, 1) ​

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/particle/index.html b/zh-Hant/api/particle/index.html
index 3f66c74..69e6206 100644
--- a/zh-Hant/api/particle/index.html
+++ b/zh-Hant/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/presets/index.html b/zh-Hant/api/presets/index.html
index 79ab0a5..38dbcbc 100644
--- a/zh-Hant/api/presets/index.html
+++ b/zh-Hant/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zh-Hant/api/presets/model/index.html b/zh-Hant/api/presets/model/index.html
index 7304f99..ba2a771 100644
--- a/zh-Hant/api/presets/model/index.html
+++ b/zh-Hant/api/presets/model/index.html
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/index.html b/zht/api/index.html
index 1d23982..beb6d85 100644
--- a/zht/api/index.html
+++ b/zht/api/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html
index 366a1d2..1c1fe14 100644
--- a/zht/api/mp_math/angle.html
+++ b/zht/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
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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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
余角：两角的和为90°。
返回:
  • 余角
源碼
python
@property
+        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
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 ​
补角：两角的和为180°。
返回:
  • 补角
源碼
python
@property
+    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
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 ​
角度。
返回:
  • 弧度
源碼
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
最小正角。
返回:
  • 最小正角度
源碼
python
@property
+    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
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 ​
最大负角。
返回:
  • 最大负角度
源碼
python
@property
+    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
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 ​
正弦值。
返回:
  • 正弦值
源碼
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
余弦值。
返回:
  • 余弦值
源碼
python
@property
+    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
正切值。
返回:
  • 正切值
源碼
python
@property
+    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
余切值。
返回:
  • 余切值
源碼
python
@property
+    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
正割值。
返回:
  • 正割值
源碼
python
@property
+    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
余割值。
返回:
  • 余割值
源碼
python
@property
+    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
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
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源碼
python
def __truediv__(self, other):
+    ...
method self / other ​
源碼
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html
index cbf5c8b..d752149 100644
--- a/zht/api/mp_math/const.html
+++ b/zht/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html
index f0f83d4..e7f06ad 100644
--- a/zht/api/mp_math/equation.html
+++ b/zht/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
求N元函数一阶偏导函数。这玩意不太稳定，慎用。
變數説明:
  • func: 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
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+    
MBCP docs
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繁體中文
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func get_partial_derivative_func(func: MultiVarsFunc = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
返回: 偏导函数
變數説明:
  • func: 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
抛出:
  • ValueError 无效变量类型
源碼
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。
     Args:
@@ -47,16 +47,16 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源碼
python
def partial_derivative_func(*args: Var) -> Var:
+        raise ValueError('Invalid var type')
func partial_derivative_func() -> Var ​
源碼
python
def partial_derivative_func(*args: Var) -> Var:
     args_list_plus = list(args)
     args_list_plus[var] += epsilon
     args_list_minus = list(args)
     args_list_minus[var] -= epsilon
-    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源碼
python
def high_order_partial_derivative_func(*args: Var) -> Var:
+    return (func(*args_list_plus) - func(*args_list_minus)) / (2 * epsilon)
func high_order_partial_derivative_func() -> Var ​
源碼
python
def high_order_partial_derivative_func(*args: Var) -> Var:
     result_func = func
     for v in var:
         result_func = get_partial_derivative_func(result_func, v, epsilon)
-    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    return result_func(*args)
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -66,7 +66,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -79,7 +79,7 @@
         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))])

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html
index 24707ce..93ba339 100644
--- a/zht/api/mp_math/index.html
+++ b/zht/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html
index 9672a3b..43508ed 100644
--- a/zht/api/mp_math/line.html
+++ b/zht/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Line3 ​
method __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。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
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繁體中文
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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: 直线上的一点
  • direction: 直线的方向向量
源碼
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:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
判断两条直线是否近似相等。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
變數説明:
  • other: 另一条直线
  • epsilon: 误差
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             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 ​
计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回:
  • 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    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。
返回: 夹角弧度
變數説明:
  • other: 另一条直线
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回:
  • 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    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。
返回: 距离
變數説明:
  • other: 平行直线或点
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回:
  • 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
返回: 交点
變數説明:
  • other: 另一条直线
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         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 ​
计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回:
  • 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    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。
返回: 垂线
變數説明:
  • point: 指定点
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method 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。
變數説明:
  • t: 参数t
返回:
  • 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
+    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。
返回: 点
變數説明:
  • t: 参数t
源碼
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:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
获取直线的参数方程。
返回:
  • x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    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 ​
判断两条直线是否近似平行。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回:
  • 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    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。
返回: 是否近似平行
變數説明:
  • other: 另一条直线
  • epsilon: 误差
源碼
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:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回:
  • 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
+    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。
返回: 是否平行
變數説明:
  • other: 另一条直线
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回:
  • 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
+    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。
返回: 是否共线
變數説明:
  • other: 另一条直线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             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 ​
判断点是否在直线上。
變數説明:
  • point: 点
返回:
  • 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
+    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。
返回: 是否在直线上
變數説明:
  • point: 点
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method 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。
變數説明:
  • other: 另一条直线
返回:
  • 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
+    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。
返回: 是否共面
變數説明:
  • other: 另一条直线
源碼
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。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method 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
源碼
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
工厂函数 由两点构造直线。
變數説明:
  • p1: 点1
  • p2: 点2
返回:
  • 直线
源碼
python
@classmethod
+        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。
返回: 直线
變數説明:
  • p1: 点1
  • p2: 点2
源碼
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __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。
變數説明:
  • other: 另一条直线
返回:
  • 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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。
返回: 交点
變數説明:
  • other: 另一条直线
源碼
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:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
+        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:
源碼
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html
index 083017f..06bd653 100644
--- a/zht/api/mp_math/mp_math_typing.html
+++ b/zht/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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var RealNumber = int | float ​
  • 類型: TypeAlias
var Number = RealNumber | complex ​
  • 類型: TypeAlias
var Var = SingleVar | ArrayVar ​
  • 類型: TypeAlias
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • 類型: TypeAlias
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • 類型: TypeAlias
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • 類型: TypeAlias
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • 類型: TypeAlias
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • 類型: TypeAlias
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • 類型: TypeAlias
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • 類型: TypeAlias
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • 類型: TypeAlias
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • 類型: TypeAlias
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • 類型: TypeAlias
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • 類型: TypeAlias
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • 類型: TypeAlias

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html
index 613fc6b..fa99191 100644
--- a/zht/api/mp_math/plane.html
+++ b/zht/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
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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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
判断两个平面是否近似相等。
變數説明:
  • other: 另一个平面
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
返回: 是否近似相等
變數説明:
  • other: 另一个平面
源碼
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         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 ​
计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回:
  • 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
返回: 夹角弧度
變數説明:
  • other: 另一个平面
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回:
  • 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
返回: 距离
變數説明:
  • other: 另一个平面或点
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     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 ​
计算两平面的交线。
變數説明:
  • other: 另一个平面
返回:
  • 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
返回: 两平面的交线
變數説明:
  • other: 另一个平面
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回:
  • 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
返回: 交点
變數説明:
  • other: 不与平面平行或在平面上的直线
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回:
  • 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
返回: 所求平面
變數説明:
  • point: 指定点
源碼
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:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回:
  • 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
返回: 是否平行
變數説明:
  • other: 另一个平面
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
平面的法向量。
返回:
  • 法向量
源碼
python
@property
+    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method 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)。
變數説明:
  • point: 平面上的一点
  • normal: 法向量
返回:
  • 平面
源碼
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
返回: 平面
變數説明:
  • point: 平面上的一点
  • normal: 法向量
源碼
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)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回:
  • 平面
源碼
python
@classmethod
+    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
返回: 平面
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
源碼
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。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回:
  • 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
返回: 平面
變數説明:
  • l1: 直线1
  • l2: 直线2
源碼
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回:
  • 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
返回: 平面
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
源碼
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。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
取两平面的交集（人话：交线）
變數説明:
  • other:
返回:
  • 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
返回: 不平行平面的交线，平面平行返回None
變數説明:
  • other:
源碼
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html
index 7e10a1f..9c85ae2 100644
--- a/zht/api/mp_math/point.html
+++ b/zht/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
繁體中文
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English
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繁體中文
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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: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
判断两个点是否近似相等。
變數説明:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
變數説明:
  • other:
  • epsilon:
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             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
python
@overload
+    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
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
+    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:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
P - P -> V
P - V -> P 已在 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html
index af1e2bc..7b55dd5 100644
--- a/zht/api/mp_math/segment.html
+++ b/zht/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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English
日本語
繁體中文
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English
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class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html
index 1af571d..b5e20e5 100644
--- a/zht/api/mp_math/utils.html
+++ b/zht/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
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日本語
繁體中文
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func clamp() -> float ​
区间限定函数
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回:
  • 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
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func clamp() -> float ​
説明: 区间限定函数
返回: 限制后的值
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,7 +28,7 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
變數説明:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回:
  • 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+    return max(min(x, max_), min_)
func approx(x: float = 0.0, y: 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。
返回: 是否近似相等
變數説明:
  • x: 数1
  • y: 数2
  • epsilon: 误差
源碼
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:
@@ -38,7 +38,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float = False) -> str ​
説明: 获取数的符号。
返回: 符号 + - ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -51,7 +51,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float = False) -> str ​
格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回:
  • 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
返回: 符号 + - ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -67,8 +67,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+        return ''
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
+    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -78,10 +78,10 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
     return not self.__eq__(other)

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html
index 08f7f2b..e1cf350 100644
--- a/zht/api/mp_math/vector.html
+++ b/zht/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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日本語
繁體中文
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class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
判断两个向量是否近似相等。
變數説明:
  • other:
  • epsilon:
返回:
  • 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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。
返回: 是否近似相等
變數説明:
  • other:
  • epsilon:
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             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 ​
计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回:
  • 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
返回: 夹角
變數説明:
  • other: 另一个向量
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • other:
返回:
  • 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
返回: 行列式的结果
變數説明:
  • other:
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    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 ​
判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回:
  • 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
返回: 是否近似平行
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
源碼
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:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回:
  • 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
返回: 是否平行
變數説明:
  • other: 另一个向量
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
向量的模。
返回:
  • 模
源碼
python
@property
+    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
获取该向量的单位向量。
返回:
  • 单位向量
源碼
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
+    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
判断两个向量是否相等。
變數説明:
  • other:
返回:
  • 是否相等
源碼
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
返回: 是否相等
變數説明:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             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 ​
P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
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:
@@ -193,18 +193,18 @@
     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
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html
index 702706e..a1fc62b 100644
--- a/zht/api/particle/index.html
+++ b/zht/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html
index 4896ac4..e46bfab 100644
--- a/zht/api/presets/index.html
+++ b/zht/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html
index d916d8f..4edce2d 100644
--- a/zht/api/presets/model/index.html
+++ b/zht/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
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
python
@staticmethod
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
返回: List[Point3]: 球体上的点集。
變數説明:
  • radius:
  • density:
源碼
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

-    
+    
     
   
 
\ No newline at end of file