diff --git a/404.html b/404.html index 7bd7310..32729f2 100644 --- a/404.html +++ b/404.html @@ -6,9 +6,9 @@ 404 | MBCP 文档 - + - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/api.html b/api/api.html deleted file mode 100644 index 5b2941e..0000000 --- a/api/api.html +++ /dev/null @@ -1,25 +0,0 @@ - - - - - - mbcp | MBCP 文档 - - - - - - - - - - - - - - -
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mbcp ​

说明: 本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- - - - \ No newline at end of file diff --git a/api/index.html b/api/index.html index f4b318e..22a143f 100644 --- a/api/index.html +++ b/api/index.html @@ -6,20 +6,20 @@ mbcp | MBCP 文档 - + - - + + - + -
MBCP 文档

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mbcp ​

说明: 本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

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mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/angle.html b/api/mp_math/angle.html index c09d3ef..0712bef 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -6,19 +6,19 @@ mbcp.mp_math.angle | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.angle ​

说明: 本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

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

说明: 任意角度。

参数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
+    
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mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
说明: 任意角度。
参数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码 或 在GitHub上查看
python
@property
+        self.radian = value * PI / 180
@property
method complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码 或 在GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码 或 在GitHub上查看
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
method supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码 或 在GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码 或 在GitHub上查看
python
@property
+    return self.radian * 180 / PI
@property
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码 或 在GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码 或 在GitHub上查看
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property
method maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码 或 在GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other):
+    ...
method self / other ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
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-    
+    return AnyAngle(self.radian / other, is_radian=True)

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+ \ No newline at end of file diff --git a/api/mp_math/const.html b/api/mp_math/const.html index 1af0d3e..3bc2b90 100644 --- a/api/mp_math/const.html +++ b/api/mp_math/const.html @@ -6,20 +6,20 @@ mbcp.mp_math.const | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.const ​

说明: 本模块定义了一些常用的常量

var PI ​

  • 说明: 常量 π

  • 默认值: math.pi

var E ​

  • 说明: 自然对数的底 exp(1)

  • 默认值: math.e

var GOLDEN_RATIO ​

  • 说明: 黄金分割比

  • 默认值: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 说明: 欧拉常数

  • 默认值: 0.5772156649015329

var EPSILON ​

  • 说明: 精度误差

  • 默认值: 0.0001

var APPROX ​

  • 说明: 约等于判定误差

  • 默认值: 0.001

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- +
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mbcp.mp_math.const ​

本模块定义了一些常用的常量

var PI ​

  • 说明: 常量 π

  • 默认值: math.pi

var E ​

  • 说明: 自然对数的底 exp(1)

  • 默认值: math.e

var GOLDEN_RATIO ​

  • 说明: 黄金分割比

  • 默认值: (1 + math.sqrt(5)) / 2

var GAMMA ​

  • 说明: 欧拉常数

  • 默认值: 0.5772156649015329

var EPSILON ​

  • 说明: 精度误差

  • 默认值: 0.0001

var APPROX ​

  • 说明: 约等于判定误差

  • 默认值: 0.001

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html index 0304557..94c3c79 100644 --- a/api/mp_math/equation.html +++ b/api/mp_math/equation.html @@ -6,19 +6,19 @@ mbcp.mp_math.equation | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.equation ​

说明: 本模块定义了方程相关的类和函数以及一些常用的数学函数

class CurveEquation ​

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

说明: 曲线方程。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
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mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
源代码 或 在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码 或 在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码 或 在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -82,8 +82,8 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        raise ValueError('Invalid var type')

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+ \ No newline at end of file diff --git a/api/mp_math/function.html b/api/mp_math/function.html index 29a614b..a807d4f 100644 --- a/api/mp_math/function.html +++ b/api/mp_math/function.html @@ -6,19 +6,19 @@ mbcp.mp_math.function | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.function ​

说明: AAA

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

说明: 计算三元函数在某点的梯度向量。

TIP

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

参数:

返回: 梯度

源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
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mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
参数:
返回: 梯度
源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -59,8 +59,8 @@
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
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-    
+    return curried_func

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+ \ No newline at end of file diff --git a/api/mp_math/index.html b/api/mp_math/index.html index a87d364..f25aab9 100644 --- a/api/mp_math/index.html +++ b/api/mp_math/index.html @@ -6,20 +6,20 @@ mbcp.mp_math | MBCP 文档 - + - - + + - + -
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mbcp.mp_math ​

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

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- +
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mbcp.mp_math ​

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

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/line.html b/api/mp_math/line.html index 6dbe441..96163bf 100644 --- a/api/mp_math/line.html +++ b/api/mp_math/line.html @@ -6,19 +6,19 @@ mbcp.mp_math.line | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.line ​

说明: 本模块定义了三维空间中的直线类

class Line3 ​

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

说明: 三维空间中的直线。由一个点和一个方向向量确定。

参数:

  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction ([`Vector3`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -43,7 +43,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -65,7 +65,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other (Line3): 另一条直线
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other (Line3): 另一条直线
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -80,7 +80,7 @@
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
返回: Line3: 垂线
源代码 或 在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
返回: Line3: 垂线
源代码 或 在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -88,7 +88,7 @@
         Returns:
             [`Line3`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
返回: Point3: 点
源代码 或 在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
返回: Point3: 点
源代码 或 在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -96,13 +96,13 @@
         Returns:
             [`Point3`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源代码 或 在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源代码 或 在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -111,7 +111,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -119,7 +119,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
返回: bool: 是否共线
源代码 或 在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
返回: bool: 是否共线
源代码 或 在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -127,7 +127,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
返回: bool: 是否在直线上
源代码 或 在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
返回: bool: 是否在直线上
源代码 或 在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -135,7 +135,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
返回: bool: 是否共面
源代码 或 在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
返回: bool: 是否共面
源代码 或 在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -144,7 +144,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码 或 在GitHub上查看
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码 或 在GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -157,7 +157,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
返回: Line3: 直线
源代码 或 在GitHub上查看
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
返回: Line3: 直线
源代码 或 在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -168,7 +168,7 @@
             [`Line3`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -181,7 +181,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -191,8 +191,8 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)

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+ \ No newline at end of file diff --git a/api/mp_math/mp_math.html b/api/mp_math/mp_math.html deleted file mode 100644 index 25041fc..0000000 --- a/api/mp_math/mp_math.html +++ /dev/null @@ -1,25 +0,0 @@ - - - - - - mbcp.mp_math | MBCP 文档 - - - - - - - - - - - - - - -
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mbcp.mp_math ​

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

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- - - - \ No newline at end of file diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html index 8bea05d..6765457 100644 --- a/api/mp_math/mp_math_typing.html +++ b/api/mp_math/mp_math_typing.html @@ -6,20 +6,20 @@ mbcp.mp_math.mp_math_typing | MBCP 文档 - + - - + + - + -
MBCP 文档

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mbcp.mp_math.mp_math_typing ​

说明: 本模块用于内部类型提示

var RealNumber ​

  • 说明: 实数

  • 类型: TypeAlias

  • 默认值: int | float

var Number ​

  • 说明: 数

  • 类型: TypeAlias

  • 默认值: RealNumber | complex

var SingleVar ​

  • 说明: 单变量

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

var ArrayVar ​

  • 说明: 数组变量

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

var Var ​

  • 说明: 变量

  • 类型: TypeAlias

  • 默认值: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 说明: 一元单变量函数

  • 类型: TypeAlias

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

var OneArrayFunc ​

  • 说明: 一元数组函数

  • 类型: TypeAlias

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

var OneVarFunc ​

  • 说明: 一元函数

  • 类型: TypeAlias

  • 默认值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 说明: 二元单变量函数

  • 类型: TypeAlias

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

var TwoArraysFunc ​

  • 说明: 二元数组函数

  • 类型: TypeAlias

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

var TwoVarsFunc ​

  • 说明: 二元函数

  • 类型: TypeAlias

  • 默认值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 说明: 三元单变量函数

  • 类型: TypeAlias

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

var ThreeArraysFunc ​

  • 说明: 三元数组函数

  • 类型: TypeAlias

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

var ThreeVarsFunc ​

  • 说明: 三元函数

  • 类型: TypeAlias

  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 说明: 多元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 说明: 多元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 说明: 多元函数

  • 类型: TypeAlias

  • 默认值: MultiSingleVarsFunc | MultiArraysFunc

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

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mbcp.mp_math.mp_math_typing ​

本模块用于内部类型提示

var RealNumber ​

  • 说明: 实数

  • 类型: TypeAlias

  • 默认值: int | float

var Number ​

  • 说明: 数

  • 类型: TypeAlias

  • 默认值: RealNumber | complex

var SingleVar ​

  • 说明: 单变量

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

var ArrayVar ​

  • 说明: 数组变量

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

var Var ​

  • 说明: 变量

  • 类型: TypeAlias

  • 默认值: SingleVar | ArrayVar

var OneSingleVarFunc ​

  • 说明: 一元单变量函数

  • 类型: TypeAlias

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

var OneArrayFunc ​

  • 说明: 一元数组函数

  • 类型: TypeAlias

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

var OneVarFunc ​

  • 说明: 一元函数

  • 类型: TypeAlias

  • 默认值: OneSingleVarFunc | OneArrayFunc

var TwoSingleVarsFunc ​

  • 说明: 二元单变量函数

  • 类型: TypeAlias

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

var TwoArraysFunc ​

  • 说明: 二元数组函数

  • 类型: TypeAlias

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

var TwoVarsFunc ​

  • 说明: 二元函数

  • 类型: TypeAlias

  • 默认值: TwoSingleVarsFunc | TwoArraysFunc

var ThreeSingleVarsFunc ​

  • 说明: 三元单变量函数

  • 类型: TypeAlias

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

var ThreeArraysFunc ​

  • 说明: 三元数组函数

  • 类型: TypeAlias

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

var ThreeVarsFunc ​

  • 说明: 三元函数

  • 类型: TypeAlias

  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc

var MultiSingleVarsFunc ​

  • 说明: 多元单变量函数

  • 类型: TypeAlias

  • 默认值: Callable[..., SingleVar]

var MultiArraysFunc ​

  • 说明: 多元数组函数

  • 类型: TypeAlias

  • 默认值: Callable[..., ArrayVar]

var MultiVarsFunc ​

  • 说明: 多元函数

  • 类型: TypeAlias

  • 默认值: MultiSingleVarsFunc | MultiArraysFunc

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html index 91844cd..314a8ce 100644 --- a/api/mp_math/plane.html +++ b/api/mp_math/plane.html @@ -6,19 +6,19 @@ mbcp.mp_math.plane | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.plane ​

说明: 本模块定义了三维空间中的平面类

class Plane3 ​

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

说明: 平面方程：ax + by + cz + d = 0

参数:

  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
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mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
返回: AnyAngle: 夹角
引发:
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
返回: AnyAngle: 夹角
引发:
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -104,7 +104,7 @@
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +118,7 @@
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +126,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +134,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: Vector3: 法向量
源代码 或 在GitHub上查看
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: Vector3: 法向量
源代码 或 在GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +153,7 @@
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +167,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +181,7 @@
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +191,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
返回: Line3 | Point3 | None: 交集
引发:
源代码 或 在GitHub上查看
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
返回: Line3 | Point3 | None: 交集
引发:
源代码 或 在GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +214,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
说明: 判断两个平面是否等价。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
说明: 判断两个平面是否等价。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +222,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return self.approx(other)

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

源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/point.html b/api/mp_math/point.html index 183ae2d..cfbf3b8 100644 --- a/api/mp_math/point.html +++ b/api/mp_math/point.html @@ -6,19 +6,19 @@ mbcp.mp_math.point | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.point ​

说明: 本模块定义了三维空间中点的类。

class Point3 ​

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

说明: 笛卡尔坐标系中的点。

参数:

  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+    
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mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
说明: P + V -> P P + P -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,7 +50,7 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -58,7 +58,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 Vector3 中实现
参数:
返回: Vector3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 Vector3 中实现
参数:
返回: Vector3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,8 +69,8 @@
             [`Vector3`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html index 3e45fed..562bfad 100644 --- a/api/mp_math/segment.html +++ b/api/mp_math/segment.html @@ -6,19 +6,19 @@ mbcp.mp_math.segment | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.segment ​

说明: 本模块定义了三维空间中的线段类

class Segment3 ​

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

说明: 三维空间中的线段。

参数:

  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
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mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。
参数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -32,8 +32,8 @@
     '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)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html index e21a2f0..9df51f0 100644 --- a/api/mp_math/utils.html +++ b/api/mp_math/utils.html @@ -6,19 +6,19 @@ mbcp.mp_math.utils | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.utils ​

说明: 本模块定义了一些常用的工具函数

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

说明: 区间限定函数

参数:

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

返回: float: 限定在区间内的值

源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
说明: 区间限定函数
参数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,13 +29,13 @@
     Returns:
         `float`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
说明: 用于近似比较对象
参数:
源代码 或 在GitHub上查看
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
说明: 用于近似比较对象
参数:
源代码 或 在GitHub上查看
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -45,8 +45,8 @@
         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)
func raise_type_error(self, other) ​
源代码 或 在GitHub上查看
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码 或 在GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -86,8 +86,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        return ''

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html index cd122ec..c49fe65 100644 --- a/api/mp_math/vector.html +++ b/api/mp_math/vector.html @@ -6,19 +6,19 @@ mbcp.mp_math.vector | MBCP 文档 - + - - + + - + -
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mbcp.mp_math.vector ​

说明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。

class Vector3 ​

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

说明: 3维向量

参数:

  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+    
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mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
返回: Vector3: 叉乘结果
源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
返回: Vector3: 叉乘结果
源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码 或 在GitHub上查看
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码 或 在GitHub上查看
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源代码 或 在GitHub上查看
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源代码 或 在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
说明: 向量的模。
返回: float: 模
源代码 或 在GitHub上查看
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
说明: 向量的模。
返回: float: 模
源代码 或 在GitHub上查看
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源代码 或 在GitHub上查看
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源代码 或 在GitHub上查看
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
源代码 或 在GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    return self / self.length
method __abs__(self) ​
源代码 或 在GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
说明: V + P -> P
V + V -> V
参数:
返回: Vector3 | Point3: 新的向量或点
源代码 或 在GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
返回: Vector3 | Point3: 新的向量或点
源代码 或 在GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -133,7 +133,7 @@
     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)}'")
func __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +141,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -151,11 +151,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
说明: V - P -> P
V - V -> V
参数:
返回: Vector3 | Point3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other):
+    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
返回: Vector3 | Point3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -170,7 +170,7 @@
     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)}"')
func self - other: Point3 ​
说明: P - V -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -181,11 +181,11 @@
     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
func self * other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
返回: Vector3: 数组运算结果
源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
返回: Vector3: 数组运算结果
源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +198,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
func self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
返回: float: 点乘结果
源代码 或 在GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
返回: float: 点乘结果
源代码 或 在GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -207,15 +207,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
说明: 取负。
返回: Vector3: 负向量
源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
说明: 取负。
返回: Vector3: 负向量
源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 说明: 零向量
  • 类型: Vector3
  • 默认值: Vector3(0, 0, 0)
var x_axis ​
  • 说明: x轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(1, 0, 0)
var y_axis ​
  • 说明: y轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(0, 1, 0)
var z_axis ​
  • 说明: z轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(0, 0, 1)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return Vector3(-self.x, -self.y, -self.z)

var zero_vector3 ​

  • 说明: 零向量

  • 类型: Vector3

  • 默认值: Vector3(0, 0, 0)

var x_axis ​

  • 说明: x轴单位向量

  • 类型: Vector3

  • 默认值: Vector3(1, 0, 0)

var y_axis ​

  • 说明: y轴单位向量

  • 类型: Vector3

  • 默认值: Vector3(0, 1, 0)

var z_axis ​

  • 说明: z轴单位向量

  • 类型: Vector3

  • 默认值: Vector3(0, 0, 1)

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/particle/index.html b/api/particle/index.html index 74a2f6b..4c45d7f 100644 --- a/api/particle/index.html +++ b/api/particle/index.html @@ -6,20 +6,20 @@ mbcp.particle | MBCP 文档 - + - - + + - + -
MBCP 文档

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

mbcp.particle ​

说明: 本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- +
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.particle ​

本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/particle/particle.html b/api/particle/particle.html deleted file mode 100644 index 392c032..0000000 --- a/api/particle/particle.html +++ /dev/null @@ -1,25 +0,0 @@ - - - - - - mbcp.particle | MBCP 文档 - - - - - - - - - - - - - - -
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.particle ​

说明: 本模块定义了粒子生成相关的工具

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- - - - \ No newline at end of file diff --git a/api/presets/index.html b/api/presets/index.html index d46bb5f..1dc3dcc 100644 --- a/api/presets/index.html +++ b/api/presets/index.html @@ -6,20 +6,20 @@ mbcp.presets | MBCP 文档 - + - - + + - + -
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.presets ​

说明: 本模块塞了一些预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- +
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.presets ​

本模块塞了一些预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/presets/model/index.html b/api/presets/model/index.html index 6e2215a..7f0d9d6 100644 --- a/api/presets/model/index.html +++ b/api/presets/model/index.html @@ -6,19 +6,19 @@ mbcp.presets.model | MBCP 文档 - + - - + + - + -
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.presets.model ​

说明: 几何模型点集

class GeometricModels ​

@staticmethod

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

说明: 生成球体上的点集。

参数:

  • radius:
  • density:

返回: List[Point3]: 球体上的点集。

源代码 或 在GitHub上查看
python
@staticmethod
+    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
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Appearance
mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码 或 在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,8 +35,8 @@
     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)]
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]

文档由 VitePress 构建 | API引用由 litedoc 生成

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

+ \ No newline at end of file diff --git a/api/presets/model/model.html b/api/presets/model/model.html deleted file mode 100644 index eb31c87..0000000 --- a/api/presets/model/model.html +++ /dev/null @@ -1,42 +0,0 @@ - - - - - - mbcp.presets.model | MBCP 文档 - - - - - - - - - - - - - - -
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.presets.model ​

说明: 几何模型点集

class GeometricModels ​

@staticmethod

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

说明: 生成球体上的点集。

参数:

  • radius:
  • density:

返回: List[Point3]: 球体上的点集。

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

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- - - - \ No newline at end of file diff --git a/api/presets/presets.html b/api/presets/presets.html deleted file mode 100644 index 7c104da..0000000 --- a/api/presets/presets.html +++ /dev/null @@ -1,25 +0,0 @@ - - - - - - mbcp.presets | MBCP 文档 - - - - - - - - - - - - - - -
MBCP 文档

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.presets ​

说明: 本模块塞了一些预设

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- - - - \ No newline at end of file diff --git a/assets/api_api.md.rnPOv6-O.js b/assets/api_api.md.rnPOv6-O.js deleted file mode 100644 index b7eb5d0..0000000 --- a/assets/api_api.md.rnPOv6-O.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as a,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/api.md","filePath":"zh/api/api.md"}'),c={name:"api/api.md"},o=p('

mbcp ​

说明: 本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

',5),r=[o];function s(_,i,d,m,n,l){return t(),a("div",null,r)}const b=e(c,[["render",s]]);export{f as __pageData,b as default}; diff --git a/assets/api_api.md.rnPOv6-O.lean.js b/assets/api_api.md.rnPOv6-O.lean.js deleted file mode 100644 index 7435396..0000000 --- a/assets/api_api.md.rnPOv6-O.lean.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as a,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/api.md","filePath":"zh/api/api.md"}'),c={name:"api/api.md"},o=p("",5),r=[o];function s(_,i,d,m,n,l){return t(),a("div",null,r)}const b=e(c,[["render",s]]);export{f as __pageData,b as default}; diff --git a/assets/api_index.md.YS-zqWwM.js b/assets/api_index.md.YS-zqWwM.js new file mode 100644 index 0000000..18243d2 --- /dev/null +++ b/assets/api_index.md.YS-zqWwM.js @@ -0,0 +1 @@ +import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/index.md","filePath":"zh/api/index.md"}'),p={name:"api/index.md"},o=c('

mbcp ​

本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

',5),r=[o];function s(d,_,i,n,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default}; diff --git a/assets/api_index.md.qnrSd__i.lean.js b/assets/api_index.md.YS-zqWwM.lean.js similarity index 100% rename from assets/api_index.md.qnrSd__i.lean.js rename to assets/api_index.md.YS-zqWwM.lean.js diff --git a/assets/api_index.md.qnrSd__i.js b/assets/api_index.md.qnrSd__i.js deleted file mode 100644 index 0203e92..0000000 --- a/assets/api_index.md.qnrSd__i.js +++ /dev/null @@ -1 +0,0 @@ -import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/index.md","filePath":"zh/api/index.md"}'),p={name:"api/index.md"},o=c('

mbcp ​

说明: 本模块是主模块，提供了一些工具 可导入

mbcp.mp_math：数学工具

mbcp.particle：粒子生成工具

mbcp.presets：预设

',5),r=[o];function s(d,_,i,n,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default}; diff --git a/assets/api_mp_math_angle.md.D0ius2dn.js b/assets/api_mp_math_angle.md.CThQB5nq.js similarity index 60% rename from assets/api_mp_math_angle.md.D0ius2dn.js rename to assets/api_mp_math_angle.md.CThQB5nq.js index 66a9b69..cdd91a9 100644 --- a/assets/api_mp_math_angle.md.D0ius2dn.js +++ b/assets/api_mp_math_angle.md.CThQB5nq.js @@ -1,4 +1,4 @@ -import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`

mbcp.mp_math.angle ​

说明: 本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

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

说明: 任意角度。

参数:

源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
说明: 任意角度。
参数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码 或 在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码 或 在GitHub上查看
python
@property
+        self.radian = value * PI / 180
@property
method complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码 或 在GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码 或 在GitHub上查看
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
method supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码 或 在GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码 或 在GitHub上查看
python
@property
+    return self.radian * 180 / PI
@property
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码 或 在GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码 或 在GitHub上查看
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property
method maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码 或 在GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码 或 在GitHub上查看
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 或 在GitHub上查看
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other):
+    ...
method self / other ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/api_mp_math_angle.md.D0ius2dn.lean.js b/assets/api_mp_math_angle.md.CThQB5nq.lean.js
similarity index 100%
rename from assets/api_mp_math_angle.md.D0ius2dn.lean.js
rename to assets/api_mp_math_angle.md.CThQB5nq.lean.js
diff --git a/assets/api_mp_math_const.md.DqjQQ6Ym.js b/assets/api_mp_math_const.md.DqjQQ6Ym.js
new file mode 100644
index 0000000..da9134c
--- /dev/null
+++ b/assets/api_mp_math_const.md.DqjQQ6Ym.js
@@ -0,0 +1 @@
+import{_ as a,c as o,o as t,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/const.md","filePath":"zh/api/mp_math/const.md"}'),r={name:"api/mp_math/const.md"},l=e('
mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • 说明: 常量 π
  • 默认值: math.pi
var E ​
  • 说明: 自然对数的底 exp(1)
  • 默认值: math.e
var GOLDEN_RATIO ​
  • 说明: 黄金分割比
  • 默认值: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 说明: 欧拉常数
  • 默认值: 0.5772156649015329
var EPSILON ​
  • 说明: 精度误差
  • 默认值: 0.0001
var APPROX ​
  • 说明: 约等于判定误差
  • 默认值: 0.001
',14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const g=a(r,[["render",i]]);export{u as __pageData,g as default};
diff --git a/assets/api_mp_math_const.md.DqjQQ6Ym.lean.js b/assets/api_mp_math_const.md.DqjQQ6Ym.lean.js
new file mode 100644
index 0000000..e5f072c
--- /dev/null
+++ b/assets/api_mp_math_const.md.DqjQQ6Ym.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as o,o as t,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/const.md","filePath":"zh/api/mp_math/const.md"}'),r={name:"api/mp_math/const.md"},l=e("",14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const g=a(r,[["render",i]]);export{u as __pageData,g as default};
diff --git a/assets/api_mp_math_const.md.O6cTulwX.js b/assets/api_mp_math_const.md.O6cTulwX.js
deleted file mode 100644
index 3b51c58..0000000
--- a/assets/api_mp_math_const.md.O6cTulwX.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as o,o as t,a4 as r}from"./chunks/framework.DpC1ZpOZ.js";const g=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/const.md","filePath":"zh/api/mp_math/const.md"}'),e={name:"api/mp_math/const.md"},l=r('
mbcp.mp_math.const ​
说明: 本模块定义了一些常用的常量
var PI ​
  • 说明: 常量 π
  • 默认值: math.pi
var E ​
  • 说明: 自然对数的底 exp(1)
  • 默认值: math.e
var GOLDEN_RATIO ​
  • 说明: 黄金分割比
  • 默认值: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 说明: 欧拉常数
  • 默认值: 0.5772156649015329
var EPSILON ​
  • 说明: 精度误差
  • 默认值: 0.0001
var APPROX ​
  • 说明: 约等于判定误差
  • 默认值: 0.001
',14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const u=a(e,[["render",i]]);export{g as __pageData,u as default};
diff --git a/assets/api_mp_math_const.md.O6cTulwX.lean.js b/assets/api_mp_math_const.md.O6cTulwX.lean.js
deleted file mode 100644
index f6a9277..0000000
--- a/assets/api_mp_math_const.md.O6cTulwX.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as o,o as t,a4 as r}from"./chunks/framework.DpC1ZpOZ.js";const g=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/const.md","filePath":"zh/api/mp_math/const.md"}'),e={name:"api/mp_math/const.md"},l=r("",14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const u=a(e,[["render",i]]);export{g as __pageData,u as default};
diff --git a/assets/api_mp_math_equation.md.D9gepkm-.js b/assets/api_mp_math_equation.md.C1YMGsIR.js
similarity index 83%
rename from assets/api_mp_math_equation.md.D9gepkm-.js
rename to assets/api_mp_math_equation.md.C1YMGsIR.js
index c81ecfd..75fa61d 100644
--- a/assets/api_mp_math_equation.md.D9gepkm-.js
+++ b/assets/api_mp_math_equation.md.C1YMGsIR.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
说明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
源代码 或 在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
源代码 或 在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码 或 在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码 或 在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/api_mp_math_equation.md.D9gepkm-.lean.js b/assets/api_mp_math_equation.md.C1YMGsIR.lean.js
similarity index 86%
rename from assets/api_mp_math_equation.md.D9gepkm-.lean.js
rename to assets/api_mp_math_equation.md.C1YMGsIR.lean.js
index 6be3a53..450e361 100644
--- a/assets/api_mp_math_equation.md.D9gepkm-.lean.js
+++ b/assets/api_mp_math_equation.md.C1YMGsIR.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/api_mp_math_function.md.C0P_-kol.js b/assets/api_mp_math_function.md.C0P_-kol.js
new file mode 100644
index 0000000..57804d5
--- /dev/null
+++ b/assets/api_mp_math_function.md.C0P_-kol.js
@@ -0,0 +1,42 @@
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),e={name:"api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
参数:
返回: 梯度
源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    """
+    计算三元函数在某点的梯度向量。
+    > [!tip]
+    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
+    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
+    Args:
+        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
+        p ([\`Point3\`](./point#class-point3)): 点
+        epsilon: 偏移量
+    Returns:
+        梯度
+    """
+    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
+    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
+    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
+    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
说明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
参数:
返回: 柯里化后的函数
示例:
python
def add(a: int, b: int, c: int) -> int:
+    return a + b + c
+add_curried = curry(add, 1, 2)
+add_curried(3)  # 6
源代码 或 在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+    """
+    对多参数函数进行柯里化。
+    > [!tip]
+    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
+    Args:
+        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
+        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
+    Returns:
+        柯里化后的函数
+    Examples:
+        \`\`\`python
+        def add(a: int, b: int, c: int) -> int:
+            return a + b + c
+        add_curried = curry(add, 1, 2)
+        add_curried(3)  # 6
+        \`\`\`
+    """
+
+    def curried_func(*args2: Var) -> Var:
+        """@litedoc-hide"""
+        return func(*args, *args2)
+    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/api_mp_math_function.md.DCuJC29A.lean.js b/assets/api_mp_math_function.md.C0P_-kol.lean.js
similarity index 100%
rename from assets/api_mp_math_function.md.DCuJC29A.lean.js
rename to assets/api_mp_math_function.md.C0P_-kol.lean.js
diff --git a/assets/api_mp_math_function.md.DCuJC29A.js b/assets/api_mp_math_function.md.DCuJC29A.js
deleted file mode 100644
index f45ba9b..0000000
--- a/assets/api_mp_math_function.md.DCuJC29A.js
+++ /dev/null
@@ -1,42 +0,0 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),e={name:"api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
说明: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
参数:
返回: 梯度
源代码 或 在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
-    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
-    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
-    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
-    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
说明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
参数:
返回: 柯里化后的函数
示例:
python
def add(a: int, b: int, c: int) -> int:
-    return a + b + c
-add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
源代码 或 在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
-
-    def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
-        return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/api_mp_math_index.md.DHhPNV6R.js b/assets/api_mp_math_index.md.DHhPNV6R.js
deleted file mode 100644
index efbf911..0000000
--- a/assets/api_mp_math_index.md.DHhPNV6R.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/mp_math/index.md","filePath":"zh/api/mp_math/index.md"}'),l={name:"api/mp_math/index.md"},o=c('
mbcp.mp_math ​
说明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function m(n,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/api_mp_math_index.md.yEj9pzOD.js b/assets/api_mp_math_index.md.yEj9pzOD.js
new file mode 100644
index 0000000..81b121c
--- /dev/null
+++ b/assets/api_mp_math_index.md.yEj9pzOD.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/mp_math/index.md","filePath":"zh/api/mp_math/index.md"}'),l={name:"api/mp_math/index.md"},o=c('
mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function m(n,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/api_mp_math_index.md.DHhPNV6R.lean.js b/assets/api_mp_math_index.md.yEj9pzOD.lean.js
similarity index 100%
rename from assets/api_mp_math_index.md.DHhPNV6R.lean.js
rename to assets/api_mp_math_index.md.yEj9pzOD.lean.js
diff --git a/assets/en_api_mp_math_line.md.CxP-i4OT.js b/assets/api_mp_math_line.md.Okmn0BTW.js
similarity index 63%
rename from assets/en_api_mp_math_line.md.CxP-i4OT.js
rename to assets/api_mp_math_line.md.Okmn0BTW.js
index aa92d9f..51f6cbf 100644
--- a/assets/en_api_mp_math_line.md.CxP-i4OT.js
+++ b/assets/api_mp_math_line.md.Okmn0BTW.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
Description: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other (Line3): 另一条直线
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -23,7 +23,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other (Line3): 另一条直线
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other (Line3): 另一条直线
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -60,7 +60,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
Return: Line3: 垂线
Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
返回: Line3: 垂线
源代码 或 在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -68,7 +68,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Line3\`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
Return: Point3: 点
Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
返回: Point3: 点
源代码 或 在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -76,13 +76,13 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Point3\`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源代码 或 在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -91,7 +91,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -99,7 +99,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
Return: bool: 是否共线
Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
返回: bool: 是否共线
源代码 或 在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -107,7 +107,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
Return: bool: 是否在直线上
Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
返回: bool: 是否在直线上
源代码 或 在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -115,7 +115,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
Return: bool: 是否共面
Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
返回: bool: 是否共面
源代码 或 在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -124,7 +124,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code or View on GitHub
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码 或 在GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -137,7 +137,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
Return: Line3: 直线
Source code or View on GitHub
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
返回: Line3: 直线
源代码 或 在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -148,7 +148,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             [\`Line3\`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other (Line3): 另一条直线
Return: Line3 | Point3 | None: 交集
Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other (Line3): 另一条直线
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -171,4 +171,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function p(h,k,r,o,d,c){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_line.md.ByGRRi0A.lean.js b/assets/api_mp_math_line.md.Okmn0BTW.lean.js
similarity index 72%
rename from assets/api_mp_math_line.md.ByGRRi0A.lean.js
rename to assets/api_mp_math_line.md.Okmn0BTW.lean.js
index 4509cf2..28b458f 100644
--- a/assets/api_mp_math_line.md.ByGRRi0A.lean.js
+++ b/assets/api_mp_math_line.md.Okmn0BTW.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n("",106),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_mp_math.md.mVabZTHd.js b/assets/api_mp_math_mp_math.md.mVabZTHd.js
deleted file mode 100644
index 17a51a4..0000000
--- a/assets/api_mp_math_mp_math.md.mVabZTHd.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/mp_math/mp_math.md","filePath":"zh/api/mp_math/mp_math.md"}'),l={name:"api/mp_math/mp_math.md"},m=c('
mbcp.mp_math ​
说明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),o=[m];function i(s,n,p,h,r,_){return t(),a("div",null,o)}const u=e(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/api_mp_math_mp_math.md.mVabZTHd.lean.js b/assets/api_mp_math_mp_math.md.mVabZTHd.lean.js
deleted file mode 100644
index 2e5b11a..0000000
--- a/assets/api_mp_math_mp_math.md.mVabZTHd.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/mp_math/mp_math.md","filePath":"zh/api/mp_math/mp_math.md"}'),l={name:"api/mp_math/mp_math.md"},m=c("",3),o=[m];function i(s,n,p,h,r,_){return t(),a("div",null,o)}const u=e(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/api_mp_math_mp_math_typing.md.CEryCREV.js b/assets/api_mp_math_mp_math_typing.md.CEryCREV.js
deleted file mode 100644
index 44c20ae..0000000
--- a/assets/api_mp_math_mp_math_typing.md.CEryCREV.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/mp_math_typing.md","filePath":"zh/api/mp_math/mp_math_typing.md"}'),l={name:"api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
说明: 本模块用于内部类型提示
var RealNumber ​
  • 说明: 实数
  • 类型: TypeAlias
  • 默认值: int | float
var Number ​
  • 说明: 数
  • 类型: TypeAlias
  • 默认值: RealNumber | complex
var SingleVar ​
  • 说明: 单变量
  • 默认值: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 说明: 数组变量
  • 默认值: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 说明: 变量
  • 类型: TypeAlias
  • 默认值: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 说明: 一元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 说明: 一元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 说明: 一元函数
  • 类型: TypeAlias
  • 默认值: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 说明: 二元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 说明: 二元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 说明: 二元函数
  • 类型: TypeAlias
  • 默认值: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 说明: 三元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 说明: 三元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 说明: 三元函数
  • 类型: TypeAlias
  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 说明: 多元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 说明: 多元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 说明: 多元函数
  • 类型: TypeAlias
  • 默认值: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,d,p,u,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/api_mp_math_mp_math_typing.md.bdiOSvFy.js b/assets/api_mp_math_mp_math_typing.md.bdiOSvFy.js
new file mode 100644
index 0000000..88efb6f
--- /dev/null
+++ b/assets/api_mp_math_mp_math_typing.md.bdiOSvFy.js
@@ -0,0 +1 @@
+import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/mp_math_typing.md","filePath":"zh/api/mp_math/mp_math_typing.md"}'),l={name:"api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • 说明: 实数
  • 类型: TypeAlias
  • 默认值: int | float
var Number ​
  • 说明: 数
  • 类型: TypeAlias
  • 默认值: RealNumber | complex
var SingleVar ​
  • 说明: 单变量
  • 默认值: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 说明: 数组变量
  • 默认值: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 说明: 变量
  • 类型: TypeAlias
  • 默认值: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 说明: 一元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 说明: 一元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 说明: 一元函数
  • 类型: TypeAlias
  • 默认值: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 说明: 二元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 说明: 二元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 说明: 二元函数
  • 类型: TypeAlias
  • 默认值: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 说明: 三元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 说明: 三元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 说明: 三元函数
  • 类型: TypeAlias
  • 默认值: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 说明: 多元单变量函数
  • 类型: TypeAlias
  • 默认值: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 说明: 多元数组函数
  • 类型: TypeAlias
  • 默认值: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 说明: 多元函数
  • 类型: TypeAlias
  • 默认值: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,d,p,u,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/api_mp_math_mp_math_typing.md.CEryCREV.lean.js b/assets/api_mp_math_mp_math_typing.md.bdiOSvFy.lean.js
similarity index 100%
rename from assets/api_mp_math_mp_math_typing.md.CEryCREV.lean.js
rename to assets/api_mp_math_mp_math_typing.md.bdiOSvFy.lean.js
diff --git a/assets/en_api_mp_math_plane.md.BsgpTZdY.js b/assets/api_mp_math_plane.md.Dl-FdXx3.js
similarity index 73%
rename from assets/en_api_mp_math_plane.md.BsgpTZdY.js
rename to assets/api_mp_math_plane.md.Dl-FdXx3.js
index 666725f..7b6359d 100644
--- a/assets/en_api_mp_math_plane.md.BsgpTZdY.js
+++ b/assets/api_mp_math_plane.md.Dl-FdXx3.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
Description: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Raises:
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
返回: AnyAngle: 夹角
引发:
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other (Plane3): 另一个平面
Return: Line3: 交线
Raises:
Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -84,7 +84,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -98,7 +98,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -106,7 +106,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -114,14 +114,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: Vector3: 法向量
Source code or View on GitHub
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: Vector3: 法向量
源代码 或 在GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [\`Vector3\`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -133,7 +133,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
Return: 平面
Source code or View on GitHub
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -147,7 +147,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
Return: 平面
Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
Return: 平面
Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -171,11 +171,11 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
Return: Line3 | Point3 | None: 交集
Raises:
Source code or View on GitHub
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
返回: Line3 | Point3 | None: 交集
引发:
源代码 或 在GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -194,7 +194,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
Description: 判断两个平面是否等价。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
说明: 判断两个平面是否等价。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -202,5 +202,5 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_plane.md.Ir4HtSn5.lean.js b/assets/api_mp_math_plane.md.Dl-FdXx3.lean.js
similarity index 69%
rename from assets/api_mp_math_plane.md.Ir4HtSn5.lean.js
rename to assets/api_mp_math_plane.md.Dl-FdXx3.lean.js
index aff7000..217bc99 100644
--- a/assets/api_mp_math_plane.md.Ir4HtSn5.lean.js
+++ b/assets/api_mp_math_plane.md.Dl-FdXx3.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_point.md.DcGqVqiO.js b/assets/api_mp_math_point.md.xU6HjeL2.js
similarity index 60%
rename from assets/en_api_mp_math_point.md.DcGqVqiO.js
rename to assets/api_mp_math_point.md.xU6HjeL2.js
index e6a82a0..64febee 100644
--- a/assets/en_api_mp_math_point.md.DcGqVqiO.js
+++ b/assets/api_mp_math_point.md.xU6HjeL2.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},l=t(`
mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t(`
mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -17,11 +17,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
Source code or View on GitHub
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 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
Description: P + V -> P P + P -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __add__(self, other):
+    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,7 +30,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 Vector3 中实现
Arguments:
Return: Vector3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 Vector3 中实现
参数:
返回: Vector3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -49,4 +49,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
             [\`Vector3\`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),e=[l];function h(p,o,k,r,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_point.md.CIRBY4Zg.lean.js b/assets/api_mp_math_point.md.xU6HjeL2.lean.js
similarity index 72%
rename from assets/api_mp_math_point.md.CIRBY4Zg.lean.js
rename to assets/api_mp_math_point.md.xU6HjeL2.lean.js
index 47771f4..0ab8c06 100644
--- a/assets/api_mp_math_point.md.CIRBY4Zg.lean.js
+++ b/assets/api_mp_math_point.md.xU6HjeL2.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t("",39),h=[l];function p(e,k,o,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t("",39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_segment.md.DFwFkY98.js b/assets/api_mp_math_segment.md.BqloNjdD.js
similarity index 73%
rename from assets/api_mp_math_segment.md.DFwFkY98.js
rename to assets/api_mp_math_segment.md.BqloNjdD.js
index d3a0a79..9500797 100644
--- a/assets/api_mp_math_segment.md.DFwFkY98.js
+++ b/assets/api_mp_math_segment.md.BqloNjdD.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
说明: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。
参数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。
参数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源代码 或 在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -12,4 +12,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function l(e,k,r,d,E,o){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/api_mp_math_segment.md.DFwFkY98.lean.js b/assets/api_mp_math_segment.md.BqloNjdD.lean.js
similarity index 86%
rename from assets/api_mp_math_segment.md.DFwFkY98.lean.js
rename to assets/api_mp_math_segment.md.BqloNjdD.lean.js
index c74d9ce..5049e34 100644
--- a/assets/api_mp_math_segment.md.DFwFkY98.lean.js
+++ b/assets/api_mp_math_segment.md.BqloNjdD.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,E,o){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/api_mp_math_utils.md.CFXHDZgH.js b/assets/api_mp_math_utils.md.CGBZjr3t.js
similarity index 79%
rename from assets/api_mp_math_utils.md.CFXHDZgH.js
rename to assets/api_mp_math_utils.md.CGBZjr3t.js
index 5904472..d89ff7f 100644
--- a/assets/api_mp_math_utils.md.CFXHDZgH.js
+++ b/assets/api_mp_math_utils.md.CGBZjr3t.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),n={name:"api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
说明: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
说明: 区间限定函数
参数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),n={name:"api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
说明: 区间限定函数
参数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源代码 或 在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,13 +9,13 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     Returns:
         \`float\`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
说明: 用于近似比较对象
参数:
源代码 或 在GitHub上查看
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
说明: 用于近似比较对象
参数:
源代码 或 在GitHub上查看
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -25,8 +25,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
         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)
func raise_type_error(self, other) ​
源代码 或 在GitHub上查看
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码 或 在GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -66,4 +66,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",p]]);export{F as __pageData,c as default};
+        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_utils.md.CFXHDZgH.lean.js b/assets/api_mp_math_utils.md.CGBZjr3t.lean.js
similarity index 72%
rename from assets/api_mp_math_utils.md.CFXHDZgH.lean.js
rename to assets/api_mp_math_utils.md.CGBZjr3t.lean.js
index 38c2963..db5f944 100644
--- a/assets/api_mp_math_utils.md.CFXHDZgH.lean.js
+++ b/assets/api_mp_math_utils.md.CGBZjr3t.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),n={name:"api/mp_math/utils.md"},l=t("",38),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",p]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),n={name:"api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_vector.md.CuQ0WDoP.js b/assets/api_mp_math_vector.md.B443ftAV.js
similarity index 62%
rename from assets/api_mp_math_vector.md.CuQ0WDoP.js
rename to assets/api_mp_math_vector.md.B443ftAV.js
index 4a40469..e145449 100644
--- a/assets/api_mp_math_vector.md.CuQ0WDoP.js
+++ b/assets/api_mp_math_vector.md.B443ftAV.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},l=t(`
mbcp.mp_math.vector ​
说明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},e=t(`
mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
返回: Vector3: 叉乘结果
源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
返回: Vector3: 叉乘结果
源代码 或 在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Vector3\`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码 或 在GitHub上查看
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码 或 在GitHub上查看
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,33 +72,33 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源代码 或 在GitHub上查看
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源代码 或 在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
说明: 向量的模。
返回: float: 模
源代码 或 在GitHub上查看
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
说明: 向量的模。
返回: float: 模
源代码 或 在GitHub上查看
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源代码 或 在GitHub上查看
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源代码 或 在GitHub上查看
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [\`Vector3\`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
源代码 或 在GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    return self / self.length
method __abs__(self) ​
源代码 或 在GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
说明: V + P -> P
V + V -> V
参数:
返回: Vector3 | Point3: 新的向量或点
源代码 或 在GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
返回: Vector3 | Point3: 新的向量或点
源代码 或 在GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -113,7 +113,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -121,7 +121,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -131,11 +131,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
说明: V - P -> P
V - V -> V
参数:
返回: Vector3 | Point3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other):
+    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
返回: Vector3 | Point3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -150,7 +150,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}"')
func self - other: Point3 ​
说明: P - V -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -161,11 +161,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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
func self * other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
返回: Vector3: 数组运算结果
源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
返回: Vector3: 数组运算结果
源代码 或 在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -178,8 +178,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
返回: float: 点乘结果
源代码 或 在GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
返回: float: 点乘结果
源代码 或 在GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -187,11 +187,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
说明: 取负。
返回: Vector3: 负向量
源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
说明: 取负。
返回: Vector3: 负向量
源代码 或 在GitHub上查看
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [\`Vector3\`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 说明: 零向量
  • 类型: Vector3
  • 默认值: Vector3(0, 0, 0)
var x_axis ​
  • 说明: x轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(1, 0, 0)
var y_axis ​
  • 说明: y轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(0, 1, 0)
var z_axis ​
  • 说明: z轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(0, 0, 1)
`,138),e=[l];function h(p,k,r,o,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 说明: 零向量
  • 类型: Vector3
  • 默认值: Vector3(0, 0, 0)
var x_axis ​
  • 说明: x轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(1, 0, 0)
var y_axis ​
  • 说明: y轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(0, 1, 0)
var z_axis ​
  • 说明: z轴单位向量
  • 类型: Vector3
  • 默认值: Vector3(0, 0, 1)
`,138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_vector.md.CuQ0WDoP.lean.js b/assets/api_mp_math_vector.md.B443ftAV.lean.js
similarity index 72%
rename from assets/api_mp_math_vector.md.CuQ0WDoP.lean.js
rename to assets/api_mp_math_vector.md.B443ftAV.lean.js
index bc7bcb5..76a19a4 100644
--- a/assets/api_mp_math_vector.md.CuQ0WDoP.lean.js
+++ b/assets/api_mp_math_vector.md.B443ftAV.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},l=t("",138),e=[l];function h(p,k,r,o,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},e=t("",138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/api_particle_index.md.BxLVuqry.js b/assets/api_particle_index.md.BxLVuqry.js
deleted file mode 100644
index 9477dab..0000000
--- a/assets/api_particle_index.md.BxLVuqry.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/particle/index.md","filePath":"zh/api/particle/index.md"}'),i={name:"api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"说明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[p,l];function n(o,d,_,m,h,f){return r(),c("div",null,s)}const u=t(i,[["render",n]]);export{b as __pageData,u as default};
diff --git a/assets/api_particle_index.md.BxLVuqry.lean.js b/assets/api_particle_index.md.BxLVuqry.lean.js
deleted file mode 100644
index 9477dab..0000000
--- a/assets/api_particle_index.md.BxLVuqry.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/particle/index.md","filePath":"zh/api/particle/index.md"}'),i={name:"api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"说明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[p,l];function n(o,d,_,m,h,f){return r(),c("div",null,s)}const u=t(i,[["render",n]]);export{b as __pageData,u as default};
diff --git a/assets/api_particle_index.md.VxgsHiZa.js b/assets/api_particle_index.md.VxgsHiZa.js
new file mode 100644
index 0000000..0e6c15b
--- /dev/null
+++ b/assets/api_particle_index.md.VxgsHiZa.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/particle/index.md","filePath":"zh/api/particle/index.md"}'),i={name:"api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),s=e("p",null,"本模块定义了粒子生成相关的工具",-1),l=[p,s];function o(n,d,_,m,h,f){return c(),t("div",null,l)}const u=a(i,[["render",o]]);export{b as __pageData,u as default};
diff --git a/assets/api_particle_index.md.VxgsHiZa.lean.js b/assets/api_particle_index.md.VxgsHiZa.lean.js
new file mode 100644
index 0000000..0e6c15b
--- /dev/null
+++ b/assets/api_particle_index.md.VxgsHiZa.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/particle/index.md","filePath":"zh/api/particle/index.md"}'),i={name:"api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),s=e("p",null,"本模块定义了粒子生成相关的工具",-1),l=[p,s];function o(n,d,_,m,h,f){return c(),t("div",null,l)}const u=a(i,[["render",o]]);export{b as __pageData,u as default};
diff --git a/assets/api_particle_particle.md.CioLG9Ab.js b/assets/api_particle_particle.md.CioLG9Ab.js
deleted file mode 100644
index 5be86d4..0000000
--- a/assets/api_particle_particle.md.CioLG9Ab.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/particle/particle.md","filePath":"zh/api/particle/particle.md"}'),p={name:"api/particle/particle.md"},l=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),i=e("p",null,[e("strong",null,"说明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[l,i];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=t(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/api_particle_particle.md.CioLG9Ab.lean.js b/assets/api_particle_particle.md.CioLG9Ab.lean.js
deleted file mode 100644
index 5be86d4..0000000
--- a/assets/api_particle_particle.md.CioLG9Ab.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/particle/particle.md","filePath":"zh/api/particle/particle.md"}'),p={name:"api/particle/particle.md"},l=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),i=e("p",null,[e("strong",null,"说明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[l,i];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=t(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/api_presets_index.md.BEZBx6Gj.js b/assets/api_presets_index.md.BEZBx6Gj.js
new file mode 100644
index 0000000..ee491b3
--- /dev/null
+++ b/assets/api_presets_index.md.BEZBx6Gj.js
@@ -0,0 +1 @@
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/index.md","filePath":"zh/api/presets/index.md"}'),p={name:"api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,"本模块塞了一些预设",-1),n=[c,o];function d(i,l,_,m,h,f){return a(),s("div",null,n)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/api_presets_index.md.BEZBx6Gj.lean.js b/assets/api_presets_index.md.BEZBx6Gj.lean.js
new file mode 100644
index 0000000..ee491b3
--- /dev/null
+++ b/assets/api_presets_index.md.BEZBx6Gj.lean.js
@@ -0,0 +1 @@
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/index.md","filePath":"zh/api/presets/index.md"}'),p={name:"api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,"本模块塞了一些预设",-1),n=[c,o];function d(i,l,_,m,h,f){return a(),s("div",null,n)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/api_presets_index.md.C7sBj6Q8.js b/assets/api_presets_index.md.C7sBj6Q8.js
deleted file mode 100644
index df120f9..0000000
--- a/assets/api_presets_index.md.C7sBj6Q8.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/index.md","filePath":"zh/api/presets/index.md"}'),p={name:"api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),n=e("p",null,[e("strong",null,"说明"),t(": 本模块塞了一些预设")],-1),o=[c,n];function d(i,l,_,m,h,f){return r(),a("div",null,o)}const u=s(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/api_presets_index.md.C7sBj6Q8.lean.js b/assets/api_presets_index.md.C7sBj6Q8.lean.js
deleted file mode 100644
index df120f9..0000000
--- a/assets/api_presets_index.md.C7sBj6Q8.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/index.md","filePath":"zh/api/presets/index.md"}'),p={name:"api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),n=e("p",null,[e("strong",null,"说明"),t(": 本模块塞了一些预设")],-1),o=[c,n];function d(i,l,_,m,h,f){return r(),a("div",null,o)}const u=s(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/api_presets_model_index.md.BcL7qpu8.js b/assets/api_presets_model_index.md.CzrZX1Li.js
similarity index 80%
rename from assets/api_presets_model_index.md.BcL7qpu8.js
rename to assets/api_presets_model_index.md.CzrZX1Li.js
index 5fc2697..05acf16 100644
--- a/assets/api_presets_model_index.md.BcL7qpu8.js
+++ b/assets/api_presets_model_index.md.CzrZX1Li.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n(`
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码 或 在GitHub上查看
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),n={name:"api/presets/model/index.md"},h=t(`
mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码 或 在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_model_index.md.BcL7qpu8.lean.js b/assets/api_presets_model_index.md.CzrZX1Li.lean.js
similarity index 61%
rename from assets/api_presets_model_index.md.BcL7qpu8.lean.js
rename to assets/api_presets_model_index.md.CzrZX1Li.lean.js
index e43f650..adb0c48 100644
--- a/assets/api_presets_model_index.md.BcL7qpu8.lean.js
+++ b/assets/api_presets_model_index.md.CzrZX1Li.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),n={name:"api/presets/model/index.md"},h=t("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_model_model.md.Ch05JNzT.js b/assets/api_presets_model_model.md.Ch05JNzT.js
deleted file mode 100644
index 0fb7911..0000000
--- a/assets/api_presets_model_model.md.Ch05JNzT.js
+++ /dev/null
@@ -1,18 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/model.md","filePath":"zh/api/presets/model/model.md"}'),t={name:"api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码 或 在GitHub上查看
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
-    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
-    z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_model_model.md.Ch05JNzT.lean.js b/assets/api_presets_model_model.md.Ch05JNzT.lean.js
deleted file mode 100644
index 9be95df..0000000
--- a/assets/api_presets_model_model.md.Ch05JNzT.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/model.md","filePath":"zh/api/presets/model/model.md"}'),t={name:"api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_presets.md.kIUJtfck.js b/assets/api_presets_presets.md.kIUJtfck.js
deleted file mode 100644
index 9bc22c3..0000000
--- a/assets/api_presets_presets.md.kIUJtfck.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c as a,o as r,j as e,a as s}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/presets.md","filePath":"zh/api/presets/presets.md"}'),p={name:"api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[s("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"说明"),s(": 本模块塞了一些预设")],-1),n=[c,o];function l(d,i,_,m,h,f){return r(),a("div",null,n)}const x=t(p,[["render",l]]);export{u as __pageData,x as default};
diff --git a/assets/api_presets_presets.md.kIUJtfck.lean.js b/assets/api_presets_presets.md.kIUJtfck.lean.js
deleted file mode 100644
index 9bc22c3..0000000
--- a/assets/api_presets_presets.md.kIUJtfck.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c as a,o as r,j as e,a as s}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/presets.md","filePath":"zh/api/presets/presets.md"}'),p={name:"api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[s("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"说明"),s(": 本模块塞了一些预设")],-1),n=[c,o];function l(d,i,_,m,h,f){return r(),a("div",null,n)}const x=t(p,[["render",l]]);export{u as __pageData,x as default};
diff --git a/assets/app.CaA7Rfbk.js b/assets/app.iiidcsxa.js
similarity index 95%
rename from assets/app.CaA7Rfbk.js
rename to assets/app.iiidcsxa.js
index 023a2c1..7833e98 100644
--- a/assets/app.CaA7Rfbk.js
+++ b/assets/app.iiidcsxa.js
@@ -1 +1 @@
-import{t as p}from"./chunks/theme.BhGtk3iD.js";import{U as o,a5 as u,a6 as c,a7 as l,a8 as f,a9 as d,aa as m,ab as h,ac as g,ad as A,ae as y,d as P,u as v,y as C,x as b,af as w,ag as E,ah as R,ai as S}from"./chunks/framework.DpC1ZpOZ.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return C(()=>{b(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&w(),E(),R(),s.setup&&s.setup(),()=>S(s.Layout)}});async function x(){globalThis.__VITEPRESS__=!0;const e=_(),a=D();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function D(){return g(T)}function _(){let e=o,a;return A(t=>{let n=y(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&x().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{x as createApp};
+import{t as p}from"./chunks/theme.BKKsDm5-.js";import{U as o,a5 as u,a6 as c,a7 as l,a8 as f,a9 as d,aa as m,ab as h,ac as g,ad as A,ae as y,d as P,u as v,y as C,x as b,af as w,ag as E,ah as R,ai as S}from"./chunks/framework.DpC1ZpOZ.js";function i(e){if(e.extends){const a=i(e.extends);return{...a,...e,async enhanceApp(t){a.enhanceApp&&await a.enhanceApp(t),e.enhanceApp&&await e.enhanceApp(t)}}}return e}const s=i(p),T=P({name:"VitePressApp",setup(){const{site:e,lang:a,dir:t}=v();return C(()=>{b(()=>{document.documentElement.lang=a.value,document.documentElement.dir=t.value})}),e.value.router.prefetchLinks&&w(),E(),R(),s.setup&&s.setup(),()=>S(s.Layout)}});async function x(){globalThis.__VITEPRESS__=!0;const e=_(),a=D();a.provide(c,e);const t=l(e.route);return a.provide(f,t),a.component("Content",d),a.component("ClientOnly",m),Object.defineProperties(a.config.globalProperties,{$frontmatter:{get(){return t.frontmatter.value}},$params:{get(){return t.page.value.params}}}),s.enhanceApp&&await s.enhanceApp({app:a,router:e,siteData:h}),{app:a,router:e,data:t}}function D(){return g(T)}function _(){let e=o,a;return A(t=>{let n=y(t),r=null;return n&&(e&&(a=n),(e||a===n)&&(n=n.replace(/\.js$/,".lean.js")),r=import(n)),o&&(e=!1),r},s.NotFound)}o&&x().then(({app:e,router:a,data:t})=>{a.go().then(()=>{u(a.route,t.site),e.mount("#app")})});export{x as createApp};
diff --git a/assets/chunks/@localSearchIndexen.CHzCNdBP.js b/assets/chunks/@localSearchIndexen.CHzCNdBP.js
new file mode 100644
index 0000000..05fb4b9
--- /dev/null
+++ b/assets/chunks/@localSearchIndexen.CHzCNdBP.js
@@ -0,0 +1 @@
+const 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__eq__(self, other) -> bool","titles":["mbcp.mp_math.line","class Line3"]},"76":{"title":"mbcp.mp_math.plane","titles":[]},"77":{"title":"class Plane3","titles":["mbcp.mp_math.plane"]},"78":{"title":"method __init__(self, a: float, b: float, c: float, d: float)","titles":["mbcp.mp_math.plane","class Plane3"]},"79":{"title":"method approx(self, other: Plane3) -> bool","titles":["mbcp.mp_math.plane","class Plane3"]},"80":{"title":"method cal_angle(self, other: Line3 | Plane3) -> AnyAngle","titles":["mbcp.mp_math.plane","class Plane3"]},"81":{"title":"method cal_distance(self, other: Plane3 | Point3) -> float","titles":["mbcp.mp_math.plane","class Plane3"]},"82":{"title":"method cal_intersection_line3(self, other: Plane3) -> Line3","titles":["mbcp.mp_math.plane","class Plane3"]},"83":{"title":"method cal_intersection_point3(self, other: Line3) -> Point3","titles":["mbcp.mp_math.plane","class Plane3"]},"84":{"title":"method cal_parallel_plane3(self, point: Point3) -> 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 * focus-trap 7.5.4
 * @license MIT, https://github.com/focus-trap/focus-trap/blob/master/LICENSE
-*/function ct(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var s=Object.getOwnPropertySymbols(a);e&&(s=s.filter(function(n){return Object.getOwnPropertyDescriptor(a,n).enumerable})),t.push.apply(t,s)}return t}function lt(a){for(var e=1;e0){var s=e[e.length-1];s!==t&&s.pause()}var n=e.indexOf(t);n===-1||e.splice(n,1),e.push(t)},deactivateTrap:function(e,t){var s=e.indexOf(t);s!==-1&&e.splice(s,1),e.length>0&&e[e.length-1].unpause()}},Ns=function(e){return e.tagName&&e.tagName.toLowerCase()==="input"&&typeof e.select=="function"},ks=function(e){return(e==null?void 0:e.key)==="Escape"||(e==null?void 0:e.key)==="Esc"||(e==null?void 0:e.keyCode)===27},me=function(e){return(e==null?void 0:e.key)==="Tab"||(e==null?void 0:e.keyCode)===9},Fs=function(e){return me(e)&&!e.shiftKey},Os=function(e){return me(e)&&e.shiftKey},dt=function(e){return setTimeout(e,0)},ht=function(e,t){var s=-1;return e.every(function(n,r){return t(n)?(s=r,!1):!0}),s},pe=function(e){for(var t=arguments.length,s=new Array(t>1?t-1:0),n=1;n1?m-1:0),E=1;E=0)u=s.activeElement;else{var d=i.tabbableGroups[0],m=d&&d.firstTabbableNode;u=m||h("fallbackFocus")}if(!u)throw new Error("Your focus-trap needs to have at least one focusable element");return u},f=function(){if(i.containerGroups=i.containers.map(function(u){var d=_s(u,r.tabbableOptions),m=xs(u,r.tabbableOptions),S=d.length>0?d[0]:void 0,E=d.length>0?d[d.length-1]:void 0,k=m.find(function(p){return ae(p)}),F=m.slice().reverse().find(function(p){return ae(p)}),M=!!d.find(function(p){return ie(p)>0});return{container:u,tabbableNodes:d,focusableNodes:m,posTabIndexesFound:M,firstTabbableNode:S,lastTabbableNode:E,firstDomTabbableNode:k,lastDomTabbableNode:F,nextTabbableNode:function(g){var N=arguments.length>1&&arguments[1]!==void 0?arguments[1]:!0,O=d.indexOf(g);return O<0?N?m.slice(m.indexOf(g)+1).find(function(P){return ae(P)}):m.slice(0,m.indexOf(g)).reverse().find(function(P){return ae(P)}):d[O+(N?1:-1)]}}}),i.tabbableGroups=i.containerGroups.filter(function(u){return u.tabbableNodes.length>0}),i.tabbableGroups.length<=0&&!h("fallbackFocus"))throw new Error("Your focus-trap must have at least one container with at least one tabbable node in it at all times");if(i.containerGroups.find(function(u){return u.posTabIndexesFound})&&i.containerGroups.length>1)throw new Error("At least one node with a positive tabindex was found in one of your focus-trap's multiple containers. 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t=window.navigator.userAgent;(t.indexOf("MSIE")>-1||t.indexOf("Trident")>-1)&&(this.ie=!0)}set opt(e){this._opt=Object.assign({},{element:"",className:"",exclude:[],iframes:!1,iframesTimeout:5e3,separateWordSearch:!0,diacritics:!0,synonyms:{},accuracy:"partially",acrossElements:!1,caseSensitive:!1,ignoreJoiners:!1,ignoreGroups:0,ignorePunctuation:[],wildcards:"disabled",each:()=>{},noMatch:()=>{},filter:()=>!0,done:()=>{},debug:!1,log:window.console},e)}get opt(){return this._opt}get iterator(){return new ce(this.ctx,this.opt.iframes,this.opt.exclude,this.opt.iframesTimeout)}log(e,t="debug"){const s=this.opt.log;this.opt.debug&&typeof s=="object"&&typeof s[t]=="function"&&s[t](`mark.js: ${e}`)}escapeStr(e){return e.replace(/[\-\[\]\/\{\}\(\)\*\+\?\.\\\^\$\|]/g,"\\$&")}createRegExp(e){return 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diff --git a/assets/chunks/theme.BhGtk3iD.js b/assets/chunks/theme.BKKsDm5-.js
similarity index 69%
rename from assets/chunks/theme.BhGtk3iD.js
rename to assets/chunks/theme.BKKsDm5-.js
index fd17615..79a795d 100644
--- a/assets/chunks/theme.BhGtk3iD.js
+++ b/assets/chunks/theme.BKKsDm5-.js
@@ -1,2 +1,2 @@
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diff --git a/assets/en_api_api.md.D31N0-_j.js b/assets/en_api_api.md.D31N0-_j.js
deleted file mode 100644
index d881019..0000000
--- a/assets/en_api_api.md.D31N0-_j.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/api.md","filePath":"en/api/api.md"}'),c={name:"en/api/api.md"},o=p('
mbcp ​
Description: 本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(i,_,n,d,m,l){return t(),a("div",null,r)}const b=e(c,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/en_api_api.md.D31N0-_j.lean.js b/assets/en_api_api.md.D31N0-_j.lean.js
deleted file mode 100644
index 52b27f0..0000000
--- a/assets/en_api_api.md.D31N0-_j.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/api.md","filePath":"en/api/api.md"}'),c={name:"en/api/api.md"},o=p("",5),r=[o];function s(i,_,n,d,m,l){return t(),a("div",null,r)}const b=e(c,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/en_api_index.md.BrJlad-k.js b/assets/en_api_index.md.BrJlad-k.js
new file mode 100644
index 0000000..74d78b3
--- /dev/null
+++ b/assets/en_api_index.md.BrJlad-k.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/index.md","filePath":"en/api/index.md"}'),p={name:"en/api/index.md"},o=c('
mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(d,_,n,i,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/en_api_index.md.CpTS_pfZ.lean.js b/assets/en_api_index.md.BrJlad-k.lean.js
similarity index 85%
rename from assets/en_api_index.md.CpTS_pfZ.lean.js
rename to assets/en_api_index.md.BrJlad-k.lean.js
index d925b97..2206d73 100644
--- a/assets/en_api_index.md.CpTS_pfZ.lean.js
+++ b/assets/en_api_index.md.BrJlad-k.lean.js
@@ -1 +1 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/index.md","filePath":"en/api/index.md"}'),p={name:"en/api/index.md"},o=c("",5),r=[o];function s(n,d,i,_,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/index.md","filePath":"en/api/index.md"}'),p={name:"en/api/index.md"},o=c("",5),r=[o];function s(d,_,n,i,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/en_api_index.md.CpTS_pfZ.js b/assets/en_api_index.md.CpTS_pfZ.js
deleted file mode 100644
index d8d723e..0000000
--- a/assets/en_api_index.md.CpTS_pfZ.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/index.md","filePath":"en/api/index.md"}'),p={name:"en/api/index.md"},o=c('
mbcp ​
Description: 本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(n,d,i,_,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/en_api_mp_math_angle.md.DTo0bIGQ.js b/assets/en_api_mp_math_angle.md.BvzeTdtj.js
similarity index 59%
rename from assets/en_api_mp_math_angle.md.DTo0bIGQ.js
rename to assets/en_api_mp_math_angle.md.BvzeTdtj.js
index 195131e..49cb54e 100644
--- a/assets/en_api_mp_math_angle.md.DTo0bIGQ.js
+++ b/assets/en_api_mp_math_angle.md.BvzeTdtj.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
Description: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
func __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code or View on GitHub
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 or View on GitHub
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code or View on GitHub
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 or View on GitHub
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code or View on GitHub
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 or View on GitHub
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code or View on GitHub
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 or View on GitHub
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code or View on GitHub
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 or View on GitHub
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code or View on GitHub
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 or View on GitHub
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code or View on GitHub
python
@property
+    return math.sin(self.radian)
@property
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code or View on GitHub
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code or View on GitHub
python
@property
+    return math.cos(self.radian)
@property
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code or View on GitHub
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code or View on GitHub
python
@property
+    return math.tan(self.radian)
@property
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code or View on GitHub
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code or View on GitHub
python
@property
+    return 1 / math.tan(self.radian)
@property
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code or View on GitHub
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code or View on GitHub
python
@property
+    return 1 / math.cos(self.radian)
@property
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code or View on GitHub
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
Source code or View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
Source code or View on GitHub
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code or View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
Source code or View on GitHub
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
Source code or View on GitHub
python
def __truediv__(self, other):
+    ...
method self / other ​
Source code or View on GitHub
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{y as __pageData,F as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.DTo0bIGQ.lean.js b/assets/en_api_mp_math_angle.md.BvzeTdtj.lean.js
similarity index 72%
rename from assets/en_api_mp_math_angle.md.DTo0bIGQ.lean.js
rename to assets/en_api_mp_math_angle.md.BvzeTdtj.lean.js
index 150c5ed..8f233a1 100644
--- a/assets/en_api_mp_math_angle.md.DTo0bIGQ.lean.js
+++ b/assets/en_api_mp_math_angle.md.BvzeTdtj.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),t={name:"en/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_const.md.CrUt_3FV.js b/assets/en_api_mp_math_const.md.CrUt_3FV.js
new file mode 100644
index 0000000..bd4aed6
--- /dev/null
+++ b/assets/en_api_mp_math_const.md.CrUt_3FV.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const _=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/const.md","filePath":"en/api/mp_math/const.md"}'),r={name:"en/api/mp_math/const.md"},i=o('
mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • Description: 常量 π
  • Default: math.pi
var E ​
  • Description: 自然对数的底 exp(1)
  • Default: math.e
var GOLDEN_RATIO ​
  • Description: 黄金分割比
  • Default: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • Description: 欧拉常数
  • Default: 0.5772156649015329
var EPSILON ​
  • Description: 精度误差
  • Default: 0.0001
var APPROX ​
  • Description: 约等于判定误差
  • Default: 0.001
',14),l=[i];function n(s,c,p,d,h,m){return e(),t("div",null,l)}const g=a(r,[["render",n]]);export{_ as __pageData,g as default};
diff --git a/assets/en_api_mp_math_const.md.CrUt_3FV.lean.js b/assets/en_api_mp_math_const.md.CrUt_3FV.lean.js
new file mode 100644
index 0000000..9b0e34a
--- /dev/null
+++ b/assets/en_api_mp_math_const.md.CrUt_3FV.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const _=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/const.md","filePath":"en/api/mp_math/const.md"}'),r={name:"en/api/mp_math/const.md"},i=o("",14),l=[i];function n(s,c,p,d,h,m){return e(),t("div",null,l)}const g=a(r,[["render",n]]);export{_ as __pageData,g as default};
diff --git a/assets/en_api_mp_math_const.md.DjbxFoGO.js b/assets/en_api_mp_math_const.md.DjbxFoGO.js
deleted file mode 100644
index 2f542a1..0000000
--- a/assets/en_api_mp_math_const.md.DjbxFoGO.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as t,o,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const _=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/const.md","filePath":"en/api/mp_math/const.md"}'),r={name:"en/api/mp_math/const.md"},i=e('
mbcp.mp_math.const ​
Description: 本模块定义了一些常用的常量
var PI ​
  • Description: 常量 π
  • Default: math.pi
var E ​
  • Description: 自然对数的底 exp(1)
  • Default: math.e
var GOLDEN_RATIO ​
  • Description: 黄金分割比
  • Default: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • Description: 欧拉常数
  • Default: 0.5772156649015329
var EPSILON ​
  • Description: 精度误差
  • Default: 0.0001
var APPROX ​
  • Description: 约等于判定误差
  • Default: 0.001
',14),n=[i];function l(s,c,p,d,h,m){return o(),t("div",null,n)}const g=a(r,[["render",l]]);export{_ as __pageData,g as default};
diff --git a/assets/en_api_mp_math_const.md.DjbxFoGO.lean.js b/assets/en_api_mp_math_const.md.DjbxFoGO.lean.js
deleted file mode 100644
index 4241446..0000000
--- a/assets/en_api_mp_math_const.md.DjbxFoGO.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as t,o,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const _=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/const.md","filePath":"en/api/mp_math/const.md"}'),r={name:"en/api/mp_math/const.md"},i=e("",14),n=[i];function l(s,c,p,d,h,m){return o(),t("div",null,n)}const g=a(r,[["render",l]]);export{_ as __pageData,g as default};
diff --git a/assets/en_api_mp_math_equation.md.NTcIjf_k.js b/assets/en_api_mp_math_equation.md.CHBtH4v6.js
similarity index 82%
rename from assets/en_api_mp_math_equation.md.NTcIjf_k.js
rename to assets/en_api_mp_math_equation.md.CHBtH4v6.js
index d8a1c2d..5714a40 100644
--- a/assets/en_api_mp_math_equation.md.NTcIjf_k.js
+++ b/assets/en_api_mp_math_equation.md.CHBtH4v6.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
Description: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
Source code or View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
Source code or View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code or View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code or View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,c,d){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default};
+        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default};
diff --git a/assets/en_api_mp_math_equation.md.NTcIjf_k.lean.js b/assets/en_api_mp_math_equation.md.CHBtH4v6.lean.js
similarity index 86%
rename from assets/en_api_mp_math_equation.md.NTcIjf_k.lean.js
rename to assets/en_api_mp_math_equation.md.CHBtH4v6.lean.js
index 4358d3e..ec4bd2d 100644
--- a/assets/en_api_mp_math_equation.md.NTcIjf_k.lean.js
+++ b/assets/en_api_mp_math_equation.md.CHBtH4v6.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,c,d){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default};
diff --git a/assets/en_api_mp_math_function.md.BXNFIE6F.js b/assets/en_api_mp_math_function.md.BXNFIE6F.js
deleted file mode 100644
index 052be13..0000000
--- a/assets/en_api_mp_math_function.md.BXNFIE6F.js
+++ /dev/null
@@ -1,42 +0,0 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),e={name:"en/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
Description: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
Arguments:
Return: 梯度
Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
-    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
-    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
-    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
-    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
Description: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
Arguments:
Return: 柯里化后的函数
Examples:
python
def add(a: int, b: int, c: int) -> int:
-    return a + b + c
-add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
Source code or View on GitHub
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
-
-    def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
-        return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const Z=l(e,[["render",x]]);export{V as __pageData,Z as default};
diff --git a/assets/en_api_mp_math_function.md.D68bTyed.js b/assets/en_api_mp_math_function.md.D68bTyed.js
new file mode 100644
index 0000000..9c5c7a0
--- /dev/null
+++ b/assets/en_api_mp_math_function.md.D68bTyed.js
@@ -0,0 +1,42 @@
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),e={name:"en/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
Arguments:
Return: 梯度
Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    """
+    计算三元函数在某点的梯度向量。
+    > [!tip]
+    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
+    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
+    Args:
+        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
+        p ([\`Point3\`](./point#class-point3)): 点
+        epsilon: 偏移量
+    Returns:
+        梯度
+    """
+    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
+    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
+    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
+    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
Description: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
Arguments:
Return: 柯里化后的函数
Examples:
python
def add(a: int, b: int, c: int) -> int:
+    return a + b + c
+add_curried = curry(add, 1, 2)
+add_curried(3)  # 6
Source code or View on GitHub
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+    """
+    对多参数函数进行柯里化。
+    > [!tip]
+    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
+    Args:
+        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
+        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
+    Returns:
+        柯里化后的函数
+    Examples:
+        \`\`\`python
+        def add(a: int, b: int, c: int) -> int:
+            return a + b + c
+        add_curried = curry(add, 1, 2)
+        add_curried(3)  # 6
+        \`\`\`
+    """
+
+    def curried_func(*args2: Var) -> Var:
+        """@litedoc-hide"""
+        return func(*args, *args2)
+    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const Z=l(e,[["render",x]]);export{V as __pageData,Z as default};
diff --git a/assets/en_api_mp_math_function.md.BXNFIE6F.lean.js b/assets/en_api_mp_math_function.md.D68bTyed.lean.js
similarity index 100%
rename from assets/en_api_mp_math_function.md.BXNFIE6F.lean.js
rename to assets/en_api_mp_math_function.md.D68bTyed.lean.js
diff --git a/assets/en_api_mp_math_index.md.D331As7i.js b/assets/en_api_mp_math_index.md.D331As7i.js
new file mode 100644
index 0000000..2e4bdec
--- /dev/null
+++ b/assets/en_api_mp_math_index.md.D331As7i.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/mp_math/index.md","filePath":"en/api/mp_math/index.md"}'),l={name:"en/api/mp_math/index.md"},o=c('
mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function n(m,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",n]]);export{f as __pageData,u as default};
diff --git a/assets/en_api_mp_math_index.md.ypHGEnmb.lean.js b/assets/en_api_mp_math_index.md.D331As7i.lean.js
similarity index 72%
rename from assets/en_api_mp_math_index.md.ypHGEnmb.lean.js
rename to assets/en_api_mp_math_index.md.D331As7i.lean.js
index eaeabe2..064b681 100644
--- a/assets/en_api_mp_math_index.md.ypHGEnmb.lean.js
+++ b/assets/en_api_mp_math_index.md.D331As7i.lean.js
@@ -1 +1 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/mp_math/index.md","filePath":"en/api/mp_math/index.md"}'),l={name:"en/api/mp_math/index.md"},o=c("",3),n=[o];function i(m,s,p,r,d,h){return t(),a("div",null,n)}const u=e(l,[["render",i]]);export{f as __pageData,u as default};
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/mp_math/index.md","filePath":"en/api/mp_math/index.md"}'),l={name:"en/api/mp_math/index.md"},o=c("",3),i=[o];function n(m,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",n]]);export{f as __pageData,u as default};
diff --git a/assets/en_api_mp_math_index.md.ypHGEnmb.js b/assets/en_api_mp_math_index.md.ypHGEnmb.js
deleted file mode 100644
index 082e842..0000000
--- a/assets/en_api_mp_math_index.md.ypHGEnmb.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/mp_math/index.md","filePath":"en/api/mp_math/index.md"}'),l={name:"en/api/mp_math/index.md"},o=c('
mbcp.mp_math ​
Description: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),n=[o];function i(m,s,p,r,d,h){return t(),a("div",null,n)}const u=e(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/api_mp_math_line.md.ByGRRi0A.js b/assets/en_api_mp_math_line.md.B69kHoPc.js
similarity index 59%
rename from assets/api_mp_math_line.md.ByGRRi0A.js
rename to assets/en_api_mp_math_line.md.B69kHoPc.js
index f408df4..0ddc9b7 100644
--- a/assets/api_mp_math_line.md.ByGRRi0A.js
+++ b/assets/en_api_mp_math_line.md.B69kHoPc.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
说明: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源代码 或 在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other (Line3): 另一条直线
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -23,7 +23,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other (Line3): 另一条直线
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other (Line3): 另一条直线
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -60,7 +60,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
返回: Line3: 垂线
源代码 或 在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
Return: Line3: 垂线
Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -68,7 +68,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Line3\`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
返回: Point3: 点
源代码 或 在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
Return: Point3: 点
Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -76,13 +76,13 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Point3\`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源代码 或 在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源代码 或 在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -91,7 +91,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -99,7 +99,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
返回: bool: 是否共线
源代码 或 在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
Return: bool: 是否共线
Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -107,7 +107,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
返回: bool: 是否在直线上
源代码 或 在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
Return: bool: 是否在直线上
Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -115,7 +115,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
返回: bool: 是否共面
源代码 或 在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
Return: bool: 是否共面
Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -124,7 +124,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码 或 在GitHub上查看
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code or View on GitHub
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -137,7 +137,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
返回: Line3: 直线
源代码 或 在GitHub上查看
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
Return: Line3: 直线
Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -148,7 +148,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             [\`Line3\`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源代码 或 在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other (Line3): 另一条直线
Return: Line3 | Point3 | None: 交集
Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other (Line3): 另一条直线
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -171,4 +171,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/en_api_mp_math_line.md.CxP-i4OT.lean.js b/assets/en_api_mp_math_line.md.B69kHoPc.lean.js
similarity index 72%
rename from assets/en_api_mp_math_line.md.CxP-i4OT.lean.js
rename to assets/en_api_mp_math_line.md.B69kHoPc.lean.js
index 8a7176f..0ed5ff5 100644
--- a/assets/en_api_mp_math_line.md.CxP-i4OT.lean.js
+++ b/assets/en_api_mp_math_line.md.B69kHoPc.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n("",106),e=[l];function p(h,k,r,o,d,c){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),t={name:"en/api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/en_api_mp_math_mp_math.md.5IisTIt3.js b/assets/en_api_mp_math_mp_math.md.5IisTIt3.js
deleted file mode 100644
index ef46adc..0000000
--- a/assets/en_api_mp_math_mp_math.md.5IisTIt3.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/mp_math/mp_math.md","filePath":"en/api/mp_math/mp_math.md"}'),l={name:"en/api/mp_math/mp_math.md"},m=c('
mbcp.mp_math ​
Description: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),o=[m];function n(i,s,p,r,h,_){return t(),a("div",null,o)}const u=e(l,[["render",n]]);export{f as __pageData,u as default};
diff --git a/assets/en_api_mp_math_mp_math.md.5IisTIt3.lean.js b/assets/en_api_mp_math_mp_math.md.5IisTIt3.lean.js
deleted file mode 100644
index bc6deb2..0000000
--- a/assets/en_api_mp_math_mp_math.md.5IisTIt3.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/mp_math/mp_math.md","filePath":"en/api/mp_math/mp_math.md"}'),l={name:"en/api/mp_math/mp_math.md"},m=c("",3),o=[m];function n(i,s,p,r,h,_){return t(),a("div",null,o)}const u=e(l,[["render",n]]);export{f as __pageData,u as default};
diff --git a/assets/en_api_mp_math_mp_math_typing.md.DWjztCj6.js b/assets/en_api_mp_math_mp_math_typing.md.DWjztCj6.js
deleted file mode 100644
index 16065e0..0000000
--- a/assets/en_api_mp_math_mp_math_typing.md.DWjztCj6.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/mp_math_typing.md","filePath":"en/api/mp_math/mp_math_typing.md"}'),l={name:"en/api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
Description: 本模块用于内部类型提示
var RealNumber ​
  • Description: 实数
  • Type: TypeAlias
  • Default: int | float
var Number ​
  • Description: 数
  • Type: TypeAlias
  • Default: RealNumber | complex
var SingleVar ​
  • Description: 单变量
  • Default: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • Description: 数组变量
  • Default: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • Description: 变量
  • Type: TypeAlias
  • Default: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • Description: 一元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • Description: 一元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • Description: 一元函数
  • Type: TypeAlias
  • Default: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • Description: 二元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • Description: 二元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • Description: 二元函数
  • Type: TypeAlias
  • Default: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • Description: 三元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • Description: 三元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • Description: 三元函数
  • Type: TypeAlias
  • Default: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • Description: 多元单变量函数
  • Type: TypeAlias
  • Default: Callable[..., SingleVar]
var MultiArraysFunc ​
  • Description: 多元数组函数
  • Type: TypeAlias
  • Default: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • Description: 多元函数
  • Type: TypeAlias
  • Default: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,p,u,d,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/en_api_mp_math_mp_math_typing.md.xRGJGUMm.js b/assets/en_api_mp_math_mp_math_typing.md.xRGJGUMm.js
new file mode 100644
index 0000000..a59d1b5
--- /dev/null
+++ b/assets/en_api_mp_math_mp_math_typing.md.xRGJGUMm.js
@@ -0,0 +1 @@
+import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/mp_math_typing.md","filePath":"en/api/mp_math/mp_math_typing.md"}'),l={name:"en/api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • Description: 实数
  • Type: TypeAlias
  • Default: int | float
var Number ​
  • Description: 数
  • Type: TypeAlias
  • Default: RealNumber | complex
var SingleVar ​
  • Description: 单变量
  • Default: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • Description: 数组变量
  • Default: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • Description: 变量
  • Type: TypeAlias
  • Default: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • Description: 一元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • Description: 一元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • Description: 一元函数
  • Type: TypeAlias
  • Default: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • Description: 二元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • Description: 二元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • Description: 二元函数
  • Type: TypeAlias
  • Default: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • Description: 三元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • Description: 三元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • Description: 三元函数
  • Type: TypeAlias
  • Default: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • Description: 多元单变量函数
  • Type: TypeAlias
  • Default: Callable[..., SingleVar]
var MultiArraysFunc ​
  • Description: 多元数组函数
  • Type: TypeAlias
  • Default: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • Description: 多元函数
  • Type: TypeAlias
  • Default: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,p,u,d,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/en_api_mp_math_mp_math_typing.md.DWjztCj6.lean.js b/assets/en_api_mp_math_mp_math_typing.md.xRGJGUMm.lean.js
similarity index 100%
rename from assets/en_api_mp_math_mp_math_typing.md.DWjztCj6.lean.js
rename to assets/en_api_mp_math_mp_math_typing.md.xRGJGUMm.lean.js
diff --git a/assets/api_mp_math_plane.md.Ir4HtSn5.js b/assets/en_api_mp_math_plane.md.BdKgRumw.js
similarity index 68%
rename from assets/api_mp_math_plane.md.Ir4HtSn5.js
rename to assets/en_api_mp_math_plane.md.BdKgRumw.js
index 33c0d60..93b9110 100644
--- a/assets/api_mp_math_plane.md.Ir4HtSn5.js
+++ b/assets/en_api_mp_math_plane.md.BdKgRumw.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
说明: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源代码 或 在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),t={name:"en/api/mp_math/plane.md"},l=n(`
mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
返回: AnyAngle: 夹角
引发:
源代码 或 在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Raises:
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
返回: float: 距离
引发:
源代码 或 在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other (Plane3): 另一个平面
返回: Line3: 交线
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other (Plane3): 另一个平面
Return: Line3: 交线
Raises:
Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -84,7 +84,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
返回: Point3: 交点
引发:
源代码 或 在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -98,7 +98,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -106,7 +106,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源代码 或 在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -114,14 +114,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: Vector3: 法向量
源代码 或 在GitHub上查看
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: Vector3: 法向量
Source code or View on GitHub
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [\`Vector3\`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
返回: Plane3: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -133,7 +133,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
Return: 平面
Source code or View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -147,7 +147,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
Return: 平面
Source code or View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
返回: 平面
源代码 或 在GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
Return: 平面
Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -171,11 +171,11 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
返回: Line3 | Point3 | None: 交集
引发:
源代码 或 在GitHub上查看
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
Return: Line3 | Point3 | None: 交集
Raises:
Source code or View on GitHub
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -194,7 +194,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
说明: 判断两个平面是否等价。
参数:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源代码 或 在GitHub上查看
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Description: 判断两个平面是否等价。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -202,5 +202,5 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,113),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const c=s(t,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_mp_math_plane.md.BdKgRumw.lean.js b/assets/en_api_mp_math_plane.md.BdKgRumw.lean.js
new file mode 100644
index 0000000..16cca30
--- /dev/null
+++ b/assets/en_api_mp_math_plane.md.BdKgRumw.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),t={name:"en/api/mp_math/plane.md"},l=n("",113),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const c=s(t,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_mp_math_plane.md.BsgpTZdY.lean.js b/assets/en_api_mp_math_plane.md.BsgpTZdY.lean.js
deleted file mode 100644
index d91e863..0000000
--- a/assets/en_api_mp_math_plane.md.BsgpTZdY.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
diff --git a/assets/api_mp_math_point.md.CIRBY4Zg.js b/assets/en_api_mp_math_point.md.BeT2oqIN.js
similarity index 54%
rename from assets/api_mp_math_point.md.CIRBY4Zg.js
rename to assets/en_api_mp_math_point.md.BeT2oqIN.js
index c9710a1..8e1989e 100644
--- a/assets/api_mp_math_point.md.CIRBY4Zg.js
+++ b/assets/en_api_mp_math_point.md.BeT2oqIN.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t(`
mbcp.mp_math.point ​
说明: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源代码 或 在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},e=t(`
mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -17,11 +17,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
源代码 或 在GitHub上查看
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 or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
说明: P + V -> P P + P -> P
参数:
返回: Point3: 新的点
源代码 或 在GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,7 +30,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
返回: bool: 是否相等
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 Vector3 中实现
参数:
返回: Vector3: 新的向量
源代码 或 在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 Vector3 中实现
Arguments:
Return: Vector3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -49,4 +49,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
             [\`Vector3\`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),h=[l];function p(e,k,o,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",p]]);export{E as __pageData,y as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),h=[e];function l(p,o,k,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_point.md.DcGqVqiO.lean.js b/assets/en_api_mp_math_point.md.BeT2oqIN.lean.js
similarity index 72%
rename from assets/en_api_mp_math_point.md.DcGqVqiO.lean.js
rename to assets/en_api_mp_math_point.md.BeT2oqIN.lean.js
index 1533944..de9a344 100644
--- a/assets/en_api_mp_math_point.md.DcGqVqiO.lean.js
+++ b/assets/en_api_mp_math_point.md.BeT2oqIN.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},l=t("",39),e=[l];function h(p,o,k,r,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},e=t("",39),h=[e];function l(p,o,k,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_segment.md.Cge1J0TK.js b/assets/en_api_mp_math_segment.md.DbFvInHk.js
similarity index 71%
rename from assets/en_api_mp_math_segment.md.Cge1J0TK.js
rename to assets/en_api_mp_math_segment.md.DbFvInHk.js
index f6dc84f..d7bde09 100644
--- a/assets/en_api_mp_math_segment.md.Cge1J0TK.js
+++ b/assets/en_api_mp_math_segment.md.DbFvInHk.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
Description: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。
Arguments:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。
Arguments:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -12,4 +12,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function l(e,k,r,d,o,E){return a(),i("div",null,h)}const F=s(t,[["render",l]]);export{c as __pageData,F as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function e(l,k,r,d,o,E){return a(),i("div",null,h)}const c=s(t,[["render",e]]);export{F as __pageData,c as default};
diff --git a/assets/en_api_mp_math_segment.md.Cge1J0TK.lean.js b/assets/en_api_mp_math_segment.md.DbFvInHk.lean.js
similarity index 53%
rename from assets/en_api_mp_math_segment.md.Cge1J0TK.lean.js
rename to assets/en_api_mp_math_segment.md.DbFvInHk.lean.js
index 8e9289f..f54225f 100644
--- a/assets/en_api_mp_math_segment.md.Cge1J0TK.lean.js
+++ b/assets/en_api_mp_math_segment.md.DbFvInHk.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,o,E){return a(),i("div",null,h)}const F=s(t,[["render",l]]);export{c as __pageData,F as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},p=n("",8),h=[p];function e(l,k,r,d,o,E){return a(),i("div",null,h)}const c=s(t,[["render",e]]);export{F as __pageData,c as default};
diff --git a/assets/en_api_mp_math_utils.md.Bu0IGkds.lean.js b/assets/en_api_mp_math_utils.md.Bu0IGkds.lean.js
deleted file mode 100644
index 80d9fc9..0000000
--- a/assets/en_api_mp_math_utils.md.Bu0IGkds.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),t={name:"en/api/mp_math/utils.md"},l=n("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_utils.md.Bu0IGkds.js b/assets/en_api_mp_math_utils.md.CYq8hncD.js
similarity index 79%
rename from assets/en_api_mp_math_utils.md.Bu0IGkds.js
rename to assets/en_api_mp_math_utils.md.CYq8hncD.js
index dffb3c5..0b82404 100644
--- a/assets/en_api_mp_math_utils.md.Bu0IGkds.js
+++ b/assets/en_api_mp_math_utils.md.CYq8hncD.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),t={name:"en/api/mp_math/utils.md"},l=n(`
mbcp.mp_math.utils ​
Description: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
Description: 区间限定函数
Arguments:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
Return: float: 限定在区间内的值
Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),n={name:"en/api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
Description: 区间限定函数
Arguments:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
Return: float: 限定在区间内的值
Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,13 +9,13 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     Returns:
         \`float\`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
Description: 用于近似比较对象
Arguments:
Source code or View on GitHub
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
Description: 用于近似比较对象
Arguments:
Source code or View on GitHub
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -25,8 +25,8 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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)
func raise_type_error(self, other) ​
Source code or View on GitHub
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code or View on GitHub
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -66,4 +66,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{c as __pageData,F as default};
+        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{F as __pageData,c as default};
diff --git a/assets/en_api_mp_math_utils.md.CYq8hncD.lean.js b/assets/en_api_mp_math_utils.md.CYq8hncD.lean.js
new file mode 100644
index 0000000..292eb4c
--- /dev/null
+++ b/assets/en_api_mp_math_utils.md.CYq8hncD.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),n={name:"en/api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{F as __pageData,c as default};
diff --git a/assets/en_api_mp_math_vector.md.DpvjNLj_.js b/assets/en_api_mp_math_vector.md.CPGkZzwr.js
similarity index 64%
rename from assets/en_api_mp_math_vector.md.DpvjNLj_.js
rename to assets/en_api_mp_math_vector.md.CPGkZzwr.js
index 89b3469..b314987 100644
--- a/assets/en_api_mp_math_vector.md.DpvjNLj_.js
+++ b/assets/en_api_mp_math_vector.md.CPGkZzwr.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},e=t(`
mbcp.mp_math.vector ​
Description: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},e=t(`
mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
Return: Vector3: 叉乘结果
Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
Return: Vector3: 叉乘结果
Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Vector3\`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code or View on GitHub
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code or View on GitHub
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,33 +72,33 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
Return: np.ndarray: numpy数组
Source code or View on GitHub
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
Return: np.ndarray: numpy数组
Source code or View on GitHub
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
Description: 向量的模。
Return: float: 模
Source code or View on GitHub
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
Description: 向量的模。
Return: float: 模
Source code or View on GitHub
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: Vector3: 单位向量
Source code or View on GitHub
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: Vector3: 单位向量
Source code or View on GitHub
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [\`Vector3\`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
Source code or View on GitHub
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+    return self / self.length
method __abs__(self) ​
Source code or View on GitHub
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
Description: V + P -> P
V + V -> V
Arguments:
Return: Vector3 | Point3: 新的向量或点
Source code or View on GitHub
python
def __add__(self, other):
+    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
Return: Vector3 | Point3: 新的向量或点
Source code or View on GitHub
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -113,7 +113,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -121,7 +121,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -131,11 +131,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
Description: V - P -> P
V - V -> V
Arguments:
Return: Vector3 | Point3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other):
+    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
Return: Vector3 | Point3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -150,7 +150,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}"')
func self - other: Point3 ​
Description: P - V -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -161,11 +161,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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
func self * other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
Return: Vector3: 数组运算结果
Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
Return: Vector3: 数组运算结果
Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -178,8 +178,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
Return: float: 点乘结果
Source code or View on GitHub
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
Return: float: 点乘结果
Source code or View on GitHub
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -187,11 +187,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
Description: 取负。
Return: Vector3: 负向量
Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
Description: 取负。
Return: Vector3: 负向量
Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [\`Vector3\`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • Description: 零向量
  • Type: Vector3
  • Default: Vector3(0, 0, 0)
var x_axis ​
  • Description: x轴单位向量
  • Type: Vector3
  • Default: Vector3(1, 0, 0)
var y_axis ​
  • Description: y轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 1, 0)
var z_axis ​
  • Description: z轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 0, 1)
`,138),l=[e];function h(p,k,r,o,d,c){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • Description: 零向量
  • Type: Vector3
  • Default: Vector3(0, 0, 0)
var x_axis ​
  • Description: x轴单位向量
  • Type: Vector3
  • Default: Vector3(1, 0, 0)
var y_axis ​
  • Description: y轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 1, 0)
var z_axis ​
  • Description: z轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 0, 1)
`,138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_vector.md.DpvjNLj_.lean.js b/assets/en_api_mp_math_vector.md.CPGkZzwr.lean.js
similarity index 72%
rename from assets/en_api_mp_math_vector.md.DpvjNLj_.lean.js
rename to assets/en_api_mp_math_vector.md.CPGkZzwr.lean.js
index 12b0de0..c32f366 100644
--- a/assets/en_api_mp_math_vector.md.DpvjNLj_.lean.js
+++ b/assets/en_api_mp_math_vector.md.CPGkZzwr.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},e=t("",138),l=[e];function h(p,k,r,o,d,c){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},e=t("",138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_particle_index.md.NezC90nG.js b/assets/en_api_particle_index.md.NezC90nG.js
deleted file mode 100644
index 1ef2adf..0000000
--- a/assets/en_api_particle_index.md.NezC90nG.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/particle/index.md","filePath":"en/api/particle/index.md"}'),i={name:"en/api/particle/index.md"},n=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),p=e("p",null,[e("strong",null,"Description"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[n,p];function l(o,d,_,m,h,f){return r(),c("div",null,s)}const u=a(i,[["render",l]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_particle_index.md.NezC90nG.lean.js b/assets/en_api_particle_index.md.NezC90nG.lean.js
deleted file mode 100644
index 1ef2adf..0000000
--- a/assets/en_api_particle_index.md.NezC90nG.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/particle/index.md","filePath":"en/api/particle/index.md"}'),i={name:"en/api/particle/index.md"},n=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),p=e("p",null,[e("strong",null,"Description"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[n,p];function l(o,d,_,m,h,f){return r(),c("div",null,s)}const u=a(i,[["render",l]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_particle_index.md.ZKByd_x0.js b/assets/en_api_particle_index.md.ZKByd_x0.js
new file mode 100644
index 0000000..6f0cf06
--- /dev/null
+++ b/assets/en_api_particle_index.md.ZKByd_x0.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/particle/index.md","filePath":"en/api/particle/index.md"}'),i={name:"en/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),n=e("p",null,"本模块定义了粒子生成相关的工具",-1),s=[p,n];function l(o,d,_,m,h,f){return c(),t("div",null,s)}const u=a(i,[["render",l]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_particle_index.md.ZKByd_x0.lean.js b/assets/en_api_particle_index.md.ZKByd_x0.lean.js
new file mode 100644
index 0000000..6f0cf06
--- /dev/null
+++ b/assets/en_api_particle_index.md.ZKByd_x0.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/particle/index.md","filePath":"en/api/particle/index.md"}'),i={name:"en/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),n=e("p",null,"本模块定义了粒子生成相关的工具",-1),s=[p,n];function l(o,d,_,m,h,f){return c(),t("div",null,s)}const u=a(i,[["render",l]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_particle_particle.md.BTk7xB-d.js b/assets/en_api_particle_particle.md.BTk7xB-d.js
deleted file mode 100644
index d6e8e1f..0000000
--- a/assets/en_api_particle_particle.md.BTk7xB-d.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/particle/particle.md","filePath":"en/api/particle/particle.md"}'),p={name:"en/api/particle/particle.md"},i=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"Description"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[i,l];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=a(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/en_api_particle_particle.md.BTk7xB-d.lean.js b/assets/en_api_particle_particle.md.BTk7xB-d.lean.js
deleted file mode 100644
index d6e8e1f..0000000
--- a/assets/en_api_particle_particle.md.BTk7xB-d.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/particle/particle.md","filePath":"en/api/particle/particle.md"}'),p={name:"en/api/particle/particle.md"},i=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"Description"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[i,l];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=a(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/en_api_presets_index.md.BhoZyGSV.js b/assets/en_api_presets_index.md.BhoZyGSV.js
new file mode 100644
index 0000000..33395a8
--- /dev/null
+++ b/assets/en_api_presets_index.md.BhoZyGSV.js
@@ -0,0 +1 @@
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/index.md","filePath":"en/api/presets/index.md"}'),p={name:"en/api/presets/index.md"},n=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),c=e("p",null,"本模块塞了一些预设",-1),o=[n,c];function d(i,l,_,m,h,f){return a(),s("div",null,o)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_presets_index.md.BhoZyGSV.lean.js b/assets/en_api_presets_index.md.BhoZyGSV.lean.js
new file mode 100644
index 0000000..33395a8
--- /dev/null
+++ b/assets/en_api_presets_index.md.BhoZyGSV.lean.js
@@ -0,0 +1 @@
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/index.md","filePath":"en/api/presets/index.md"}'),p={name:"en/api/presets/index.md"},n=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),c=e("p",null,"本模块塞了一些预设",-1),o=[n,c];function d(i,l,_,m,h,f){return a(),s("div",null,o)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_presets_index.md.Clhg0YLX.js b/assets/en_api_presets_index.md.Clhg0YLX.js
deleted file mode 100644
index d0958d0..0000000
--- a/assets/en_api_presets_index.md.Clhg0YLX.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/index.md","filePath":"en/api/presets/index.md"}'),n={name:"en/api/presets/index.md"},p=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),c=e("p",null,[e("strong",null,"Description"),t(": 本模块塞了一些预设")],-1),o=[p,c];function i(d,l,_,m,h,f){return r(),a("div",null,o)}const u=s(n,[["render",i]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_presets_index.md.Clhg0YLX.lean.js b/assets/en_api_presets_index.md.Clhg0YLX.lean.js
deleted file mode 100644
index d0958d0..0000000
--- a/assets/en_api_presets_index.md.Clhg0YLX.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/index.md","filePath":"en/api/presets/index.md"}'),n={name:"en/api/presets/index.md"},p=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),c=e("p",null,[e("strong",null,"Description"),t(": 本模块塞了一些预设")],-1),o=[p,c];function i(d,l,_,m,h,f){return r(),a("div",null,o)}const u=s(n,[["render",i]]);export{b as __pageData,u as default};
diff --git a/assets/en_api_presets_model_index.md.BJWo1DBU.js b/assets/en_api_presets_model_index.md.BM4zzWd9.js
similarity index 82%
rename from assets/en_api_presets_model_index.md.BJWo1DBU.js
rename to assets/en_api_presets_model_index.md.BM4zzWd9.js
index acf033b..6c27e1f 100644
--- a/assets/en_api_presets_model_index.md.BJWo1DBU.js
+++ b/assets/en_api_presets_model_index.md.BM4zzWd9.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n(`
mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n(`
mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
diff --git a/assets/en_api_presets_model_index.md.BJWo1DBU.lean.js b/assets/en_api_presets_model_index.md.BM4zzWd9.lean.js
similarity index 100%
rename from assets/en_api_presets_model_index.md.BJWo1DBU.lean.js
rename to assets/en_api_presets_model_index.md.BM4zzWd9.lean.js
diff --git a/assets/en_api_presets_model_model.md.Cmq9KKw_.js b/assets/en_api_presets_model_model.md.Cmq9KKw_.js
deleted file mode 100644
index e1b5d6c..0000000
--- a/assets/en_api_presets_model_model.md.Cmq9KKw_.js
+++ /dev/null
@@ -1,18 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/model.md","filePath":"en/api/presets/model/model.md"}'),t={name:"en/api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
-    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
-    z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_presets_model_model.md.Cmq9KKw_.lean.js b/assets/en_api_presets_model_model.md.Cmq9KKw_.lean.js
deleted file mode 100644
index 189d8f7..0000000
--- a/assets/en_api_presets_model_model.md.Cmq9KKw_.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/model.md","filePath":"en/api/presets/model/model.md"}'),t={name:"en/api/presets/model/model.md"},h=n("",10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_presets_presets.md.5pMosEdX.js b/assets/en_api_presets_presets.md.5pMosEdX.js
deleted file mode 100644
index 24113c5..0000000
--- a/assets/en_api_presets_presets.md.5pMosEdX.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c as a,o as r,j as e,a as s}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/presets.md","filePath":"en/api/presets/presets.md"}'),p={name:"en/api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[s("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"Description"),s(": 本模块塞了一些预设")],-1),n=[c,o];function i(l,d,_,m,h,f){return r(),a("div",null,n)}const x=t(p,[["render",i]]);export{u as __pageData,x as default};
diff --git a/assets/en_api_presets_presets.md.5pMosEdX.lean.js b/assets/en_api_presets_presets.md.5pMosEdX.lean.js
deleted file mode 100644
index 24113c5..0000000
--- a/assets/en_api_presets_presets.md.5pMosEdX.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c as a,o as r,j as e,a as s}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/presets.md","filePath":"en/api/presets/presets.md"}'),p={name:"en/api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[s("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"Description"),s(": 本模块塞了一些预设")],-1),n=[c,o];function i(l,d,_,m,h,f){return r(),a("div",null,n)}const x=t(p,[["render",i]]);export{u as __pageData,x as default};
diff --git a/assets/guide_index.md.BVhQ0kPy.js b/assets/guide_index.md.BVhQ0kPy.js
deleted file mode 100644
index 5f9a4ba..0000000
--- a/assets/guide_index.md.BVhQ0kPy.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as t,j as a,a as o,a4 as T,o as e}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"开始不了一点","description":"","frontmatter":{},"headers":[],"relativePath":"guide/index.md","filePath":"zh/guide/index.md","lastUpdated":1724999398000}'),d={name:"guide/index.md"},l=a("h1",{id:"开始不了一点",tabindex:"-1"},[o("开始不了一点 "),a("a",{class:"header-anchor",href:"#开始不了一点","aria-label":'Permalink to "开始不了一点"'},"​")],-1),n={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.771ex"},xmlns:"http://www.w3.org/2000/svg",width:"7.561ex",height:"3.042ex",role:"img",focusable:"false",viewBox:"0 -1003.5 3342.1 1344.3","aria-hidden":"true"},Q=T('',1),i=[Q],h=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msubsup",null,[a("mo",{"data-mjx-texclass":"OP"},"∫"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])]),a("mi",null,"x"),a("mn",null,"111")])],-1),m=T('
AAA ​
BBB ​
C ​
ddd ​
',4);function c(p,_,x,u,g,V){return e(),t("div",null,[l,a("p",null,[a("mjx-container",n,[(e(),t("svg",r,i)),h])]),m])}const b=s(d,[["render",c]]);export{f as __pageData,b as default};
diff --git a/assets/guide_index.md.BVhQ0kPy.lean.js b/assets/guide_index.md.BVhQ0kPy.lean.js
deleted file mode 100644
index ffcc397..0000000
--- a/assets/guide_index.md.BVhQ0kPy.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as t,j as a,a as o,a4 as T,o as e}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"开始不了一点","description":"","frontmatter":{},"headers":[],"relativePath":"guide/index.md","filePath":"zh/guide/index.md","lastUpdated":1724999398000}'),d={name:"guide/index.md"},l=a("h1",{id:"开始不了一点",tabindex:"-1"},[o("开始不了一点 "),a("a",{class:"header-anchor",href:"#开始不了一点","aria-label":'Permalink to "开始不了一点"'},"​")],-1),n={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.771ex"},xmlns:"http://www.w3.org/2000/svg",width:"7.561ex",height:"3.042ex",role:"img",focusable:"false",viewBox:"0 -1003.5 3342.1 1344.3","aria-hidden":"true"},Q=T("",1),i=[Q],h=a("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[a("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[a("msubsup",null,[a("mo",{"data-mjx-texclass":"OP"},"∫"),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"1")]),a("mrow",{"data-mjx-texclass":"ORD"},[a("mn",null,"2")])]),a("mi",null,"x"),a("mn",null,"111")])],-1),m=T("",4);function c(p,_,x,u,g,V){return e(),t("div",null,[l,a("p",null,[a("mjx-container",n,[(e(),t("svg",r,i)),h])]),m])}const b=s(d,[["render",c]]);export{f as __pageData,b as default};
diff --git a/assets/guide_index.md.CJOqvlSE.js b/assets/guide_index.md.CJOqvlSE.js
new file mode 100644
index 0000000..2054f2a
--- /dev/null
+++ b/assets/guide_index.md.CJOqvlSE.js
@@ -0,0 +1 @@
+import{_ as a,c as e,o as t,a4 as s}from"./chunks/framework.DpC1ZpOZ.js";const k=JSON.parse('{"title":"快速开始","description":"","frontmatter":{},"headers":[],"relativePath":"guide/index.md","filePath":"zh/guide/index.md","lastUpdated":1725373766000}'),i={name:"guide/index.md"},l=s('
快速开始 ​
TIP
建议：把你项目所使用的Python换成PyPy，这样可以提高性能(兼容性优先)
安装 ​
shell
pip install mbcp
',4),n=[l];function o(d,c,h,p,r,_){return t(),e("div",null,n)}const m=a(i,[["render",o]]);export{k as __pageData,m as default};
diff --git a/assets/guide_index.md.CJOqvlSE.lean.js b/assets/guide_index.md.CJOqvlSE.lean.js
new file mode 100644
index 0000000..439e486
--- /dev/null
+++ b/assets/guide_index.md.CJOqvlSE.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as e,o as t,a4 as s}from"./chunks/framework.DpC1ZpOZ.js";const k=JSON.parse('{"title":"快速开始","description":"","frontmatter":{},"headers":[],"relativePath":"guide/index.md","filePath":"zh/guide/index.md","lastUpdated":1725373766000}'),i={name:"guide/index.md"},l=s("",4),n=[l];function o(d,c,h,p,r,_){return t(),e("div",null,n)}const m=a(i,[["render",o]]);export{k as __pageData,m as default};
diff --git a/assets/ja_api_api.md.DD7b0jH_.js b/assets/ja_api_api.md.DD7b0jH_.js
deleted file mode 100644
index 32b5829..0000000
--- a/assets/ja_api_api.md.DD7b0jH_.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as e,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/api.md","filePath":"ja/api/api.md"}'),c={name:"ja/api/api.md"},o=p('
mbcp ​
説明: 本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(_,i,d,m,n,l){return t(),e("div",null,r)}const b=a(c,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/ja_api_api.md.DD7b0jH_.lean.js b/assets/ja_api_api.md.DD7b0jH_.lean.js
deleted file mode 100644
index b3b68cf..0000000
--- a/assets/ja_api_api.md.DD7b0jH_.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as e,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/api.md","filePath":"ja/api/api.md"}'),c={name:"ja/api/api.md"},o=p("",5),r=[o];function s(_,i,d,m,n,l){return t(),e("div",null,r)}const b=a(c,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/ja_api_index.md.3bCCqhm9.js b/assets/ja_api_index.md.3bCCqhm9.js
deleted file mode 100644
index b2e76d6..0000000
--- a/assets/ja_api_index.md.3bCCqhm9.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/index.md","filePath":"ja/api/index.md"}'),p={name:"ja/api/index.md"},o=c('
mbcp ​
説明: 本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(d,_,i,n,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/ja_api_index.md.6u5f7W7q.js b/assets/ja_api_index.md.6u5f7W7q.js
new file mode 100644
index 0000000..aab2498
--- /dev/null
+++ b/assets/ja_api_index.md.6u5f7W7q.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/index.md","filePath":"ja/api/index.md"}'),p={name:"ja/api/index.md"},o=c('
mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(d,_,i,n,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/ja_api_index.md.3bCCqhm9.lean.js b/assets/ja_api_index.md.6u5f7W7q.lean.js
similarity index 100%
rename from assets/ja_api_index.md.3bCCqhm9.lean.js
rename to assets/ja_api_index.md.6u5f7W7q.lean.js
diff --git a/assets/ja_api_mp_math_angle.md.DmogilJK.js b/assets/ja_api_mp_math_angle.md.CbTFNFpP.js
similarity index 60%
rename from assets/ja_api_mp_math_angle.md.DmogilJK.js
rename to assets/ja_api_mp_math_angle.md.CbTFNFpP.js
index 56307b2..99a3d04 100644
--- a/assets/ja_api_mp_math_angle.md.DmogilJK.js
+++ b/assets/ja_api_mp_math_angle.md.CbTFNFpP.js
@@ -1,4 +1,4 @@
-import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
func __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード または GitHubで表示
python
@property
+        self.radian = value * PI / 180
@property
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード または GitHubで表示
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード または GitHubで表示
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
method degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード または GitHubで表示
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード または GitHubで表示
python
@property
+    return self.radian * 180 / PI
@property
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード または GitHubで表示
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード または GitHubで表示
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
method sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード または GitHubで表示
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード または GitHubで表示
python
@property
+    return math.sin(self.radian)
@property
method cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード または GitHubで表示
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード または GitHubで表示
python
@property
+    return math.cos(self.radian)
@property
method tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード または GitHubで表示
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード または GitHubで表示
python
@property
+    return math.tan(self.radian)
@property
method cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード または GitHubで表示
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード または GitHubで表示
python
@property
+    return 1 / math.tan(self.radian)
@property
method sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード または GitHubで表示
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード または GitHubで表示
python
@property
+    return 1 / math.cos(self.radian)
@property
method csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード または GitHubで表示
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
ソースコード または GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
ソースコード または GitHubで表示
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード または GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
ソースコード または GitHubで表示
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
ソースコード または GitHubで表示
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
ソースコード または GitHubで表示
python
def __truediv__(self, other):
+    ...
method self / other ​
ソースコード または GitHubで表示
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_angle.md.DmogilJK.lean.js b/assets/ja_api_mp_math_angle.md.CbTFNFpP.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_angle.md.DmogilJK.lean.js
rename to assets/ja_api_mp_math_angle.md.CbTFNFpP.lean.js
diff --git a/assets/ja_api_mp_math_const.md.CACmM3Q4.js b/assets/ja_api_mp_math_const.md.CACmM3Q4.js
deleted file mode 100644
index 8bb1d79..0000000
--- a/assets/ja_api_mp_math_const.md.CACmM3Q4.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as o,o as t,a4 as r}from"./chunks/framework.DpC1ZpOZ.js";const g=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/const.md","filePath":"ja/api/mp_math/const.md"}'),e={name:"ja/api/mp_math/const.md"},l=r('
mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • デフォルト: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • デフォルト: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • デフォルト: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • デフォルト: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • デフォルト: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • デフォルト: 0.001
',14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const u=a(e,[["render",i]]);export{g as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_const.md.CACmM3Q4.lean.js b/assets/ja_api_mp_math_const.md.CACmM3Q4.lean.js
deleted file mode 100644
index c3371fc..0000000
--- a/assets/ja_api_mp_math_const.md.CACmM3Q4.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as o,o as t,a4 as r}from"./chunks/framework.DpC1ZpOZ.js";const g=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/const.md","filePath":"ja/api/mp_math/const.md"}'),e={name:"ja/api/mp_math/const.md"},l=r("",14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const u=a(e,[["render",i]]);export{g as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_const.md.HrVLdLVW.js b/assets/ja_api_mp_math_const.md.HrVLdLVW.js
new file mode 100644
index 0000000..cb8b857
--- /dev/null
+++ b/assets/ja_api_mp_math_const.md.HrVLdLVW.js
@@ -0,0 +1 @@
+import{_ as a,c as o,o as t,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/const.md","filePath":"ja/api/mp_math/const.md"}'),r={name:"ja/api/mp_math/const.md"},l=e('
mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • デフォルト: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • デフォルト: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • デフォルト: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • デフォルト: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • デフォルト: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • デフォルト: 0.001
',14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const g=a(r,[["render",i]]);export{u as __pageData,g as default};
diff --git a/assets/ja_api_mp_math_const.md.HrVLdLVW.lean.js b/assets/ja_api_mp_math_const.md.HrVLdLVW.lean.js
new file mode 100644
index 0000000..beb0186
--- /dev/null
+++ b/assets/ja_api_mp_math_const.md.HrVLdLVW.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as o,o as t,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/const.md","filePath":"ja/api/mp_math/const.md"}'),r={name:"ja/api/mp_math/const.md"},l=e("",14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const g=a(r,[["render",i]]);export{u as __pageData,g as default};
diff --git a/assets/ja_api_mp_math_equation.md.DuGNts4i.js b/assets/ja_api_mp_math_equation.md.BR_cjYxP.js
similarity index 82%
rename from assets/ja_api_mp_math_equation.md.DuGNts4i.js
rename to assets/ja_api_mp_math_equation.md.BR_cjYxP.js
index 723e7dd..9d98083 100644
--- a/assets/ja_api_mp_math_equation.md.DuGNts4i.js
+++ b/assets/ja_api_mp_math_equation.md.BR_cjYxP.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
ソースコード または GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
ソースコード または GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード または GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード または GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_equation.md.DuGNts4i.lean.js b/assets/ja_api_mp_math_equation.md.BR_cjYxP.lean.js
similarity index 73%
rename from assets/ja_api_mp_math_equation.md.DuGNts4i.lean.js
rename to assets/ja_api_mp_math_equation.md.BR_cjYxP.lean.js
index f4c7504..3aac2d8 100644
--- a/assets/ja_api_mp_math_equation.md.DuGNts4i.lean.js
+++ b/assets/ja_api_mp_math_equation.md.BR_cjYxP.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n("",23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_function.md.CeNPnpri.js b/assets/ja_api_mp_math_function.md.CeNPnpri.js
new file mode 100644
index 0000000..ce036af
--- /dev/null
+++ b/assets/ja_api_mp_math_function.md.CeNPnpri.js
@@ -0,0 +1,42 @@
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),e={name:"ja/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
引数:
戻り値: 梯度
ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    """
+    计算三元函数在某点的梯度向量。
+    > [!tip]
+    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
+    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
+    Args:
+        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
+        p ([\`Point3\`](./point#class-point3)): 点
+        epsilon: 偏移量
+    Returns:
+        梯度
+    """
+    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
+    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
+    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
+    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
引数:
戻り値: 柯里化后的函数
例:
python
def add(a: int, b: int, c: int) -> int:
+    return a + b + c
+add_curried = curry(add, 1, 2)
+add_curried(3)  # 6
ソースコード または GitHubで表示
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+    """
+    对多参数函数进行柯里化。
+    > [!tip]
+    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
+    Args:
+        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
+        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
+    Returns:
+        柯里化后的函数
+    Examples:
+        \`\`\`python
+        def add(a: int, b: int, c: int) -> int:
+            return a + b + c
+        add_curried = curry(add, 1, 2)
+        add_curried(3)  # 6
+        \`\`\`
+    """
+
+    def curried_func(*args2: Var) -> Var:
+        """@litedoc-hide"""
+        return func(*args, *args2)
+    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/ja_api_mp_math_function.md.DIn5uL0A.lean.js b/assets/ja_api_mp_math_function.md.CeNPnpri.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_function.md.DIn5uL0A.lean.js
rename to assets/ja_api_mp_math_function.md.CeNPnpri.lean.js
diff --git a/assets/ja_api_mp_math_function.md.DIn5uL0A.js b/assets/ja_api_mp_math_function.md.DIn5uL0A.js
deleted file mode 100644
index 4bc4e78..0000000
--- a/assets/ja_api_mp_math_function.md.DIn5uL0A.js
+++ /dev/null
@@ -1,42 +0,0 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),e={name:"ja/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
説明: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
引数:
戻り値: 梯度
ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
-    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
-    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
-    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
-    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
引数:
戻り値: 柯里化后的函数
例:
python
def add(a: int, b: int, c: int) -> int:
-    return a + b + c
-add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
ソースコード または GitHubで表示
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
-
-    def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
-        return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/ja_api_mp_math_index.md.BVYYBcgX.js b/assets/ja_api_mp_math_index.md.BVYYBcgX.js
new file mode 100644
index 0000000..f911f93
--- /dev/null
+++ b/assets/ja_api_mp_math_index.md.BVYYBcgX.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/mp_math/index.md","filePath":"ja/api/mp_math/index.md"}'),l={name:"ja/api/mp_math/index.md"},o=c('
mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function m(n,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_index.md.B_UDRWJp.lean.js b/assets/ja_api_mp_math_index.md.BVYYBcgX.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_index.md.B_UDRWJp.lean.js
rename to assets/ja_api_mp_math_index.md.BVYYBcgX.lean.js
diff --git a/assets/ja_api_mp_math_index.md.B_UDRWJp.js b/assets/ja_api_mp_math_index.md.B_UDRWJp.js
deleted file mode 100644
index e5500a8..0000000
--- a/assets/ja_api_mp_math_index.md.B_UDRWJp.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/mp_math/index.md","filePath":"ja/api/mp_math/index.md"}'),l={name:"ja/api/mp_math/index.md"},o=c('
mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function m(n,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_line.md.Ber05s-D.js b/assets/ja_api_mp_math_line.md.CmVmq6PC.js
similarity index 59%
rename from assets/ja_api_mp_math_line.md.Ber05s-D.js
rename to assets/ja_api_mp_math_line.md.CmVmq6PC.js
index 0ad60c2..ee042dd 100644
--- a/assets/ja_api_mp_math_line.md.Ber05s-D.js
+++ b/assets/ja_api_mp_math_line.md.CmVmq6PC.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other (Line3): 另一条直线
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other (Line3): 另一条直线
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -23,7 +23,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other (Line3): 另一条直线
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other (Line3): 另一条直线
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -60,7 +60,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
戻り値: Line3: 垂线
ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
戻り値: Line3: 垂线
ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -68,7 +68,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Line3\`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
戻り値: Point3: 点
ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
戻り値: Point3: 点
ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -76,13 +76,13 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Point3\`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -91,7 +91,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -99,7 +99,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
戻り値: bool: 是否共线
ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
戻り値: bool: 是否共线
ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -107,7 +107,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
戻り値: bool: 是否在直线上
ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
戻り値: bool: 是否在直线上
ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -115,7 +115,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
戻り値: bool: 是否共面
ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
戻り値: bool: 是否共面
ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -124,7 +124,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード または GitHubで表示
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード または GitHubで表示
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -137,7 +137,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
戻り値: Line3: 直线
ソースコード または GitHubで表示
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
戻り値: Line3: 直线
ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -148,7 +148,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             [\`Line3\`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other (Line3): 另一条直线
戻り値: Line3 | Point3 | None: 交集
ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other (Line3): 另一条直线
戻り値: Line3 | Point3 | None: 交集
ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other (Line3): 另一条直线
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other (Line3): 另一条直线
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -171,4 +171,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_line.md.Ber05s-D.lean.js b/assets/ja_api_mp_math_line.md.CmVmq6PC.lean.js
similarity index 72%
rename from assets/ja_api_mp_math_line.md.Ber05s-D.lean.js
rename to assets/ja_api_mp_math_line.md.CmVmq6PC.lean.js
index c156750..572538c 100644
--- a/assets/ja_api_mp_math_line.md.Ber05s-D.lean.js
+++ b/assets/ja_api_mp_math_line.md.CmVmq6PC.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n("",106),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),t={name:"ja/api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_mp_math.md.DGl-Yqoj.js b/assets/ja_api_mp_math_mp_math.md.DGl-Yqoj.js
deleted file mode 100644
index da20679..0000000
--- a/assets/ja_api_mp_math_mp_math.md.DGl-Yqoj.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as e,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/mp_math/mp_math.md","filePath":"ja/api/mp_math/mp_math.md"}'),l={name:"ja/api/mp_math/mp_math.md"},m=c('
mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),o=[m];function i(s,n,p,h,r,_){return t(),e("div",null,o)}const u=a(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_mp_math.md.DGl-Yqoj.lean.js b/assets/ja_api_mp_math_mp_math.md.DGl-Yqoj.lean.js
deleted file mode 100644
index 1bd00a0..0000000
--- a/assets/ja_api_mp_math_mp_math.md.DGl-Yqoj.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as e,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/mp_math/mp_math.md","filePath":"ja/api/mp_math/mp_math.md"}'),l={name:"ja/api/mp_math/mp_math.md"},m=c("",3),o=[m];function i(s,n,p,h,r,_){return t(),e("div",null,o)}const u=a(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_mp_math_typing.md.BANGfx9Q.js b/assets/ja_api_mp_math_mp_math_typing.md.BANGfx9Q.js
deleted file mode 100644
index 08da1ec..0000000
--- a/assets/ja_api_mp_math_mp_math_typing.md.BANGfx9Q.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/mp_math_typing.md","filePath":"ja/api/mp_math/mp_math_typing.md"}'),l={name:"ja/api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • タイプ: TypeAlias
  • デフォルト: int | float
var Number ​
  • 説明: 数
  • タイプ: TypeAlias
  • デフォルト: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • デフォルト: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • タイプ: TypeAlias
  • デフォルト: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • タイプ: TypeAlias
  • デフォルト: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • タイプ: TypeAlias
  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • タイプ: TypeAlias
  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • タイプ: TypeAlias
  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,d,p,u,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/ja_api_mp_math_mp_math_typing.md.BnSHEEFC.js b/assets/ja_api_mp_math_mp_math_typing.md.BnSHEEFC.js
new file mode 100644
index 0000000..be55956
--- /dev/null
+++ b/assets/ja_api_mp_math_mp_math_typing.md.BnSHEEFC.js
@@ -0,0 +1 @@
+import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/mp_math_typing.md","filePath":"ja/api/mp_math/mp_math_typing.md"}'),l={name:"ja/api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • タイプ: TypeAlias
  • デフォルト: int | float
var Number ​
  • 説明: 数
  • タイプ: TypeAlias
  • デフォルト: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • デフォルト: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • タイプ: TypeAlias
  • デフォルト: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • タイプ: TypeAlias
  • デフォルト: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • タイプ: TypeAlias
  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • タイプ: TypeAlias
  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • タイプ: TypeAlias
  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,d,p,u,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/ja_api_mp_math_mp_math_typing.md.BANGfx9Q.lean.js b/assets/ja_api_mp_math_mp_math_typing.md.BnSHEEFC.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_mp_math_typing.md.BANGfx9Q.lean.js
rename to assets/ja_api_mp_math_mp_math_typing.md.BnSHEEFC.lean.js
diff --git a/assets/ja_api_mp_math_plane.md.BlhqSUWq.js b/assets/ja_api_mp_math_plane.md.D7v3q_U8.js
similarity index 69%
rename from assets/ja_api_mp_math_plane.md.BlhqSUWq.js
rename to assets/ja_api_mp_math_plane.md.D7v3q_U8.js
index 113b075..8bf77b6 100644
--- a/assets/ja_api_mp_math_plane.md.BlhqSUWq.js
+++ b/assets/ja_api_mp_math_plane.md.D7v3q_U8.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
戻り値: AnyAngle: 夹角
例外:
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
戻り値: AnyAngle: 夹角
例外:
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other (Plane3): 另一个平面
戻り値: Line3: 交线
例外:
ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other (Plane3): 另一个平面
戻り値: Line3: 交线
例外:
ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -84,7 +84,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -98,7 +98,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -106,7 +106,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -114,14 +114,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: Vector3: 法向量
ソースコード または GitHubで表示
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: Vector3: 法向量
ソースコード または GitHubで表示
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [\`Vector3\`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -133,7 +133,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -147,7 +147,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -171,11 +171,11 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
ソースコード または GitHubで表示
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
戻り値: Line3 | Point3 | None: 交集
例外:
ソースコード または GitHubで表示
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
戻り値: Line3 | Point3 | None: 交集
例外:
ソースコード または GitHubで表示
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -194,7 +194,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -202,5 +202,5 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_plane.md.BlhqSUWq.lean.js b/assets/ja_api_mp_math_plane.md.D7v3q_U8.lean.js
similarity index 68%
rename from assets/ja_api_mp_math_plane.md.BlhqSUWq.lean.js
rename to assets/ja_api_mp_math_plane.md.D7v3q_U8.lean.js
index 711844a..8a72354 100644
--- a/assets/ja_api_mp_math_plane.md.BlhqSUWq.lean.js
+++ b/assets/ja_api_mp_math_plane.md.D7v3q_U8.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_point.md.Czyuzvxa.js b/assets/ja_api_mp_math_point.md.BqC8JgjG.js
similarity index 57%
rename from assets/ja_api_mp_math_point.md.Czyuzvxa.js
rename to assets/ja_api_mp_math_point.md.BqC8JgjG.js
index be1e367..81cdef8 100644
--- a/assets/ja_api_mp_math_point.md.Czyuzvxa.js
+++ b/assets/ja_api_mp_math_point.md.BqC8JgjG.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},l=t(`
mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},h=t(`
mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -17,11 +17,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
ソースコード または GitHubで表示
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 または GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: P + V -> P P + P -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,7 +30,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
引数:
戻り値: Vector3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
引数:
戻り値: Vector3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -49,4 +49,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
             [\`Vector3\`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),h=[l];function p(e,k,o,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",p]]);export{E as __pageData,y as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_point.md.Czyuzvxa.lean.js b/assets/ja_api_mp_math_point.md.BqC8JgjG.lean.js
similarity index 72%
rename from assets/ja_api_mp_math_point.md.Czyuzvxa.lean.js
rename to assets/ja_api_mp_math_point.md.BqC8JgjG.lean.js
index c278532..891c12b 100644
--- a/assets/ja_api_mp_math_point.md.Czyuzvxa.lean.js
+++ b/assets/ja_api_mp_math_point.md.BqC8JgjG.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},l=t("",39),h=[l];function p(e,k,o,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/point.md","filePath":"ja/api/mp_math/point.md"}'),n={name:"ja/api/mp_math/point.md"},h=t("",39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_segment.md.DfoJ389C.js b/assets/ja_api_mp_math_segment.md.vi1FH0--.js
similarity index 73%
rename from assets/ja_api_mp_math_segment.md.DfoJ389C.js
rename to assets/ja_api_mp_math_segment.md.vi1FH0--.js
index be1679f..e3af5c0 100644
--- a/assets/ja_api_mp_math_segment.md.DfoJ389C.js
+++ b/assets/ja_api_mp_math_segment.md.vi1FH0--.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
引数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
引数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -12,4 +12,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function l(e,k,r,d,E,o){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_segment.md.DfoJ389C.lean.js b/assets/ja_api_mp_math_segment.md.vi1FH0--.lean.js
similarity index 86%
rename from assets/ja_api_mp_math_segment.md.DfoJ389C.lean.js
rename to assets/ja_api_mp_math_segment.md.vi1FH0--.lean.js
index a0c12b2..19cb825 100644
--- a/assets/ja_api_mp_math_segment.md.DfoJ389C.lean.js
+++ b/assets/ja_api_mp_math_segment.md.vi1FH0--.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,E,o){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_utils.md.Dnl5rkoo.js b/assets/ja_api_mp_math_utils.md.DhPmcvK-.js
similarity index 79%
rename from assets/ja_api_mp_math_utils.md.Dnl5rkoo.js
rename to assets/ja_api_mp_math_utils.md.DhPmcvK-.js
index 29d1c44..8e991bf 100644
--- a/assets/ja_api_mp_math_utils.md.Dnl5rkoo.js
+++ b/assets/ja_api_mp_math_utils.md.DhPmcvK-.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),n={name:"ja/api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
引数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
戻り値: float: 限定在区间内的值
ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),n={name:"ja/api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
引数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
戻り値: float: 限定在区间内的值
ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,13 +9,13 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     Returns:
         \`float\`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
引数:
ソースコード または GitHubで表示
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
引数:
ソースコード または GitHubで表示
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -25,8 +25,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
         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)
func raise_type_error(self, other) ​
ソースコード または GitHubで表示
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
ソースコード または GitHubで表示
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード または GitHubで表示
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード または GitHubで表示
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -66,4 +66,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",p]]);export{F as __pageData,c as default};
+        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_utils.md.Dnl5rkoo.lean.js b/assets/ja_api_mp_math_utils.md.DhPmcvK-.lean.js
similarity index 68%
rename from assets/ja_api_mp_math_utils.md.Dnl5rkoo.lean.js
rename to assets/ja_api_mp_math_utils.md.DhPmcvK-.lean.js
index 48b11b3..935a7fb 100644
--- a/assets/ja_api_mp_math_utils.md.Dnl5rkoo.lean.js
+++ b/assets/ja_api_mp_math_utils.md.DhPmcvK-.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),n={name:"ja/api/mp_math/utils.md"},l=t("",38),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",p]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),n={name:"ja/api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_vector.md.CD5nfzHo.js b/assets/ja_api_mp_math_vector.md.B7oDy-SU.js
similarity index 63%
rename from assets/ja_api_mp_math_vector.md.CD5nfzHo.js
rename to assets/ja_api_mp_math_vector.md.B7oDy-SU.js
index 3617bc2..3c5fd40 100644
--- a/assets/ja_api_mp_math_vector.md.CD5nfzHo.js
+++ b/assets/ja_api_mp_math_vector.md.B7oDy-SU.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},l=t(`
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},e=t(`
mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
戻り値: Vector3: 叉乘结果
ソースコード または GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
戻り値: Vector3: 叉乘结果
ソースコード または GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Vector3\`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード または GitHubで表示
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード または GitHubで表示
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,33 +72,33 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
戻り値: np.ndarray: numpy数组
ソースコード または GitHubで表示
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
戻り値: np.ndarray: numpy数组
ソースコード または GitHubで表示
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
説明: 向量的模。
戻り値: float: 模
ソースコード または GitHubで表示
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
説明: 向量的模。
戻り値: float: 模
ソースコード または GitHubで表示
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: Vector3: 单位向量
ソースコード または GitHubで表示
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: Vector3: 单位向量
ソースコード または GitHubで表示
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [\`Vector3\`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
ソースコード または GitHubで表示
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    return self / self.length
method __abs__(self) ​
ソースコード または GitHubで表示
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: V + P -> P
V + V -> V
引数:
戻り値: Vector3 | Point3: 新的向量或点
ソースコード または GitHubで表示
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
戻り値: Vector3 | Point3: 新的向量或点
ソースコード または GitHubで表示
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -113,7 +113,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -121,7 +121,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -131,11 +131,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
説明: V - P -> P
V - V -> V
引数:
戻り値: Vector3 | Point3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
戻り値: Vector3 | Point3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -150,7 +150,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}"')
func self - other: Point3 ​
説明: P - V -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -161,11 +161,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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
func self * other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
戻り値: Vector3: 数组运算结果
ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
戻り値: Vector3: 数组运算结果
ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -178,8 +178,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
戻り値: float: 点乘结果
ソースコード または GitHubで表示
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
戻り値: float: 点乘结果
ソースコード または GitHubで表示
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -187,11 +187,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
説明: 取负。
戻り値: Vector3: 负向量
ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
説明: 取负。
戻り値: Vector3: 负向量
ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [\`Vector3\`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 1)
`,138),e=[l];function h(p,k,r,o,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 1)
`,138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_vector.md.CD5nfzHo.lean.js b/assets/ja_api_mp_math_vector.md.B7oDy-SU.lean.js
similarity index 72%
rename from assets/ja_api_mp_math_vector.md.CD5nfzHo.lean.js
rename to assets/ja_api_mp_math_vector.md.B7oDy-SU.lean.js
index 8a862f9..3b9776f 100644
--- a/assets/ja_api_mp_math_vector.md.CD5nfzHo.lean.js
+++ b/assets/ja_api_mp_math_vector.md.B7oDy-SU.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},l=t("",138),e=[l];function h(p,k,r,o,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},e=t("",138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_particle_index.md.SXvJHpqE.js b/assets/ja_api_particle_index.md.SXvJHpqE.js
deleted file mode 100644
index 4887b5c..0000000
--- a/assets/ja_api_particle_index.md.SXvJHpqE.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/particle/index.md","filePath":"ja/api/particle/index.md"}'),i={name:"ja/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"説明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[p,l];function n(o,d,_,m,h,f){return r(),c("div",null,s)}const u=t(i,[["render",n]]);export{b as __pageData,u as default};
diff --git a/assets/ja_api_particle_index.md.SXvJHpqE.lean.js b/assets/ja_api_particle_index.md.SXvJHpqE.lean.js
deleted file mode 100644
index 4887b5c..0000000
--- a/assets/ja_api_particle_index.md.SXvJHpqE.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/particle/index.md","filePath":"ja/api/particle/index.md"}'),i={name:"ja/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"説明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[p,l];function n(o,d,_,m,h,f){return r(),c("div",null,s)}const u=t(i,[["render",n]]);export{b as __pageData,u as default};
diff --git a/assets/ja_api_particle_index.md.ighey3JD.js b/assets/ja_api_particle_index.md.ighey3JD.js
new file mode 100644
index 0000000..73a8a75
--- /dev/null
+++ b/assets/ja_api_particle_index.md.ighey3JD.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/particle/index.md","filePath":"ja/api/particle/index.md"}'),i={name:"ja/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),s=e("p",null,"本模块定义了粒子生成相关的工具",-1),l=[p,s];function o(n,d,_,m,h,f){return c(),t("div",null,l)}const u=a(i,[["render",o]]);export{b as __pageData,u as default};
diff --git a/assets/ja_api_particle_index.md.ighey3JD.lean.js b/assets/ja_api_particle_index.md.ighey3JD.lean.js
new file mode 100644
index 0000000..73a8a75
--- /dev/null
+++ b/assets/ja_api_particle_index.md.ighey3JD.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as t,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/particle/index.md","filePath":"ja/api/particle/index.md"}'),i={name:"ja/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),s=e("p",null,"本模块定义了粒子生成相关的工具",-1),l=[p,s];function o(n,d,_,m,h,f){return c(),t("div",null,l)}const u=a(i,[["render",o]]);export{b as __pageData,u as default};
diff --git a/assets/ja_api_particle_particle.md.DpDqAPA7.js b/assets/ja_api_particle_particle.md.DpDqAPA7.js
deleted file mode 100644
index 4d746c6..0000000
--- a/assets/ja_api_particle_particle.md.DpDqAPA7.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/particle/particle.md","filePath":"ja/api/particle/particle.md"}'),p={name:"ja/api/particle/particle.md"},l=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),i=e("p",null,[e("strong",null,"説明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[l,i];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=t(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/ja_api_particle_particle.md.DpDqAPA7.lean.js b/assets/ja_api_particle_particle.md.DpDqAPA7.lean.js
deleted file mode 100644
index 4d746c6..0000000
--- a/assets/ja_api_particle_particle.md.DpDqAPA7.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c,o as r,j as e,a}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/particle/particle.md","filePath":"ja/api/particle/particle.md"}'),p={name:"ja/api/particle/particle.md"},l=e("h1",{id:"mbcp-particle",tabindex:"-1"},[a("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),i=e("p",null,[e("strong",null,"説明"),a(": 本模块定义了粒子生成相关的工具")],-1),s=[l,i];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=t(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/ja_api_presets_index.md.DrJ0aeZq.js b/assets/ja_api_presets_index.md.Bow22HNO.js
similarity index 53%
rename from assets/ja_api_presets_index.md.DrJ0aeZq.js
rename to assets/ja_api_presets_index.md.Bow22HNO.js
index 14797b2..4f75828 100644
--- a/assets/ja_api_presets_index.md.DrJ0aeZq.js
+++ b/assets/ja_api_presets_index.md.Bow22HNO.js
@@ -1 +1 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/index.md","filePath":"ja/api/presets/index.md"}'),p={name:"ja/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),n=e("p",null,[e("strong",null,"説明"),t(": 本模块塞了一些预设")],-1),o=[c,n];function d(i,l,_,m,h,f){return r(),a("div",null,o)}const u=s(p,[["render",d]]);export{b as __pageData,u as default};
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/index.md","filePath":"ja/api/presets/index.md"}'),p={name:"ja/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,"本模块塞了一些预设",-1),n=[c,o];function d(i,l,_,m,h,f){return a(),s("div",null,n)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/ja_api_presets_index.md.DrJ0aeZq.lean.js b/assets/ja_api_presets_index.md.Bow22HNO.lean.js
similarity index 53%
rename from assets/ja_api_presets_index.md.DrJ0aeZq.lean.js
rename to assets/ja_api_presets_index.md.Bow22HNO.lean.js
index 14797b2..4f75828 100644
--- a/assets/ja_api_presets_index.md.DrJ0aeZq.lean.js
+++ b/assets/ja_api_presets_index.md.Bow22HNO.lean.js
@@ -1 +1 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/index.md","filePath":"ja/api/presets/index.md"}'),p={name:"ja/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),n=e("p",null,[e("strong",null,"説明"),t(": 本模块塞了一些预设")],-1),o=[c,n];function d(i,l,_,m,h,f){return r(),a("div",null,o)}const u=s(p,[["render",d]]);export{b as __pageData,u as default};
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/index.md","filePath":"ja/api/presets/index.md"}'),p={name:"ja/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,"本模块塞了一些预设",-1),n=[c,o];function d(i,l,_,m,h,f){return a(),s("div",null,n)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/ja_api_presets_model_index.md.D3Q5KLfq.js b/assets/ja_api_presets_model_index.md.C-uCqjXi.js
similarity index 80%
rename from assets/ja_api_presets_model_index.md.D3Q5KLfq.js
rename to assets/ja_api_presets_model_index.md.C-uCqjXi.js
index cf0be25..29454a9 100644
--- a/assets/ja_api_presets_model_index.md.D3Q5KLfq.js
+++ b/assets/ja_api_presets_model_index.md.C-uCqjXi.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),n={name:"ja/api/presets/model/index.md"},h=t(`
mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_model_index.md.D3Q5KLfq.lean.js b/assets/ja_api_presets_model_index.md.C-uCqjXi.lean.js
similarity index 61%
rename from assets/ja_api_presets_model_index.md.D3Q5KLfq.lean.js
rename to assets/ja_api_presets_model_index.md.C-uCqjXi.lean.js
index 940bca4..0301c86 100644
--- a/assets/ja_api_presets_model_index.md.D3Q5KLfq.lean.js
+++ b/assets/ja_api_presets_model_index.md.C-uCqjXi.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),n={name:"ja/api/presets/model/index.md"},h=t("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_model_model.md.vKB1wVU9.js b/assets/ja_api_presets_model_model.md.vKB1wVU9.js
deleted file mode 100644
index 8d90f28..0000000
--- a/assets/ja_api_presets_model_model.md.vKB1wVU9.js
+++ /dev/null
@@ -1,18 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/model.md","filePath":"ja/api/presets/model/model.md"}'),t={name:"ja/api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
-    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
-    z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_model_model.md.vKB1wVU9.lean.js b/assets/ja_api_presets_model_model.md.vKB1wVU9.lean.js
deleted file mode 100644
index 1f52640..0000000
--- a/assets/ja_api_presets_model_model.md.vKB1wVU9.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/model.md","filePath":"ja/api/presets/model/model.md"}'),t={name:"ja/api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_presets.md.Bm4b0yEm.js b/assets/ja_api_presets_presets.md.Bm4b0yEm.js
deleted file mode 100644
index cc99525..0000000
--- a/assets/ja_api_presets_presets.md.Bm4b0yEm.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c as a,o as r,j as e,a as s}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/presets.md","filePath":"ja/api/presets/presets.md"}'),p={name:"ja/api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[s("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"説明"),s(": 本模块塞了一些预设")],-1),n=[c,o];function l(d,i,_,m,h,f){return r(),a("div",null,n)}const x=t(p,[["render",l]]);export{u as __pageData,x as default};
diff --git a/assets/ja_api_presets_presets.md.Bm4b0yEm.lean.js b/assets/ja_api_presets_presets.md.Bm4b0yEm.lean.js
deleted file mode 100644
index cc99525..0000000
--- a/assets/ja_api_presets_presets.md.Bm4b0yEm.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as t,c as a,o as r,j as e,a as s}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/presets.md","filePath":"ja/api/presets/presets.md"}'),p={name:"ja/api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[s("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"説明"),s(": 本模块塞了一些预设")],-1),n=[c,o];function l(d,i,_,m,h,f){return r(),a("div",null,n)}const x=t(p,[["render",l]]);export{u as __pageData,x as default};
diff --git a/assets/style.D-YKQyMb.css b/assets/style.Dtv83zbR.css
similarity index 69%
rename from assets/style.D-YKQyMb.css
rename to assets/style.Dtv83zbR.css
index 0e2e363..a56e1ee 100644
--- a/assets/style.D-YKQyMb.css
+++ b/assets/style.Dtv83zbR.css
@@ -1 +1 @@
-:root{--vp-c-white: #ffffff;--vp-c-black: #000000;--vp-c-neutral: var(--vp-c-black);--vp-c-neutral-inverse: var(--vp-c-white)}.dark{--vp-c-neutral: var(--vp-c-white);--vp-c-neutral-inverse: var(--vp-c-black)}:root{--vp-c-gray-1: #dddde3;--vp-c-gray-2: #e4e4e9;--vp-c-gray-3: #ebebef;--vp-c-gray-soft: rgba(142, 150, 170, .14);--vp-c-indigo-1: #3451b2;--vp-c-indigo-2: #3a5ccc;--vp-c-indigo-3: #5672cd;--vp-c-indigo-soft: rgba(100, 108, 255, .14);--vp-c-purple-1: #6f42c1;--vp-c-purple-2: #7e4cc9;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .14);--vp-c-green-1: #18794e;--vp-c-green-2: #299764;--vp-c-green-3: #30a46c;--vp-c-green-soft: rgba(16, 185, 129, .14);--vp-c-yellow-1: #915930;--vp-c-yellow-2: #946300;--vp-c-yellow-3: #9f6a00;--vp-c-yellow-soft: rgba(234, 179, 8, .14);--vp-c-red-1: #b8272c;--vp-c-red-2: #d5393e;--vp-c-red-3: #e0575b;--vp-c-red-soft: rgba(244, 63, 94, .14);--vp-c-sponsor: #db2777}.dark{--vp-c-gray-1: #515c67;--vp-c-gray-2: #414853;--vp-c-gray-3: #32363f;--vp-c-gray-soft: rgba(101, 117, 133, .16);--vp-c-indigo-1: #a8b1ff;--vp-c-indigo-2: #5c73e7;--vp-c-indigo-3: #3e63dd;--vp-c-indigo-soft: rgba(100, 108, 255, .16);--vp-c-purple-1: #c8abfa;--vp-c-purple-2: #a879e6;--vp-c-purple-3: #8e5cd9;--vp-c-purple-soft: rgba(159, 122, 234, .16);--vp-c-green-1: #3dd68c;--vp-c-green-2: #30a46c;--vp-c-green-3: #298459;--vp-c-green-soft: rgba(16, 185, 129, .16);--vp-c-yellow-1: #f9b44e;--vp-c-yellow-2: #da8b17;--vp-c-yellow-3: #a46a0a;--vp-c-yellow-soft: rgba(234, 179, 8, .16);--vp-c-red-1: #f66f81;--vp-c-red-2: #f14158;--vp-c-red-3: #b62a3c;--vp-c-red-soft: rgba(244, 63, 94, .16)}:root{--vp-c-bg: #ffffff;--vp-c-bg-alt: #f6f6f7;--vp-c-bg-elv: #ffffff;--vp-c-bg-soft: #f6f6f7}.dark{--vp-c-bg: #1b1b1f;--vp-c-bg-alt: #161618;--vp-c-bg-elv: #202127;--vp-c-bg-soft: #202127}:root{--vp-c-border: #c2c2c4;--vp-c-divider: #e2e2e3;--vp-c-gutter: #e2e2e3}.dark{--vp-c-border: #3c3f44;--vp-c-divider: #2e2e32;--vp-c-gutter: #000000}:root{--vp-c-text-1: rgba(60, 60, 67);--vp-c-text-2: rgba(60, 60, 67, .78);--vp-c-text-3: rgba(60, 60, 67, .56)}.dark{--vp-c-text-1: rgba(255, 255, 245, .86);--vp-c-text-2: rgba(235, 235, 245, .6);--vp-c-text-3: rgba(235, 235, 245, .38)}:root{--vp-c-default-1: var(--vp-c-gray-1);--vp-c-default-2: var(--vp-c-gray-2);--vp-c-default-3: var(--vp-c-gray-3);--vp-c-default-soft: var(--vp-c-gray-soft);--vp-c-brand-1: var(--vp-c-indigo-1);--vp-c-brand-2: var(--vp-c-indigo-2);--vp-c-brand-3: var(--vp-c-indigo-3);--vp-c-brand-soft: var(--vp-c-indigo-soft);--vp-c-brand: var(--vp-c-brand-1);--vp-c-tip-1: var(--vp-c-brand-1);--vp-c-tip-2: var(--vp-c-brand-2);--vp-c-tip-3: var(--vp-c-brand-3);--vp-c-tip-soft: var(--vp-c-brand-soft);--vp-c-note-1: var(--vp-c-brand-1);--vp-c-note-2: var(--vp-c-brand-2);--vp-c-note-3: var(--vp-c-brand-3);--vp-c-note-soft: var(--vp-c-brand-soft);--vp-c-success-1: var(--vp-c-green-1);--vp-c-success-2: var(--vp-c-green-2);--vp-c-success-3: var(--vp-c-green-3);--vp-c-success-soft: var(--vp-c-green-soft);--vp-c-important-1: var(--vp-c-purple-1);--vp-c-important-2: var(--vp-c-purple-2);--vp-c-important-3: var(--vp-c-purple-3);--vp-c-important-soft: var(--vp-c-purple-soft);--vp-c-warning-1: var(--vp-c-yellow-1);--vp-c-warning-2: var(--vp-c-yellow-2);--vp-c-warning-3: var(--vp-c-yellow-3);--vp-c-warning-soft: var(--vp-c-yellow-soft);--vp-c-danger-1: var(--vp-c-red-1);--vp-c-danger-2: var(--vp-c-red-2);--vp-c-danger-3: var(--vp-c-red-3);--vp-c-danger-soft: var(--vp-c-red-soft);--vp-c-caution-1: var(--vp-c-red-1);--vp-c-caution-2: var(--vp-c-red-2);--vp-c-caution-3: var(--vp-c-red-3);--vp-c-caution-soft: var(--vp-c-red-soft)}:root{--vp-font-family-base: "Inter", ui-sans-serif, system-ui, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--vp-font-family-mono: ui-monospace, "Menlo", "Monaco", "Consolas", "Liberation Mono", "Courier New", monospace;font-optical-sizing:auto}:root:where(:lang(zh)){--vp-font-family-base: "Punctuation SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: 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rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: 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SC", "Inter", ui-sans-serif, system-ui, "PingFang SC", "Noto Sans CJK SC", "Noto Sans SC", "Heiti SC", "Microsoft YaHei", "DengXian", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji"}:root{--vp-shadow-1: 0 1px 2px rgba(0, 0, 0, .04), 0 1px 2px rgba(0, 0, 0, .06);--vp-shadow-2: 0 3px 12px rgba(0, 0, 0, .07), 0 1px 4px rgba(0, 0, 0, .07);--vp-shadow-3: 0 12px 32px rgba(0, 0, 0, .1), 0 2px 6px rgba(0, 0, 0, .08);--vp-shadow-4: 0 14px 44px rgba(0, 0, 0, .12), 0 3px 9px rgba(0, 0, 0, .12);--vp-shadow-5: 0 18px 56px rgba(0, 0, 0, .16), 0 4px 12px rgba(0, 0, 0, .16)}:root{--vp-z-index-footer: 10;--vp-z-index-local-nav: 20;--vp-z-index-nav: 30;--vp-z-index-layout-top: 40;--vp-z-index-backdrop: 50;--vp-z-index-sidebar: 60}@media (min-width: 960px){:root{--vp-z-index-sidebar: 25}}:root{--vp-layout-max-width: 1440px}:root{--vp-header-anchor-symbol: "#"}:root{--vp-code-line-height: 1.7;--vp-code-font-size: .875em;--vp-code-color: var(--vp-c-brand-1);--vp-code-link-color: var(--vp-c-brand-1);--vp-code-link-hover-color: var(--vp-c-brand-2);--vp-code-bg: var(--vp-c-default-soft);--vp-code-block-color: var(--vp-c-text-2);--vp-code-block-bg: var(--vp-c-bg-alt);--vp-code-block-divider-color: var(--vp-c-gutter);--vp-code-lang-color: var(--vp-c-text-3);--vp-code-line-highlight-color: var(--vp-c-default-soft);--vp-code-line-number-color: var(--vp-c-text-3);--vp-code-line-diff-add-color: var(--vp-c-success-soft);--vp-code-line-diff-add-symbol-color: var(--vp-c-success-1);--vp-code-line-diff-remove-color: var(--vp-c-danger-soft);--vp-code-line-diff-remove-symbol-color: var(--vp-c-danger-1);--vp-code-line-warning-color: var(--vp-c-warning-soft);--vp-code-line-error-color: var(--vp-c-danger-soft);--vp-code-copy-code-border-color: var(--vp-c-divider);--vp-code-copy-code-bg: var(--vp-c-bg-soft);--vp-code-copy-code-hover-border-color: var(--vp-c-divider);--vp-code-copy-code-hover-bg: var(--vp-c-bg);--vp-code-copy-code-active-text: var(--vp-c-text-2);--vp-code-copy-copied-text-content: "Copied";--vp-code-tab-divider: var(--vp-code-block-divider-color);--vp-code-tab-text-color: var(--vp-c-text-2);--vp-code-tab-bg: var(--vp-code-block-bg);--vp-code-tab-hover-text-color: var(--vp-c-text-1);--vp-code-tab-active-text-color: var(--vp-c-text-1);--vp-code-tab-active-bar-color: var(--vp-c-brand-1)}:root{--vp-button-brand-border: transparent;--vp-button-brand-text: var(--vp-c-white);--vp-button-brand-bg: var(--vp-c-brand-3);--vp-button-brand-hover-border: transparent;--vp-button-brand-hover-text: var(--vp-c-white);--vp-button-brand-hover-bg: var(--vp-c-brand-2);--vp-button-brand-active-border: transparent;--vp-button-brand-active-text: var(--vp-c-white);--vp-button-brand-active-bg: var(--vp-c-brand-1);--vp-button-alt-border: transparent;--vp-button-alt-text: var(--vp-c-text-1);--vp-button-alt-bg: var(--vp-c-default-3);--vp-button-alt-hover-border: transparent;--vp-button-alt-hover-text: var(--vp-c-text-1);--vp-button-alt-hover-bg: var(--vp-c-default-2);--vp-button-alt-active-border: transparent;--vp-button-alt-active-text: var(--vp-c-text-1);--vp-button-alt-active-bg: var(--vp-c-default-1);--vp-button-sponsor-border: var(--vp-c-text-2);--vp-button-sponsor-text: var(--vp-c-text-2);--vp-button-sponsor-bg: transparent;--vp-button-sponsor-hover-border: var(--vp-c-sponsor);--vp-button-sponsor-hover-text: var(--vp-c-sponsor);--vp-button-sponsor-hover-bg: transparent;--vp-button-sponsor-active-border: var(--vp-c-sponsor);--vp-button-sponsor-active-text: var(--vp-c-sponsor);--vp-button-sponsor-active-bg: transparent}:root{--vp-custom-block-font-size: 14px;--vp-custom-block-code-font-size: 13px;--vp-custom-block-info-border: transparent;--vp-custom-block-info-text: var(--vp-c-text-1);--vp-custom-block-info-bg: var(--vp-c-default-soft);--vp-custom-block-info-code-bg: var(--vp-c-default-soft);--vp-custom-block-note-border: transparent;--vp-custom-block-note-text: var(--vp-c-text-1);--vp-custom-block-note-bg: var(--vp-c-default-soft);--vp-custom-block-note-code-bg: var(--vp-c-default-soft);--vp-custom-block-tip-border: transparent;--vp-custom-block-tip-text: var(--vp-c-text-1);--vp-custom-block-tip-bg: var(--vp-c-tip-soft);--vp-custom-block-tip-code-bg: var(--vp-c-tip-soft);--vp-custom-block-important-border: transparent;--vp-custom-block-important-text: var(--vp-c-text-1);--vp-custom-block-important-bg: var(--vp-c-important-soft);--vp-custom-block-important-code-bg: var(--vp-c-important-soft);--vp-custom-block-warning-border: transparent;--vp-custom-block-warning-text: var(--vp-c-text-1);--vp-custom-block-warning-bg: var(--vp-c-warning-soft);--vp-custom-block-warning-code-bg: var(--vp-c-warning-soft);--vp-custom-block-danger-border: transparent;--vp-custom-block-danger-text: var(--vp-c-text-1);--vp-custom-block-danger-bg: var(--vp-c-danger-soft);--vp-custom-block-danger-code-bg: var(--vp-c-danger-soft);--vp-custom-block-caution-border: transparent;--vp-custom-block-caution-text: var(--vp-c-text-1);--vp-custom-block-caution-bg: var(--vp-c-caution-soft);--vp-custom-block-caution-code-bg: var(--vp-c-caution-soft);--vp-custom-block-details-border: var(--vp-custom-block-info-border);--vp-custom-block-details-text: var(--vp-custom-block-info-text);--vp-custom-block-details-bg: var(--vp-custom-block-info-bg);--vp-custom-block-details-code-bg: var(--vp-custom-block-info-code-bg)}:root{--vp-input-border-color: var(--vp-c-border);--vp-input-bg-color: var(--vp-c-bg-alt);--vp-input-switch-bg-color: var(--vp-c-default-soft)}:root{--vp-nav-height: 64px;--vp-nav-bg-color: var(--vp-c-bg);--vp-nav-screen-bg-color: var(--vp-c-bg);--vp-nav-logo-height: 24px}.hide-nav{--vp-nav-height: 0px}.hide-nav .VPSidebar{--vp-nav-height: 22px}:root{--vp-local-nav-bg-color: var(--vp-c-bg)}:root{--vp-sidebar-width: 272px;--vp-sidebar-bg-color: var(--vp-c-bg-alt)}:root{--vp-backdrop-bg-color: rgba(0, 0, 0, .6)}:root{--vp-home-hero-name-color: var(--vp-c-brand-1);--vp-home-hero-name-background: transparent;--vp-home-hero-image-background-image: none;--vp-home-hero-image-filter: none}:root{--vp-badge-info-border: transparent;--vp-badge-info-text: var(--vp-c-text-2);--vp-badge-info-bg: var(--vp-c-default-soft);--vp-badge-tip-border: transparent;--vp-badge-tip-text: var(--vp-c-tip-1);--vp-badge-tip-bg: var(--vp-c-tip-soft);--vp-badge-warning-border: transparent;--vp-badge-warning-text: var(--vp-c-warning-1);--vp-badge-warning-bg: var(--vp-c-warning-soft);--vp-badge-danger-border: transparent;--vp-badge-danger-text: var(--vp-c-danger-1);--vp-badge-danger-bg: var(--vp-c-danger-soft)}:root{--vp-carbon-ads-text-color: var(--vp-c-text-1);--vp-carbon-ads-poweredby-color: var(--vp-c-text-2);--vp-carbon-ads-bg-color: var(--vp-c-bg-soft);--vp-carbon-ads-hover-text-color: var(--vp-c-brand-1);--vp-carbon-ads-hover-poweredby-color: var(--vp-c-text-1)}:root{--vp-local-search-bg: 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diff --git a/assets/zht_api_api.md.DgGLhN7H.js b/assets/zht_api_api.md.DgGLhN7H.js
deleted file mode 100644
index 95a4367..0000000
--- a/assets/zht_api_api.md.DgGLhN7H.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/api.md","filePath":"zht/api/api.md"}'),c={name:"zht/api/api.md"},o=p('
mbcp ​
説明: 本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(_,i,d,m,n,l){return t(),a("div",null,r)}const b=e(c,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/zht_api_api.md.DgGLhN7H.lean.js b/assets/zht_api_api.md.DgGLhN7H.lean.js
deleted file mode 100644
index 772aec3..0000000
--- a/assets/zht_api_api.md.DgGLhN7H.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as p}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/api.md","filePath":"zht/api/api.md"}'),c={name:"zht/api/api.md"},o=p("",5),r=[o];function s(_,i,d,m,n,l){return t(),a("div",null,r)}const b=e(c,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/zht_api_index.md.DMjE1xBr.js b/assets/zht_api_index.md.DMjE1xBr.js
new file mode 100644
index 0000000..7c72da9
--- /dev/null
+++ b/assets/zht_api_index.md.DMjE1xBr.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/index.md","filePath":"zht/api/index.md"}'),p={name:"zht/api/index.md"},o=c('
mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(d,_,i,n,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/zht_api_index.md.DNSdsCcq.lean.js b/assets/zht_api_index.md.DMjE1xBr.lean.js
similarity index 70%
rename from assets/zht_api_index.md.DNSdsCcq.lean.js
rename to assets/zht_api_index.md.DMjE1xBr.lean.js
index 2c1fc39..7027d4c 100644
--- a/assets/zht_api_index.md.DNSdsCcq.lean.js
+++ b/assets/zht_api_index.md.DMjE1xBr.lean.js
@@ -1 +1 @@
-import{_ as e,c as t,o as a,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/index.md","filePath":"zht/api/index.md"}'),p={name:"zht/api/index.md"},o=c("",5),r=[o];function s(d,_,i,n,m,l){return a(),t("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/index.md","filePath":"zht/api/index.md"}'),p={name:"zht/api/index.md"},o=c("",5),r=[o];function s(d,_,i,n,m,l){return t(),a("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/zht_api_index.md.DNSdsCcq.js b/assets/zht_api_index.md.DNSdsCcq.js
deleted file mode 100644
index d211cc3..0000000
--- a/assets/zht_api_index.md.DNSdsCcq.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as t,o as a,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp","description":"","frontmatter":{"title":"mbcp","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/index.md","filePath":"zht/api/index.md"}'),p={name:"zht/api/index.md"},o=c('
mbcp ​
説明: 本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
',5),r=[o];function s(d,_,i,n,m,l){return a(),t("div",null,r)}const b=e(p,[["render",s]]);export{f as __pageData,b as default};
diff --git a/assets/zht_api_mp_math_angle.md.CEIly6_X.js b/assets/zht_api_mp_math_angle.md.D6i--7zd.js
similarity index 60%
rename from assets/zht_api_mp_math_angle.md.CEIly6_X.js
rename to assets/zht_api_mp_math_angle.md.D6i--7zd.js
index b872440..eb8e529 100644
--- a/assets/zht_api_mp_math_angle.md.CEIly6_X.js
+++ b/assets/zht_api_mp_math_angle.md.D6i--7zd.js
@@ -1,4 +1,4 @@
-import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
func __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n(`
mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼 或 於GitHub上查看
python
@property
+        self.radian = value * PI / 180
@property
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼 或 於GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼 或 於GitHub上查看
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼 或 於GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼 或 於GitHub上查看
python
@property
+    return self.radian * 180 / PI
@property
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼 或 於GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼 或 於GitHub上查看
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼 或 於GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼 或 於GitHub上查看
python
@property
+    return math.sin(self.radian)
@property
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼 或 於GitHub上查看
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼 或 於GitHub上查看
python
@property
+    return math.cos(self.radian)
@property
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼 或 於GitHub上查看
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼 或 於GitHub上查看
python
@property
+    return math.tan(self.radian)
@property
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼 或 於GitHub上查看
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other):
+    ...
method self / other ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_angle.md.CEIly6_X.lean.js b/assets/zht_api_mp_math_angle.md.D6i--7zd.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_angle.md.CEIly6_X.lean.js
rename to assets/zht_api_mp_math_angle.md.D6i--7zd.lean.js
diff --git a/assets/zht_api_mp_math_const.md.DI0xAyWX.js b/assets/zht_api_mp_math_const.md.DI0xAyWX.js
new file mode 100644
index 0000000..0577efa
--- /dev/null
+++ b/assets/zht_api_mp_math_const.md.DI0xAyWX.js
@@ -0,0 +1 @@
+import{_ as a,c as o,o as t,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/const.md","filePath":"zht/api/mp_math/const.md"}'),r={name:"zht/api/mp_math/const.md"},l=e('
mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • 默認值: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • 默認值: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • 默認值: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • 默認值: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • 默認值: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • 默認值: 0.001
',14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const g=a(r,[["render",i]]);export{u as __pageData,g as default};
diff --git a/assets/zht_api_mp_math_const.md.DI0xAyWX.lean.js b/assets/zht_api_mp_math_const.md.DI0xAyWX.lean.js
new file mode 100644
index 0000000..8d3900f
--- /dev/null
+++ b/assets/zht_api_mp_math_const.md.DI0xAyWX.lean.js
@@ -0,0 +1 @@
+import{_ as a,c as o,o as t,a4 as e}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/const.md","filePath":"zht/api/mp_math/const.md"}'),r={name:"zht/api/mp_math/const.md"},l=e("",14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const g=a(r,[["render",i]]);export{u as __pageData,g as default};
diff --git a/assets/zht_api_mp_math_const.md.DhnGo46u.js b/assets/zht_api_mp_math_const.md.DhnGo46u.js
deleted file mode 100644
index 9e55827..0000000
--- a/assets/zht_api_mp_math_const.md.DhnGo46u.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as o,o as t,a4 as r}from"./chunks/framework.DpC1ZpOZ.js";const g=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/const.md","filePath":"zht/api/mp_math/const.md"}'),e={name:"zht/api/mp_math/const.md"},l=r('
mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • 默認值: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • 默認值: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • 默認值: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • 默認值: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • 默認值: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • 默認值: 0.001
',14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const u=a(e,[["render",i]]);export{g as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_const.md.DhnGo46u.lean.js b/assets/zht_api_mp_math_const.md.DhnGo46u.lean.js
deleted file mode 100644
index 572edc0..0000000
--- a/assets/zht_api_mp_math_const.md.DhnGo46u.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as o,o as t,a4 as r}from"./chunks/framework.DpC1ZpOZ.js";const g=JSON.parse('{"title":"mbcp.mp_math.const","description":"","frontmatter":{"title":"mbcp.mp_math.const","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/const.md","filePath":"zht/api/mp_math/const.md"}'),e={name:"zht/api/mp_math/const.md"},l=r("",14),n=[l];function i(s,c,p,d,h,m){return t(),o("div",null,n)}const u=a(e,[["render",i]]);export{g as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_equation.md.BPMLYcpO.js b/assets/zht_api_mp_math_equation.md.B3rt0Pgw.js
similarity index 82%
rename from assets/zht_api_mp_math_equation.md.BPMLYcpO.js
rename to assets/zht_api_mp_math_equation.md.B3rt0Pgw.js
index 0f4d793..26db594 100644
--- a/assets/zht_api_mp_math_equation.md.BPMLYcpO.js
+++ b/assets/zht_api_mp_math_equation.md.B3rt0Pgw.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼 或 於GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼 或 於GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_equation.md.BPMLYcpO.lean.js b/assets/zht_api_mp_math_equation.md.B3rt0Pgw.lean.js
similarity index 73%
rename from assets/zht_api_mp_math_equation.md.BPMLYcpO.lean.js
rename to assets/zht_api_mp_math_equation.md.B3rt0Pgw.lean.js
index 593b902..b4dd5c1 100644
--- a/assets/zht_api_mp_math_equation.md.BPMLYcpO.lean.js
+++ b/assets/zht_api_mp_math_equation.md.B3rt0Pgw.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n("",23),p=[l];function h(k,e,r,E,c,d){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_function.md.Cf9utaTV.js b/assets/zht_api_mp_math_function.md.Cf9utaTV.js
new file mode 100644
index 0000000..c243aa6
--- /dev/null
+++ b/assets/zht_api_mp_math_function.md.Cf9utaTV.js
@@ -0,0 +1,42 @@
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),e={name:"zht/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
變數説明:
返回: 梯度
源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    """
+    计算三元函数在某点的梯度向量。
+    > [!tip]
+    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
+    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
+    Args:
+        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
+        p ([\`Point3\`](./point#class-point3)): 点
+        epsilon: 偏移量
+    Returns:
+        梯度
+    """
+    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
+    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
+    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
+    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
變數説明:
返回: 柯里化后的函数
範例:
python
def add(a: int, b: int, c: int) -> int:
+    return a + b + c
+add_curried = curry(add, 1, 2)
+add_curried(3)  # 6
源碼 或 於GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+    """
+    对多参数函数进行柯里化。
+    > [!tip]
+    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
+    Args:
+        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
+        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
+    Returns:
+        柯里化后的函数
+    Examples:
+        \`\`\`python
+        def add(a: int, b: int, c: int) -> int:
+            return a + b + c
+        add_curried = curry(add, 1, 2)
+        add_curried(3)  # 6
+        \`\`\`
+    """
+
+    def curried_func(*args2: Var) -> Var:
+        """@litedoc-hide"""
+        return func(*args, *args2)
+    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/zht_api_mp_math_function.md.D9y8K44X.lean.js b/assets/zht_api_mp_math_function.md.Cf9utaTV.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_function.md.D9y8K44X.lean.js
rename to assets/zht_api_mp_math_function.md.Cf9utaTV.lean.js
diff --git a/assets/zht_api_mp_math_function.md.D9y8K44X.js b/assets/zht_api_mp_math_function.md.D9y8K44X.js
deleted file mode 100644
index 1eab202..0000000
--- a/assets/zht_api_mp_math_function.md.D9y8K44X.js
+++ /dev/null
@@ -1,42 +0,0 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),e={name:"zht/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
説明: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
變數説明:
返回: 梯度
源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
-    """
-    计算三元函数在某点的梯度向量。
-    > [!tip]
-    > 已知一个函数$f(x, y, z)$，则其在点$(x_0, y_0, z_0)$处的梯度向量为:
-    $\\\\nabla f(x_0, y_0, z_0) = \\\\left(\\\\frac{\\\\partial f}{\\\\partial x}, \\\\frac{\\\\partial f}{\\\\partial y}, \\\\frac{\\\\partial f}{\\\\partial z}\\\\right)$
-    Args:
-        func ([\`ThreeSingleVarsFunc\`](./mp_math_typing#var-threesinglevarsfunc)): 三元函数
-        p ([\`Point3\`](./point#class-point3)): 点
-        epsilon: 偏移量
-    Returns:
-        梯度
-    """
-    dx = (func(p.x + epsilon, p.y, p.z) - func(p.x - epsilon, p.y, p.z)) / (2 * epsilon)
-    dy = (func(p.x, p.y + epsilon, p.z) - func(p.x, p.y - epsilon, p.z)) / (2 * epsilon)
-    dz = (func(p.x, p.y, p.z + epsilon) - func(p.x, p.y, p.z - epsilon)) / (2 * epsilon)
-    return Vector3(dx, dy, dz)
func curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
變數説明:
返回: 柯里化后的函数
範例:
python
def add(a: int, b: int, c: int) -> int:
-    return a + b + c
-add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
源碼 或 於GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
-    """
-    对多参数函数进行柯里化。
-    > [!tip]
-    > 有关函数柯里化，可参考[函数式编程--柯理化（Currying）](https://zhuanlan.zhihu.com/p/355859667)
-    Args:
-        func ([\`MultiVarsFunc\`](./mp_math_typing#var-multivarsfunc)): 函数
-        *args ([\`Var\`](./mp_math_typing#var-var)): 参数
-    Returns:
-        柯里化后的函数
-    Examples:
-        \`\`\`python
-        def add(a: int, b: int, c: int) -> int:
-            return a + b + c
-        add_curried = curry(add, 1, 2)
-        add_curried(3)  # 6
-        \`\`\`
-    """
-
-    def curried_func(*args2: Var) -> Var:
-        """@litedoc-hide"""
-        return func(*args, *args2)
-    return curried_func
`,13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/zht_api_mp_math_index.md.C-ytwIT_.js b/assets/zht_api_mp_math_index.md.C-ytwIT_.js
deleted file mode 100644
index 4c87c9a..0000000
--- a/assets/zht_api_mp_math_index.md.C-ytwIT_.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/mp_math/index.md","filePath":"zht/api/mp_math/index.md"}'),l={name:"zht/api/mp_math/index.md"},o=c('
mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function m(n,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_index.md.DbgI3vD1.js b/assets/zht_api_mp_math_index.md.DbgI3vD1.js
new file mode 100644
index 0000000..6dc6c51
--- /dev/null
+++ b/assets/zht_api_mp_math_index.md.DbgI3vD1.js
@@ -0,0 +1 @@
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/mp_math/index.md","filePath":"zht/api/mp_math/index.md"}'),l={name:"zht/api/mp_math/index.md"},o=c('
mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),i=[o];function m(n,s,d,p,h,r){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_index.md.C-ytwIT_.lean.js b/assets/zht_api_mp_math_index.md.DbgI3vD1.lean.js
similarity index 86%
rename from assets/zht_api_mp_math_index.md.C-ytwIT_.lean.js
rename to assets/zht_api_mp_math_index.md.DbgI3vD1.lean.js
index cd5548f..678567c 100644
--- a/assets/zht_api_mp_math_index.md.C-ytwIT_.lean.js
+++ b/assets/zht_api_mp_math_index.md.DbgI3vD1.lean.js
@@ -1 +1 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/mp_math/index.md","filePath":"zht/api/mp_math/index.md"}'),l={name:"zht/api/mp_math/index.md"},o=c("",3),i=[o];function m(n,s,d,p,r,h){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
+import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/mp_math/index.md","filePath":"zht/api/mp_math/index.md"}'),l={name:"zht/api/mp_math/index.md"},o=c("",3),i=[o];function m(n,s,d,p,h,r){return t(),a("div",null,i)}const u=e(l,[["render",m]]);export{f as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_line.md.V0JKiMxX.js b/assets/zht_api_mp_math_line.md.-wtKMTMJ.js
similarity index 60%
rename from assets/zht_api_mp_math_line.md.V0JKiMxX.js
rename to assets/zht_api_mp_math_line.md.-wtKMTMJ.js
index 8ba92ac..8d13236 100644
--- a/assets/zht_api_mp_math_line.md.V0JKiMxX.js
+++ b/assets/zht_api_mp_math_line.md.-wtKMTMJ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n(`
mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             direction ([\`Vector3\`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -23,7 +23,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other (Line3): 另一条直线
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other (Line3): 另一条直线
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -60,7 +60,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
返回: Line3: 垂线
源碼 或 於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
返回: Line3: 垂线
源碼 或 於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -68,7 +68,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Line3\`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
返回: Point3: 点
源碼 或 於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
返回: Point3: 点
源碼 或 於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -76,13 +76,13 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`Point3\`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源碼 或 於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源碼 或 於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [\`tuple\`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[\`OneSingleVarFunc\`](./mp_math_typing#var-onesinglevarfunc), \`OneSingleVarFunc\`, \`OneSingleVarFunc\`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -91,7 +91,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -99,7 +99,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
返回: bool: 是否共线
源碼 或 於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
返回: bool: 是否共线
源碼 或 於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -107,7 +107,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
返回: bool: 是否在直线上
源碼 或 於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
返回: bool: 是否在直线上
源碼 或 於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -115,7 +115,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
返回: bool: 是否共面
源碼 或 於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
返回: bool: 是否共面
源碼 或 於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -124,7 +124,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼 或 於GitHub上查看
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼 或 於GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -137,7 +137,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
返回: Line3: 直线
源碼 或 於GitHub上查看
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
返回: Line3: 直线
源碼 或 於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -148,7 +148,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
             [\`Line3\`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -171,4 +171,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_line.md.V0JKiMxX.lean.js b/assets/zht_api_mp_math_line.md.-wtKMTMJ.lean.js
similarity index 72%
rename from assets/zht_api_mp_math_line.md.V0JKiMxX.lean.js
rename to assets/zht_api_mp_math_line.md.-wtKMTMJ.lean.js
index d21d980..62d797b 100644
--- a/assets/zht_api_mp_math_line.md.V0JKiMxX.lean.js
+++ b/assets/zht_api_mp_math_line.md.-wtKMTMJ.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n("",106),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),t={name:"zht/api/mp_math/line.md"},l=n("",106),e=[l];function h(p,k,o,r,d,g){return a(),i("div",null,e)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_mp_math.md.WAo96wsQ.js b/assets/zht_api_mp_math_mp_math.md.WAo96wsQ.js
deleted file mode 100644
index c4715d5..0000000
--- a/assets/zht_api_mp_math_mp_math.md.WAo96wsQ.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/mp_math/mp_math.md","filePath":"zht/api/mp_math/mp_math.md"}'),l={name:"zht/api/mp_math/mp_math.md"},m=c('
mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
',3),o=[m];function i(s,n,p,h,r,_){return t(),a("div",null,o)}const u=e(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_mp_math.md.WAo96wsQ.lean.js b/assets/zht_api_mp_math_mp_math.md.WAo96wsQ.lean.js
deleted file mode 100644
index 59a0fde..0000000
--- a/assets/zht_api_mp_math_mp_math.md.WAo96wsQ.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as e,c as a,o as t,a4 as c}from"./chunks/framework.DpC1ZpOZ.js";const f=JSON.parse('{"title":"mbcp.mp_math","description":"","frontmatter":{"title":"mbcp.mp_math","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/mp_math/mp_math.md","filePath":"zht/api/mp_math/mp_math.md"}'),l={name:"zht/api/mp_math/mp_math.md"},m=c("",3),o=[m];function i(s,n,p,h,r,_){return t(),a("div",null,o)}const u=e(l,[["render",i]]);export{f as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_mp_math_typing.md.2475K9x4.js b/assets/zht_api_mp_math_mp_math_typing.md.2475K9x4.js
deleted file mode 100644
index c6741fc..0000000
--- a/assets/zht_api_mp_math_mp_math_typing.md.2475K9x4.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/mp_math_typing.md","filePath":"zht/api/mp_math/mp_math_typing.md"}'),l={name:"zht/api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • 類型: TypeAlias
  • 默認值: int | float
var Number ​
  • 説明: 数
  • 類型: TypeAlias
  • 默認值: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • 默認值: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • 類型: TypeAlias
  • 默認值: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • 類型: TypeAlias
  • 默認值: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • 類型: TypeAlias
  • 默認值: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • 類型: TypeAlias
  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • 類型: TypeAlias
  • 默認值: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,d,p,u,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/zht_api_mp_math_mp_math_typing.md.BbOeRs-n.js b/assets/zht_api_mp_math_mp_math_typing.md.BbOeRs-n.js
new file mode 100644
index 0000000..7858f77
--- /dev/null
+++ b/assets/zht_api_mp_math_mp_math_typing.md.BbOeRs-n.js
@@ -0,0 +1 @@
+import{_ as a,c as r,o as e,a4 as o}from"./chunks/framework.DpC1ZpOZ.js";const v=JSON.parse('{"title":"mbcp.mp_math.mp_math_typing","description":"","frontmatter":{"title":"mbcp.mp_math.mp_math_typing","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/mp_math_typing.md","filePath":"zht/api/mp_math/mp_math_typing.md"}'),l={name:"zht/api/mp_math/mp_math_typing.md"},n=o('
mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • 類型: TypeAlias
  • 默認值: int | float
var Number ​
  • 説明: 数
  • 類型: TypeAlias
  • 默認值: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • 默認值: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • 類型: TypeAlias
  • 默認值: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • 類型: TypeAlias
  • 默認值: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • 類型: TypeAlias
  • 默認值: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • 類型: TypeAlias
  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • 類型: TypeAlias
  • 默認值: MultiSingleVarsFunc | MultiArraysFunc
',36),t=[n];function i(s,c,d,p,u,g){return e(),r("div",null,t)}const m=a(l,[["render",i]]);export{v as __pageData,m as default};
diff --git a/assets/zht_api_mp_math_mp_math_typing.md.2475K9x4.lean.js b/assets/zht_api_mp_math_mp_math_typing.md.BbOeRs-n.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_mp_math_typing.md.2475K9x4.lean.js
rename to assets/zht_api_mp_math_mp_math_typing.md.BbOeRs-n.lean.js
diff --git a/assets/zht_api_mp_math_plane.md.CKWKiFtm.js b/assets/zht_api_mp_math_plane.md.o_Vroqha.js
similarity index 71%
rename from assets/zht_api_mp_math_plane.md.CKWKiFtm.js
rename to assets/zht_api_mp_math_plane.md.o_Vroqha.js
index b4fffaf..9c26a68 100644
--- a/assets/zht_api_mp_math_plane.md.CKWKiFtm.js
+++ b/assets/zht_api_mp_math_plane.md.o_Vroqha.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},t=n(`
mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other (Plane3): 另一个平面
返回: Line3: 交线
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other (Plane3): 另一个平面
返回: Line3: 交线
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -84,7 +84,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -98,7 +98,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -106,7 +106,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -114,14 +114,14 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: Vector3: 法向量
源碼 或 於GitHub上查看
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: Vector3: 法向量
源碼 或 於GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [\`Vector3\`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -133,7 +133,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -147,7 +147,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -161,7 +161,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -171,11 +171,11 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
返回: Line3 | Point3 | None: 交集
抛出:
源碼 或 於GitHub上查看
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
返回: Line3 | Point3 | None: 交集
抛出:
源碼 或 於GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -194,7 +194,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -202,5 +202,5 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_plane.md.CKWKiFtm.lean.js b/assets/zht_api_mp_math_plane.md.o_Vroqha.lean.js
similarity index 67%
rename from assets/zht_api_mp_math_plane.md.CKWKiFtm.lean.js
rename to assets/zht_api_mp_math_plane.md.o_Vroqha.lean.js
index 00a9c41..43a9b72 100644
--- a/assets/zht_api_mp_math_plane.md.CKWKiFtm.lean.js
+++ b/assets/zht_api_mp_math_plane.md.o_Vroqha.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{c as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},t=n("",113),h=[t];function p(e,k,r,o,d,E){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_point.md.D7bOx2HI.js b/assets/zht_api_mp_math_point.md.CNwxPYyR.js
similarity index 56%
rename from assets/zht_api_mp_math_point.md.D7bOx2HI.js
rename to assets/zht_api_mp_math_point.md.CNwxPYyR.js
index 2f6fe97..39ec417 100644
--- a/assets/zht_api_mp_math_point.md.D7bOx2HI.js
+++ b/assets/zht_api_mp_math_point.md.CNwxPYyR.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},l=t(`
mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},h=t(`
mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -17,11 +17,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: P + V -> P P + P -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,7 +30,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -38,7 +38,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
變數説明:
返回: Vector3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
變數説明:
返回: Vector3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -49,4 +49,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
             [\`Vector3\`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),h=[l];function p(e,k,o,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",p]]);export{E as __pageData,y as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_point.md.D7bOx2HI.lean.js b/assets/zht_api_mp_math_point.md.CNwxPYyR.lean.js
similarity index 72%
rename from assets/zht_api_mp_math_point.md.D7bOx2HI.lean.js
rename to assets/zht_api_mp_math_point.md.CNwxPYyR.lean.js
index 54ef0dc..8ede03c 100644
--- a/assets/zht_api_mp_math_point.md.D7bOx2HI.lean.js
+++ b/assets/zht_api_mp_math_point.md.CNwxPYyR.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},l=t("",39),h=[l];function p(e,k,o,r,d,c){return a(),i("div",null,h)}const y=s(n,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},h=t("",39),l=[h];function e(p,o,k,r,d,g){return a(),i("div",null,l)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_segment.md.pWjtiCkV.js b/assets/zht_api_mp_math_segment.md.Dr21f14B.js
similarity index 69%
rename from assets/zht_api_mp_math_segment.md.pWjtiCkV.js
rename to assets/zht_api_mp_math_segment.md.Dr21f14B.js
index 515bbfd..d4c63d4 100644
--- a/assets/zht_api_mp_math_segment.md.pWjtiCkV.js
+++ b/assets/zht_api_mp_math_segment.md.Dr21f14B.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},p=n(`
mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
變數説明:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),n={name:"zht/api/mp_math/segment.md"},h=t(`
mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
變數説明:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -12,4 +12,4 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,8),p=[h];function l(e,k,r,d,E,o){return a(),i("div",null,p)}const c=s(n,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_segment.md.Dr21f14B.lean.js b/assets/zht_api_mp_math_segment.md.Dr21f14B.lean.js
new file mode 100644
index 0000000..ca0ee65
--- /dev/null
+++ b/assets/zht_api_mp_math_segment.md.Dr21f14B.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),n={name:"zht/api/mp_math/segment.md"},h=t("",8),p=[h];function l(e,k,r,d,E,o){return a(),i("div",null,p)}const c=s(n,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_segment.md.pWjtiCkV.lean.js b/assets/zht_api_mp_math_segment.md.pWjtiCkV.lean.js
deleted file mode 100644
index 7180312..0000000
--- a/assets/zht_api_mp_math_segment.md.pWjtiCkV.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},p=n("",8),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const c=s(t,[["render",l]]);export{F as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_utils.md.DIDbd5be.js b/assets/zht_api_mp_math_utils.md.B57z4IwN.js
similarity index 79%
rename from assets/zht_api_mp_math_utils.md.DIDbd5be.js
rename to assets/zht_api_mp_math_utils.md.B57z4IwN.js
index 00d94e8..4d3b2e6 100644
--- a/assets/zht_api_mp_math_utils.md.DIDbd5be.js
+++ b/assets/zht_api_mp_math_utils.md.B57z4IwN.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),n={name:"zht/api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
變數説明:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),n={name:"zht/api/mp_math/utils.md"},l=t(`
mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
變數説明:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,13 +9,13 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     Returns:
         \`float\`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -25,8 +25,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
         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)
func raise_type_error(self, other) ​
源碼 或 於GitHub上查看
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼 或 於GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -66,4 +66,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,38),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",p]]);export{F as __pageData,c as default};
+        return ''
`,38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_utils.md.DIDbd5be.lean.js b/assets/zht_api_mp_math_utils.md.B57z4IwN.lean.js
similarity index 67%
rename from assets/zht_api_mp_math_utils.md.DIDbd5be.lean.js
rename to assets/zht_api_mp_math_utils.md.B57z4IwN.lean.js
index ce79bcd..24b504f 100644
--- a/assets/zht_api_mp_math_utils.md.DIDbd5be.lean.js
+++ b/assets/zht_api_mp_math_utils.md.B57z4IwN.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),n={name:"zht/api/mp_math/utils.md"},l=t("",38),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",p]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),n={name:"zht/api/mp_math/utils.md"},l=t("",38),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_vector.md.4G7-2lGN.js b/assets/zht_api_mp_math_vector.md.DCG5CraB.js
similarity index 63%
rename from assets/zht_api_mp_math_vector.md.4G7-2lGN.js
rename to assets/zht_api_mp_math_vector.md.DCG5CraB.js
index 094f149..7b1c8b3 100644
--- a/assets/zht_api_mp_math_vector.md.4G7-2lGN.js
+++ b/assets/zht_api_mp_math_vector.md.DCG5CraB.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},l=t(`
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},e=t(`
mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`AnyAngle\`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
返回: Vector3: 叉乘结果
源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
返回: Vector3: 叉乘结果
源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Vector3\`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼 或 於GitHub上查看
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼 或 於GitHub上查看
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,33 +72,33 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源碼 或 於GitHub上查看
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源碼 或 於GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [\`np.ndarray\`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
説明: 向量的模。
返回: float: 模
源碼 或 於GitHub上查看
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
説明: 向量的模。
返回: float: 模
源碼 或 於GitHub上查看
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源碼 或 於GitHub上查看
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源碼 或 於GitHub上查看
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [\`Vector3\`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
源碼 或 於GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    return self / self.length
method __abs__(self) ​
源碼 或 於GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: V + P -> P
V + V -> V
變數説明:
返回: Vector3 | Point3: 新的向量或点
源碼 或 於GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
返回: Vector3 | Point3: 新的向量或点
源碼 或 於GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -113,7 +113,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -121,7 +121,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -131,11 +131,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`Point3\`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
説明: V - P -> P
V - V -> V
變數説明:
返回: Vector3 | Point3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
返回: Vector3 | Point3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -150,7 +150,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}"')
func self - other: Point3 ​
説明: P - V -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -161,11 +161,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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
func self * other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
返回: Vector3: 数组运算结果
源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
返回: Vector3: 数组运算结果
源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -178,8 +178,8 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
     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)}'")
func self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
返回: float: 点乘结果
源碼 或 於GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
返回: float: 点乘结果
源碼 或 於GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -187,11 +187,11 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E
         Returns:
             [\`float\`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
説明: 取负。
返回: Vector3: 负向量
源碼 或 於GitHub上查看
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
説明: 取负。
返回: Vector3: 负向量
源碼 或 於GitHub上查看
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [\`Vector3\`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 1)
`,138),e=[l];function h(p,k,r,o,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 1)
`,138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_vector.md.4G7-2lGN.lean.js b/assets/zht_api_mp_math_vector.md.DCG5CraB.lean.js
similarity index 73%
rename from assets/zht_api_mp_math_vector.md.4G7-2lGN.lean.js
rename to assets/zht_api_mp_math_vector.md.DCG5CraB.lean.js
index 0cc6efe..484aa50 100644
--- a/assets/zht_api_mp_math_vector.md.4G7-2lGN.lean.js
+++ b/assets/zht_api_mp_math_vector.md.DCG5CraB.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},l=t("",138),e=[l];function h(p,k,r,o,d,c){return a(),i("div",null,e)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},e=t("",138),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_particle_index.md.C8wv1sGB.js b/assets/zht_api_particle_index.md.C8wv1sGB.js
deleted file mode 100644
index 367307e..0000000
--- a/assets/zht_api_particle_index.md.C8wv1sGB.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/particle/index.md","filePath":"zht/api/particle/index.md"}'),i={name:"zht/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"説明"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[p,l];function n(o,d,_,m,h,f){return r(),c("div",null,s)}const u=a(i,[["render",n]]);export{b as __pageData,u as default};
diff --git a/assets/zht_api_particle_index.md.C8wv1sGB.lean.js b/assets/zht_api_particle_index.md.C8wv1sGB.lean.js
deleted file mode 100644
index 367307e..0000000
--- a/assets/zht_api_particle_index.md.C8wv1sGB.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/particle/index.md","filePath":"zht/api/particle/index.md"}'),i={name:"zht/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),l=e("p",null,[e("strong",null,"説明"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[p,l];function n(o,d,_,m,h,f){return r(),c("div",null,s)}const u=a(i,[["render",n]]);export{b as __pageData,u as default};
diff --git a/assets/zht_api_particle_index.md.DjZABivI.js b/assets/zht_api_particle_index.md.DjZABivI.js
new file mode 100644
index 0000000..32ce8e7
--- /dev/null
+++ b/assets/zht_api_particle_index.md.DjZABivI.js
@@ -0,0 +1 @@
+import{_ as t,c as a,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/particle/index.md","filePath":"zht/api/particle/index.md"}'),i={name:"zht/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),s=e("p",null,"本模块定义了粒子生成相关的工具",-1),l=[p,s];function o(n,d,_,m,h,f){return c(),a("div",null,l)}const u=t(i,[["render",o]]);export{b as __pageData,u as default};
diff --git a/assets/zht_api_particle_index.md.DjZABivI.lean.js b/assets/zht_api_particle_index.md.DjZABivI.lean.js
new file mode 100644
index 0000000..32ce8e7
--- /dev/null
+++ b/assets/zht_api_particle_index.md.DjZABivI.lean.js
@@ -0,0 +1 @@
+import{_ as t,c as a,o as c,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/particle/index.md","filePath":"zht/api/particle/index.md"}'),i={name:"zht/api/particle/index.md"},p=e("h1",{id:"mbcp-particle",tabindex:"-1"},[r("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),s=e("p",null,"本模块定义了粒子生成相关的工具",-1),l=[p,s];function o(n,d,_,m,h,f){return c(),a("div",null,l)}const u=t(i,[["render",o]]);export{b as __pageData,u as default};
diff --git a/assets/zht_api_particle_particle.md.DLxDzJsb.js b/assets/zht_api_particle_particle.md.DLxDzJsb.js
deleted file mode 100644
index 28ba6af..0000000
--- a/assets/zht_api_particle_particle.md.DLxDzJsb.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/particle/particle.md","filePath":"zht/api/particle/particle.md"}'),p={name:"zht/api/particle/particle.md"},l=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),i=e("p",null,[e("strong",null,"説明"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[l,i];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=a(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/zht_api_particle_particle.md.DLxDzJsb.lean.js b/assets/zht_api_particle_particle.md.DLxDzJsb.lean.js
deleted file mode 100644
index 28ba6af..0000000
--- a/assets/zht_api_particle_particle.md.DLxDzJsb.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as a,c,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.particle","description":"","frontmatter":{"title":"mbcp.particle","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/particle/particle.md","filePath":"zht/api/particle/particle.md"}'),p={name:"zht/api/particle/particle.md"},l=e("h1",{id:"mbcp-particle",tabindex:"-1"},[t("mbcp.particle "),e("a",{class:"header-anchor",href:"#mbcp-particle","aria-label":'Permalink to "mbcp.particle"'},"​")],-1),i=e("p",null,[e("strong",null,"説明"),t(": 本模块定义了粒子生成相关的工具")],-1),s=[l,i];function o(n,d,_,m,h,f){return r(),c("div",null,s)}const x=a(p,[["render",o]]);export{u as __pageData,x as default};
diff --git a/assets/zht_api_presets_index.md.CKWpXp08.js b/assets/zht_api_presets_index.md.Bl7tnVS9.js
similarity index 53%
rename from assets/zht_api_presets_index.md.CKWpXp08.js
rename to assets/zht_api_presets_index.md.Bl7tnVS9.js
index 60a65f1..e0923af 100644
--- a/assets/zht_api_presets_index.md.CKWpXp08.js
+++ b/assets/zht_api_presets_index.md.Bl7tnVS9.js
@@ -1 +1 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/index.md","filePath":"zht/api/presets/index.md"}'),p={name:"zht/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),n=e("p",null,[e("strong",null,"説明"),t(": 本模块塞了一些预设")],-1),o=[c,n];function d(i,l,_,m,h,f){return r(),a("div",null,o)}const u=s(p,[["render",d]]);export{b as __pageData,u as default};
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/index.md","filePath":"zht/api/presets/index.md"}'),p={name:"zht/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,"本模块塞了一些预设",-1),n=[c,o];function d(i,l,_,m,h,f){return a(),s("div",null,n)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/zht_api_presets_index.md.CKWpXp08.lean.js b/assets/zht_api_presets_index.md.Bl7tnVS9.lean.js
similarity index 53%
rename from assets/zht_api_presets_index.md.CKWpXp08.lean.js
rename to assets/zht_api_presets_index.md.Bl7tnVS9.lean.js
index 60a65f1..e0923af 100644
--- a/assets/zht_api_presets_index.md.CKWpXp08.lean.js
+++ b/assets/zht_api_presets_index.md.Bl7tnVS9.lean.js
@@ -1 +1 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/index.md","filePath":"zht/api/presets/index.md"}'),p={name:"zht/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),n=e("p",null,[e("strong",null,"説明"),t(": 本模块塞了一些预设")],-1),o=[c,n];function d(i,l,_,m,h,f){return r(),a("div",null,o)}const u=s(p,[["render",d]]);export{b as __pageData,u as default};
+import{_ as t,c as s,o as a,j as e,a as r}from"./chunks/framework.DpC1ZpOZ.js";const b=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/index.md","filePath":"zht/api/presets/index.md"}'),p={name:"zht/api/presets/index.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[r("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,"本模块塞了一些预设",-1),n=[c,o];function d(i,l,_,m,h,f){return a(),s("div",null,n)}const u=t(p,[["render",d]]);export{b as __pageData,u as default};
diff --git a/assets/zht_api_presets_model_index.md.BMgFAAtM.js b/assets/zht_api_presets_model_index.md.BMgFAAtM.js
deleted file mode 100644
index 32b7ff7..0000000
--- a/assets/zht_api_presets_model_index.md.BMgFAAtM.js
+++ /dev/null
@@ -1,18 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    x_array = radius * np.sin(phi_list) * np.cos(theta_list)
-    y_array = radius * np.sin(phi_list) * np.sin(theta_list)
-    z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_presets_model_index.md.BMgFAAtM.lean.js b/assets/zht_api_presets_model_index.md.BMgFAAtM.lean.js
deleted file mode 100644
index 971fa91..0000000
--- a/assets/zht_api_presets_model_index.md.BMgFAAtM.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),t={name:"zht/api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_presets_model_model.md.hVmtKMyB.js b/assets/zht_api_presets_model_index.md.BQanubQ0.js
similarity index 81%
rename from assets/zht_api_presets_model_model.md.hVmtKMyB.js
rename to assets/zht_api_presets_model_index.md.BQanubQ0.js
index 26da939..77500af 100644
--- a/assets/zht_api_presets_model_model.md.hVmtKMyB.js
+++ b/assets/zht_api_presets_model_index.md.BQanubQ0.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/model.md","filePath":"zht/api/presets/model/model.md"}'),n={name:"zht/api/presets/model/model.md"},h=t(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t(`
mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
diff --git a/assets/zht_api_presets_model_model.md.hVmtKMyB.lean.js b/assets/zht_api_presets_model_index.md.BQanubQ0.lean.js
similarity index 74%
rename from assets/zht_api_presets_model_model.md.hVmtKMyB.lean.js
rename to assets/zht_api_presets_model_index.md.BQanubQ0.lean.js
index 2003d15..51a0c5b 100644
--- a/assets/zht_api_presets_model_model.md.hVmtKMyB.lean.js
+++ b/assets/zht_api_presets_model_index.md.BQanubQ0.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/model.md","filePath":"zht/api/presets/model/model.md"}'),n={name:"zht/api/presets/model/model.md"},h=t("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_presets_presets.md.nxuS_hT6.js b/assets/zht_api_presets_presets.md.nxuS_hT6.js
deleted file mode 100644
index bc067b3..0000000
--- a/assets/zht_api_presets_presets.md.nxuS_hT6.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/presets.md","filePath":"zht/api/presets/presets.md"}'),p={name:"zht/api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"説明"),t(": 本模块塞了一些预设")],-1),n=[c,o];function l(d,i,_,m,h,f){return r(),a("div",null,n)}const x=s(p,[["render",l]]);export{u as __pageData,x as default};
diff --git a/assets/zht_api_presets_presets.md.nxuS_hT6.lean.js b/assets/zht_api_presets_presets.md.nxuS_hT6.lean.js
deleted file mode 100644
index bc067b3..0000000
--- a/assets/zht_api_presets_presets.md.nxuS_hT6.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as a,o as r,j as e,a as t}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.presets","description":"","frontmatter":{"title":"mbcp.presets","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/presets.md","filePath":"zht/api/presets/presets.md"}'),p={name:"zht/api/presets/presets.md"},c=e("h1",{id:"mbcp-presets",tabindex:"-1"},[t("mbcp.presets "),e("a",{class:"header-anchor",href:"#mbcp-presets","aria-label":'Permalink to "mbcp.presets"'},"​")],-1),o=e("p",null,[e("strong",null,"説明"),t(": 本模块塞了一些预设")],-1),n=[c,o];function l(d,i,_,m,h,f){return r(),a("div",null,n)}const x=s(p,[["render",l]]);export{u as __pageData,x as default};
diff --git a/demo/best-practice.html b/demo/best-practice.html
index 279bd0e..43c885f 100644
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MBCP 文档
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demo ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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MBCP 文档
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简体中文
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demo ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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     mbcp | MBCP docs
     
     
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MBCP docs
English
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繁體中文
English
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mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index 817111f..c17690b 100644
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@@ -6,19 +6,19 @@
     mbcp.mp_math.angle | MBCP docs
     
     
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mbcp.mp_math.angle ​
Description: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
func __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
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mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code or View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code or View on GitHub
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 or View on GitHub
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code or View on GitHub
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 or View on GitHub
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code or View on GitHub
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 or View on GitHub
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code or View on GitHub
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 or View on GitHub
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code or View on GitHub
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 or View on GitHub
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code or View on GitHub
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 or View on GitHub
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code or View on GitHub
python
@property
+    return math.sin(self.radian)
@property
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code or View on GitHub
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code or View on GitHub
python
@property
+    return math.cos(self.radian)
@property
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code or View on GitHub
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code or View on GitHub
python
@property
+    return math.tan(self.radian)
@property
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code or View on GitHub
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code or View on GitHub
python
@property
+    return 1 / math.tan(self.radian)
@property
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code or View on GitHub
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code or View on GitHub
python
@property
+    return 1 / math.cos(self.radian)
@property
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code or View on GitHub
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
Source code or View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
Source code or View on GitHub
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code or View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code or View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
Source code or View on GitHub
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
Source code or View on GitHub
python
def __truediv__(self, other):
+    ...
method self / other ​
Source code or View on GitHub
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return AnyAngle(self.radian / other, is_radian=True)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html
index 9a5d92b..c8f4363 100644
--- a/en/api/mp_math/const.html
+++ b/en/api/mp_math/const.html
@@ -6,20 +6,20 @@
     mbcp.mp_math.const | MBCP docs
     
     
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MBCP docs
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日本語
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mbcp.mp_math.const ​
Description: 本模块定义了一些常用的常量
var PI ​
  • Description: 常量 π
  • Default: math.pi
var E ​
  • Description: 自然对数的底 exp(1)
  • Default: math.e
var GOLDEN_RATIO ​
  • Description: 黄金分割比
  • Default: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • Description: 欧拉常数
  • Default: 0.5772156649015329
var EPSILON ​
  • Description: 精度误差
  • Default: 0.0001
var APPROX ​
  • Description: 约等于判定误差
  • Default: 0.001
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • Description: 常量 π
  • Default: math.pi
var E ​
  • Description: 自然对数的底 exp(1)
  • Default: math.e
var GOLDEN_RATIO ​
  • Description: 黄金分割比
  • Default: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • Description: 欧拉常数
  • Default: 0.5772156649015329
var EPSILON ​
  • Description: 精度误差
  • Default: 0.0001
var APPROX ​
  • Description: 约等于判定误差
  • Default: 0.001
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html
index e3a8a47..006df67 100644
--- a/en/api/mp_math/equation.html
+++ b/en/api/mp_math/equation.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.equation | MBCP docs
     
     
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MBCP docs
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mbcp.mp_math.equation ​
Description: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
Source code or View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
MBCP docs
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简体中文
日本語
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mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
Source code or View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code or View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code or View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -82,8 +82,8 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        raise ValueError('Invalid var type')
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html
index dc5b900..e0f4665 100644
--- a/en/api/mp_math/function.html
+++ b/en/api/mp_math/function.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.function | MBCP docs
     
     
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日本語
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mbcp.mp_math.function ​
Description: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
Arguments:
Return: 梯度
Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
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mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
Arguments:
Return: 梯度
Source code or View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -59,8 +59,8 @@
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return curried_func
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html
index a816b0b..d5888b6 100644
--- a/en/api/mp_math/index.html
+++ b/en/api/mp_math/index.html
@@ -6,20 +6,20 @@
     mbcp.mp_math | MBCP docs
     
     
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mbcp.mp_math ​
Description: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
English
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English
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mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html
index 351eca9..da965d6 100644
--- a/en/api/mp_math/line.html
+++ b/en/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP docs
     
     
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mbcp.mp_math.line ​
Description: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
Source code or View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction ([`Vector3`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other (Line3): 另一条直线
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other (Line3): 另一条直线
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -43,7 +43,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -65,7 +65,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other (Line3): 另一条直线
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other (Line3): 另一条直线
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -80,7 +80,7 @@
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
Return: Line3: 垂线
Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
Return: Line3: 垂线
Source code or View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -88,7 +88,7 @@
         Returns:
             [`Line3`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
Return: Point3: 点
Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
Return: Point3: 点
Source code or View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -96,13 +96,13 @@
         Returns:
             [`Point3`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
Source code or View on GitHub
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -111,7 +111,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -119,7 +119,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
Return: bool: 是否共线
Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
Return: bool: 是否共线
Source code or View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -127,7 +127,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
Return: bool: 是否在直线上
Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
Return: bool: 是否在直线上
Source code or View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -135,7 +135,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
Return: bool: 是否共面
Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
Return: bool: 是否共面
Source code or View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -144,7 +144,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code or View on GitHub
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code or View on GitHub
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -157,7 +157,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
Return: Line3: 直线
Source code or View on GitHub
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
Return: Line3: 直线
Source code or View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -168,7 +168,7 @@
             [`Line3`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other (Line3): 另一条直线
Return: Line3 | Point3 | None: 交集
Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other (Line3): 另一条直线
Return: Line3 | Point3 | None: 交集
Source code or View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -181,7 +181,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other (Line3): 另一条直线
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other (Line3): 另一条直线
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -191,8 +191,8 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/mp_math.html b/en/api/mp_math/mp_math.html
deleted file mode 100644
index 62bba41..0000000
--- a/en/api/mp_math/mp_math.html
+++ /dev/null
@@ -1,25 +0,0 @@
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MBCP docs
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简体中文
日本語
繁體中文
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mbcp.mp_math ​
Description: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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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 e2c2c0f..68d33a3 100644
--- a/en/api/mp_math/mp_math_typing.html
+++ b/en/api/mp_math/mp_math_typing.html
@@ -6,20 +6,20 @@
     mbcp.mp_math.mp_math_typing | MBCP docs
     
     
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+    
     
     
     
     
   
   
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MBCP docs
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简体中文
日本語
繁體中文
English
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日本語
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mbcp.mp_math.mp_math_typing ​
Description: 本模块用于内部类型提示
var RealNumber ​
  • Description: 实数
  • Type: TypeAlias
  • Default: int | float
var Number ​
  • Description: 数
  • Type: TypeAlias
  • Default: RealNumber | complex
var SingleVar ​
  • Description: 单变量
  • Default: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • Description: 数组变量
  • Default: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • Description: 变量
  • Type: TypeAlias
  • Default: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • Description: 一元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • Description: 一元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • Description: 一元函数
  • Type: TypeAlias
  • Default: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • Description: 二元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • Description: 二元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • Description: 二元函数
  • Type: TypeAlias
  • Default: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • Description: 三元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • Description: 三元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • Description: 三元函数
  • Type: TypeAlias
  • Default: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • Description: 多元单变量函数
  • Type: TypeAlias
  • Default: Callable[..., SingleVar]
var MultiArraysFunc ​
  • Description: 多元数组函数
  • Type: TypeAlias
  • Default: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • Description: 多元函数
  • Type: TypeAlias
  • Default: MultiSingleVarsFunc | MultiArraysFunc
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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MBCP docs
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English
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mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • Description: 实数
  • Type: TypeAlias
  • Default: int | float
var Number ​
  • Description: 数
  • Type: TypeAlias
  • Default: RealNumber | complex
var SingleVar ​
  • Description: 单变量
  • Default: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • Description: 数组变量
  • Default: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • Description: 变量
  • Type: TypeAlias
  • Default: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • Description: 一元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • Description: 一元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • Description: 一元函数
  • Type: TypeAlias
  • Default: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • Description: 二元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • Description: 二元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • Description: 二元函数
  • Type: TypeAlias
  • Default: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • Description: 三元单变量函数
  • Type: TypeAlias
  • Default: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • Description: 三元数组函数
  • Type: TypeAlias
  • Default: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • Description: 三元函数
  • Type: TypeAlias
  • Default: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • Description: 多元单变量函数
  • Type: TypeAlias
  • Default: Callable[..., SingleVar]
var MultiArraysFunc ​
  • Description: 多元数组函数
  • Type: TypeAlias
  • Default: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • Description: 多元函数
  • Type: TypeAlias
  • Default: MultiSingleVarsFunc | MultiArraysFunc
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html
index 667402d..5b0da2c 100644
--- a/en/api/mp_math/plane.html
+++ b/en/api/mp_math/plane.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.plane | MBCP docs
     
     
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mbcp.mp_math.plane ​
Description: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
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mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
Source code or View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Raises:
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Raises:
Source code or View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
Return: float: 距离
Raises:
Source code or View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other (Plane3): 另一个平面
Return: Line3: 交线
Raises:
Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other (Plane3): 另一个平面
Return: Line3: 交线
Raises:
Source code or View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -104,7 +104,7 @@
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
Return: Point3: 交点
Raises:
Source code or View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +118,7 @@
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +126,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +134,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: Vector3: 法向量
Source code or View on GitHub
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: Vector3: 法向量
Source code or View on GitHub
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
Return: Plane3: 平面
Source code or View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +153,7 @@
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
Return: 平面
Source code or View on GitHub
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
Return: 平面
Source code or View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +167,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
Return: 平面
Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
Return: 平面
Source code or View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +181,7 @@
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
Return: 平面
Source code or View on GitHub
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
Return: 平面
Source code or View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +191,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
Return: Line3 | Point3 | None: 交集
Raises:
Source code or View on GitHub
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
Return: Line3 | Point3 | None: 交集
Raises:
Source code or View on GitHub
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +214,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
Description: 判断两个平面是否等价。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Description: 判断两个平面是否等价。
Arguments:
  • other (Plane3): 另一个平面
Return: bool: 是否等价
Source code or View on GitHub
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +222,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html
index 5f38a1b..136df15 100644
--- a/en/api/mp_math/point.html
+++ b/en/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP docs
     
     
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+    
     
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+    
     
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+    
     
     
     
     
   
   
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MBCP docs
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日本語
繁體中文
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mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
Source code or View on GitHub
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 or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
Description: P + V -> P P + P -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __add__(self, other):
+    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,7 +50,7 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -58,7 +58,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 Vector3 中实现
Arguments:
Return: Vector3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 Vector3 中实现
Arguments:
Return: Vector3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,8 +69,8 @@
             [`Vector3`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html
index 7f39923..a224238 100644
--- a/en/api/mp_math/segment.html
+++ b/en/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
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mbcp.mp_math.segment ​
Description: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。
Arguments:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
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mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。
Arguments:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
Source code or View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -32,8 +32,8 @@
     '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)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html
index 95731c8..3341a35 100644
--- a/en/api/mp_math/utils.html
+++ b/en/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
MBCP docs
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English
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mbcp.mp_math.utils ​
Description: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
Description: 区间限定函数
Arguments:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
Return: float: 限定在区间内的值
Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
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日本語
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English
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mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
Description: 区间限定函数
Arguments:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
Return: float: 限定在区间内的值
Source code or View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,13 +29,13 @@
     Returns:
         `float`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
Description: 用于近似比较对象
Arguments:
Source code or View on GitHub
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
Description: 用于近似比较对象
Arguments:
Source code or View on GitHub
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -45,8 +45,8 @@
         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)
func raise_type_error(self, other) ​
Source code or View on GitHub
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code or View on GitHub
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -86,8 +86,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        return ''
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html
index 2f46eda..c48b87c 100644
--- a/en/api/mp_math/vector.html
+++ b/en/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
MBCP docs
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mbcp.mp_math.vector ​
Description: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
Source code or View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
Return: AnyAngle: 夹角
Source code or View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
Return: Vector3: 叉乘结果
Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
Return: Vector3: 叉乘结果
Source code or View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
Return: bool: 是否近似平行
Source code or View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
Return: bool: 是否平行
Source code or View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code or View on GitHub
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code or View on GitHub
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
Return: np.ndarray: numpy数组
Source code or View on GitHub
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
Return: np.ndarray: numpy数组
Source code or View on GitHub
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
Description: 向量的模。
Return: float: 模
Source code or View on GitHub
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
Description: 向量的模。
Return: float: 模
Source code or View on GitHub
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: Vector3: 单位向量
Source code or View on GitHub
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: Vector3: 单位向量
Source code or View on GitHub
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
Source code or View on GitHub
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+    return self / self.length
method __abs__(self) ​
Source code or View on GitHub
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
Description: V + P -> P
V + V -> V
Arguments:
Return: Vector3 | Point3: 新的向量或点
Source code or View on GitHub
python
def __add__(self, other):
+    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
Return: Vector3 | Point3: 新的向量或点
Source code or View on GitHub
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -133,7 +133,7 @@
     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)}'")
func __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
Return: bool: 是否相等
Source code or View on GitHub
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +141,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -151,11 +151,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
Description: V - P -> P
V - V -> V
Arguments:
Return: Vector3 | Point3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other):
+    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
Return: Vector3 | Point3: 新的向量
Source code or View on GitHub
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -170,7 +170,7 @@
     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)}"')
func self - other: Point3 ​
Description: P - V -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
Return: Point3: 新的点
Source code or View on GitHub
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -181,11 +181,11 @@
     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
func self * other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
Return: Vector3: 数组运算结果
Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
Return: Vector3: 数组运算结果
Source code or View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +198,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
func self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
Return: float: 点乘结果
Source code or View on GitHub
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
Return: float: 点乘结果
Source code or View on GitHub
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -207,15 +207,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
Description: 取负。
Return: Vector3: 负向量
Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
Description: 取负。
Return: Vector3: 负向量
Source code or View on GitHub
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • Description: 零向量
  • Type: Vector3
  • Default: Vector3(0, 0, 0)
var x_axis ​
  • Description: x轴单位向量
  • Type: Vector3
  • Default: Vector3(1, 0, 0)
var y_axis ​
  • Description: y轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 1, 0)
var z_axis ​
  • Description: z轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 0, 1)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • Description: 零向量
  • Type: Vector3
  • Default: Vector3(0, 0, 0)
var x_axis ​
  • Description: x轴单位向量
  • Type: Vector3
  • Default: Vector3(1, 0, 0)
var y_axis ​
  • Description: y轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 1, 0)
var z_axis ​
  • Description: z轴单位向量
  • Type: Vector3
  • Default: Vector3(0, 0, 1)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/particle/index.html b/en/api/particle/index.html
index 233cd34..8866dac 100644
--- a/en/api/particle/index.html
+++ b/en/api/particle/index.html
@@ -6,20 +6,20 @@
     mbcp.particle | MBCP docs
     
     
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deleted file mode 100644
index 8c0a05c..0000000
--- a/en/api/particle/particle.html
+++ /dev/null
@@ -1,25 +0,0 @@
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diff --git a/en/api/presets/index.html b/en/api/presets/index.html
index c81424c..d78ee85 100644
--- a/en/api/presets/index.html
+++ b/en/api/presets/index.html
@@ -6,20 +6,20 @@
     mbcp.presets | MBCP docs
     
     
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diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html
index ccbb1c8..2d6f4a2 100644
--- a/en/api/presets/model/index.html
+++ b/en/api/presets/model/index.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP docs
     
     
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MBCP docs
English
简体中文
日本語
繁體中文
English
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mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
+    
MBCP docs
English
简体中文
日本語
繁體中文
English
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mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,8 +35,8 @@
     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)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/presets/model/model.html b/en/api/presets/model/model.html
deleted file mode 100644
index 1cd0d71..0000000
--- a/en/api/presets/model/model.html
+++ /dev/null
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mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code or View on GitHub
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    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)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/presets/presets.html b/en/api/presets/presets.html
deleted file mode 100644
index cd15014..0000000
--- a/en/api/presets/presets.html
+++ /dev/null
@@ -1,25 +0,0 @@
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diff --git a/en/demo/best-practice.html b/en/demo/best-practice.html
index fa60012..7830192 100644
--- a/en/demo/best-practice.html
+++ b/en/demo/best-practice.html
@@ -6,10 +6,10 @@
     Best Practice | MBCP docs
     
     
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index cc1cd5e..fa0bf89 100644
--- a/en/guide/index.html
+++ b/en/guide/index.html
@@ -6,10 +6,10 @@
     开始不了一点 | MBCP docs
     
     
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MBCP docs
English
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日本語
繁體中文
English
简体中文
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开始不了一点 ​
∫12x111
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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MBCP docs
English
简体中文
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English
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开始不了一点 ​
∫12x111
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diff --git a/en/index.html b/en/index.html
index 1c07f11..76d3bfd 100644
--- a/en/index.html
+++ b/en/index.html
@@ -6,10 +6,10 @@
     MBCP docs
     
     
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MBCP docs
English
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日本語
繁體中文
English
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MBCP
More basic change particle
A Library for Python to create Minecraft particle effects and geometric figures
Get Started
API Reference
Best Practice
MBCP logo
🛠️
Easy to use
Through a simple interface, most of the geometric operations and particle production requirements have been achieved
📦
Integrated
Encapsulated and integratednumpy, scipy and sympy, making script writing as simple as using Geogebra
🧊
Rich presets
Rich presets and examples, you can use it directly, and you can also customize the parameters to create your own effects
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
MBCP
More basic change particle
A Library for Python to create Minecraft particle effects and geometric figures
Get Started
API Reference
Best Practice
MBCP logo
🛠️
Easy to use
Through a simple interface, most of the geometric operations and particle production requirements have been achieved
📦
Integrated
Encapsulated and integratednumpy, scipy and sympy, making script writing as simple as using Geogebra
🧊
Rich presets
Rich presets and examples, you can use it directly, and you can also customize the parameters to create your own effects
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/refer/index.html b/en/refer/index.html
index a691228..4c97cbb 100644
--- a/en/refer/index.html
+++ b/en/refer/index.html
@@ -6,10 +6,10 @@
     Reference | MBCP docs
     
     
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MBCP docs
English
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English
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Reference ​
help us to improve the documentation
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
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Reference ​
help us to improve the documentation
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/guide/index.html b/guide/index.html
index cbfa92b..69a6341 100644
--- a/guide/index.html
+++ b/guide/index.html
@@ -3,23 +3,23 @@
   
     
     
-    开始不了一点 | MBCP 文档
+    快速开始 | MBCP 文档
     
     
-    
+    
     
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+    
+    
     
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MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
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开始不了一点 ​
∫12x111
AAA ​
BBB ​
C ​
ddd ​
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
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MBCP 文档
简体中文
English
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快速开始 ​
TIP
建议：把你项目所使用的Python换成PyPy，这样可以提高性能(兼容性优先)
安装 ​
shell
pip install mbcp
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/hashmap.json b/hashmap.json
index 458fb13..318a8e8 100644
--- a/hashmap.json
+++ b/hashmap.json
@@ -1 +1 @@
-{"api_api.md":"rnPOv6-O","api_index.md":"qnrSd__i","api_mp_math_angle.md":"D0ius2dn","api_mp_math_const.md":"O6cTulwX","api_mp_math_equation.md":"D9gepkm-","api_mp_math_function.md":"DCuJC29A","api_mp_math_index.md":"DHhPNV6R","api_mp_math_line.md":"ByGRRi0A","api_mp_math_mp_math.md":"mVabZTHd","api_mp_math_mp_math_typing.md":"CEryCREV","api_mp_math_plane.md":"Ir4HtSn5","api_mp_math_point.md":"CIRBY4Zg","api_mp_math_segment.md":"DFwFkY98","api_mp_math_utils.md":"CFXHDZgH","api_mp_math_vector.md":"CuQ0WDoP","api_particle_index.md":"BxLVuqry","api_particle_particle.md":"CioLG9Ab","api_presets_index.md":"C7sBj6Q8","api_presets_model_index.md":"BcL7qpu8","api_presets_model_model.md":"Ch05JNzT","api_presets_presets.md":"kIUJtfck","demo_best-practice.md":"CmYjfrxd","demo_index.md":"CVAdlaFI","en_api_api.md":"D31N0-_j","en_api_index.md":"CpTS_pfZ","en_api_mp_math_angle.md":"DTo0bIGQ","en_api_mp_math_const.md":"DjbxFoGO","en_api_mp_math_equation.md":"NTcIjf_k","en_api_mp_math_function.md":"BXNFIE6F","en_api_mp_math_index.md":"ypHGEnmb","en_api_mp_math_line.md":"CxP-i4OT","en_api_mp_math_mp_math.md":"5IisTIt3","en_api_mp_math_mp_math_typing.md":"DWjztCj6","en_api_mp_math_plane.md":"BsgpTZdY","en_api_mp_math_point.md":"DcGqVqiO","en_api_mp_math_segment.md":"Cge1J0TK","en_api_mp_math_utils.md":"Bu0IGkds","en_api_mp_math_vector.md":"DpvjNLj_","en_api_particle_index.md":"NezC90nG","en_api_particle_particle.md":"BTk7xB-d","en_api_presets_index.md":"Clhg0YLX","en_api_presets_model_index.md":"BJWo1DBU","en_api_presets_model_model.md":"Cmq9KKw_","en_api_presets_presets.md":"5pMosEdX","en_demo_best-practice.md":"CmtY105n","en_guide_index.md":"C3kI8f8A","en_index.md":"Cc-Nt9Ot","en_refer_index.md":"Cq6GWi0V","guide_index.md":"BVhQ0kPy","index.md":"WVpbC1C1","ja_api_api.md":"DD7b0jH_","ja_api_index.md":"3bCCqhm9","ja_api_mp_math_angle.md":"DmogilJK","ja_api_mp_math_const.md":"CACmM3Q4","ja_api_mp_math_equation.md":"DuGNts4i","ja_api_mp_math_function.md":"DIn5uL0A","ja_api_mp_math_index.md":"B_UDRWJp","ja_api_mp_math_line.md":"Ber05s-D","ja_api_mp_math_mp_math.md":"DGl-Yqoj","ja_api_mp_math_mp_math_typing.md":"BANGfx9Q","ja_api_mp_math_plane.md":"BlhqSUWq","ja_api_mp_math_point.md":"Czyuzvxa","ja_api_mp_math_segment.md":"DfoJ389C","ja_api_mp_math_utils.md":"Dnl5rkoo","ja_api_mp_math_vector.md":"CD5nfzHo","ja_api_particle_index.md":"SXvJHpqE","ja_api_particle_particle.md":"DpDqAPA7","ja_api_presets_index.md":"DrJ0aeZq","ja_api_presets_model_index.md":"D3Q5KLfq","ja_api_presets_model_model.md":"vKB1wVU9","ja_api_presets_presets.md":"Bm4b0yEm","ja_demo_best-practice.md":"CBHiF6ec","ja_guide_index.md":"w1Tf2Adm","ja_index.md":"BvjV8RIJ","ja_refer_index.md":"DamUscs8","refer_function_curry.md":"D_oqRDd3","refer_function_function.md":"Bi_82lIJ","refer_index.md":"yFZW0kI4","zht_api_api.md":"DgGLhN7H","zht_api_index.md":"DNSdsCcq","zht_api_mp_math_angle.md":"CEIly6_X","zht_api_mp_math_const.md":"DhnGo46u","zht_api_mp_math_equation.md":"BPMLYcpO","zht_api_mp_math_function.md":"D9y8K44X","zht_api_mp_math_index.md":"C-ytwIT_","zht_api_mp_math_line.md":"V0JKiMxX","zht_api_mp_math_mp_math.md":"WAo96wsQ","zht_api_mp_math_mp_math_typing.md":"2475K9x4","zht_api_mp_math_plane.md":"CKWKiFtm","zht_api_mp_math_point.md":"D7bOx2HI","zht_api_mp_math_segment.md":"pWjtiCkV","zht_api_mp_math_utils.md":"DIDbd5be","zht_api_mp_math_vector.md":"4G7-2lGN","zht_api_particle_index.md":"C8wv1sGB","zht_api_particle_particle.md":"DLxDzJsb","zht_api_presets_index.md":"CKWpXp08","zht_api_presets_model_index.md":"BMgFAAtM","zht_api_presets_model_model.md":"hVmtKMyB","zht_api_presets_presets.md":"nxuS_hT6","zht_demo_best-practice.md":"CPNbD_Lg","zht_guide_index.md":"BNnMViC8","zht_index.md":"fkOYkZZe","zht_refer_index.md":"B7CQS2UW"}
+{"api_index.md":"YS-zqWwM","api_mp_math_angle.md":"CThQB5nq","api_mp_math_const.md":"DqjQQ6Ym","api_mp_math_equation.md":"C1YMGsIR","api_mp_math_function.md":"C0P_-kol","api_mp_math_index.md":"yEj9pzOD","api_mp_math_line.md":"Okmn0BTW","api_mp_math_mp_math_typing.md":"bdiOSvFy","api_mp_math_plane.md":"Dl-FdXx3","api_mp_math_point.md":"xU6HjeL2","api_mp_math_segment.md":"BqloNjdD","api_mp_math_utils.md":"CGBZjr3t","api_mp_math_vector.md":"B443ftAV","api_particle_index.md":"VxgsHiZa","api_presets_index.md":"BEZBx6Gj","api_presets_model_index.md":"CzrZX1Li","demo_best-practice.md":"CmYjfrxd","demo_index.md":"CVAdlaFI","en_api_index.md":"BrJlad-k","en_api_mp_math_angle.md":"BvzeTdtj","en_api_mp_math_const.md":"CrUt_3FV","en_api_mp_math_equation.md":"CHBtH4v6","en_api_mp_math_function.md":"D68bTyed","en_api_mp_math_index.md":"D331As7i","en_api_mp_math_line.md":"B69kHoPc","en_api_mp_math_mp_math_typing.md":"xRGJGUMm","en_api_mp_math_plane.md":"BdKgRumw","en_api_mp_math_point.md":"BeT2oqIN","en_api_mp_math_segment.md":"DbFvInHk","en_api_mp_math_utils.md":"CYq8hncD","en_api_mp_math_vector.md":"CPGkZzwr","en_api_particle_index.md":"ZKByd_x0","en_api_presets_index.md":"BhoZyGSV","en_api_presets_model_index.md":"BM4zzWd9","en_demo_best-practice.md":"CmtY105n","en_guide_index.md":"C3kI8f8A","en_index.md":"Cc-Nt9Ot","en_refer_index.md":"Cq6GWi0V","guide_index.md":"CJOqvlSE","index.md":"WVpbC1C1","ja_api_index.md":"6u5f7W7q","ja_api_mp_math_angle.md":"CbTFNFpP","ja_api_mp_math_const.md":"HrVLdLVW","ja_api_mp_math_equation.md":"BR_cjYxP","ja_api_mp_math_function.md":"CeNPnpri","ja_api_mp_math_index.md":"BVYYBcgX","ja_api_mp_math_line.md":"CmVmq6PC","ja_api_mp_math_mp_math_typing.md":"BnSHEEFC","ja_api_mp_math_plane.md":"D7v3q_U8","ja_api_mp_math_point.md":"BqC8JgjG","ja_api_mp_math_segment.md":"vi1FH0--","ja_api_mp_math_utils.md":"DhPmcvK-","ja_api_mp_math_vector.md":"B7oDy-SU","ja_api_particle_index.md":"ighey3JD","ja_api_presets_index.md":"Bow22HNO","ja_api_presets_model_index.md":"C-uCqjXi","ja_demo_best-practice.md":"CBHiF6ec","ja_guide_index.md":"w1Tf2Adm","ja_index.md":"BvjV8RIJ","ja_refer_index.md":"DamUscs8","refer_function_curry.md":"D_oqRDd3","refer_function_function.md":"Bi_82lIJ","refer_index.md":"yFZW0kI4","zht_api_index.md":"DMjE1xBr","zht_api_mp_math_angle.md":"D6i--7zd","zht_api_mp_math_const.md":"DI0xAyWX","zht_api_mp_math_equation.md":"B3rt0Pgw","zht_api_mp_math_function.md":"Cf9utaTV","zht_api_mp_math_index.md":"DbgI3vD1","zht_api_mp_math_line.md":"-wtKMTMJ","zht_api_mp_math_mp_math_typing.md":"BbOeRs-n","zht_api_mp_math_plane.md":"o_Vroqha","zht_api_mp_math_point.md":"CNwxPYyR","zht_api_mp_math_segment.md":"Dr21f14B","zht_api_mp_math_utils.md":"B57z4IwN","zht_api_mp_math_vector.md":"DCG5CraB","zht_api_particle_index.md":"DjZABivI","zht_api_presets_index.md":"Bl7tnVS9","zht_api_presets_model_index.md":"BQanubQ0","zht_demo_best-practice.md":"CPNbD_Lg","zht_guide_index.md":"BNnMViC8","zht_index.md":"fkOYkZZe","zht_refer_index.md":"B7CQS2UW"}
diff --git a/index.html b/index.html
index dcea9a6..6b9e6c5 100644
--- a/index.html
+++ b/index.html
@@ -6,10 +6,10 @@
     MBCP 文档
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -18,8 +18,8 @@
     
   
   
-    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
MBCP
更多基础变换粒子
用于几何运算和Minecraft粒子制作的库
快速开始
API文档
最佳实践
MBCP logo
🛠️
高可用性
通过简单的接口，实现了大部分几何运算和粒子制作的需求
📦
高集成度
对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单
🧊
内置预设
提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
MBCP
更多基础变换粒子
用于几何运算和Minecraft粒子制作的库
快速开始
API文档
最佳实践
MBCP logo
🛠️
高可用性
通过简单的接口，实现了大部分几何运算和粒子制作的需求
📦
高集成度
对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单
🧊
内置预设
提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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\ No newline at end of file
diff --git a/ja/api/api.html b/ja/api/api.html
deleted file mode 100644
index ff74f06..0000000
--- a/ja/api/api.html
+++ /dev/null
@@ -1,25 +0,0 @@
-
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-    mbcp | MBCP ドキュメント
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diff --git a/ja/api/index.html b/ja/api/index.html
index 78a64ac..66388f9 100644
--- a/ja/api/index.html
+++ b/ja/api/index.html
@@ -6,20 +6,20 @@
     mbcp | MBCP ドキュメント
     
     
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MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html
index dc9bcbf..a00175f 100644
--- a/ja/api/mp_math/angle.html
+++ b/ja/api/mp_math/angle.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.angle | MBCP ドキュメント
     
     
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MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
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mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
func __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
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mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード または GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード または GitHubで表示
python
@property
+        self.radian = value * PI / 180
@property
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード または GitHubで表示
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード または GitHubで表示
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
method degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード または GitHubで表示
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード または GitHubで表示
python
@property
+    return self.radian * 180 / PI
@property
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード または GitHubで表示
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード または GitHubで表示
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード または GitHubで表示
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
method sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード または GitHubで表示
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード または GitHubで表示
python
@property
+    return math.sin(self.radian)
@property
method cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード または GitHubで表示
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード または GitHubで表示
python
@property
+    return math.cos(self.radian)
@property
method tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード または GitHubで表示
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード または GitHubで表示
python
@property
+    return math.tan(self.radian)
@property
method cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード または GitHubで表示
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード または GitHubで表示
python
@property
+    return 1 / math.tan(self.radian)
@property
method sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード または GitHubで表示
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード または GitHubで表示
python
@property
+    return 1 / math.cos(self.radian)
@property
method csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード または GitHubで表示
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
ソースコード または GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
ソースコード または GitHubで表示
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード または GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード または GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
ソースコード または GitHubで表示
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
ソースコード または GitHubで表示
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
ソースコード または GitHubで表示
python
def __truediv__(self, other):
+    ...
method self / other ​
ソースコード または GitHubで表示
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
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-    
+    return AnyAngle(self.radian / other, is_radian=True)
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html
index 63f2ceb..710db57 100644
--- a/ja/api/mp_math/const.html
+++ b/ja/api/mp_math/const.html
@@ -6,20 +6,20 @@
     mbcp.mp_math.const | MBCP ドキュメント
     
     
-    
+    
     
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mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • デフォルト: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • デフォルト: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • デフォルト: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • デフォルト: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • デフォルト: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • デフォルト: 0.001
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-    
+    
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mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • デフォルト: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • デフォルト: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • デフォルト: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • デフォルト: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • デフォルト: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • デフォルト: 0.001
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html
index efeac0f..cb93c1b 100644
--- a/ja/api/mp_math/equation.html
+++ b/ja/api/mp_math/equation.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.equation | MBCP ドキュメント
     
     
-    
+    
     
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+    
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mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
ソースコード または GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
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mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
ソースコード または GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード または GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード または GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -82,8 +82,8 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        raise ValueError('Invalid var type')
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html
index c173582..995c2f3 100644
--- a/ja/api/mp_math/function.html
+++ b/ja/api/mp_math/function.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.function | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
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mbcp.mp_math.function ​
説明: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
引数:
戻り値: 梯度
ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
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mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
引数:
戻り値: 梯度
ソースコード または GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -59,8 +59,8 @@
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return curried_func
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html
index 6f59f4b..c76f0a7 100644
--- a/ja/api/mp_math/index.html
+++ b/ja/api/mp_math/index.html
@@ -6,20 +6,20 @@
     mbcp.mp_math | MBCP ドキュメント
     
     
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+    
     
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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
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mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html
index f7f110c..18a3f27 100644
--- a/ja/api/mp_math/line.html
+++ b/ja/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
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mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
ソースコード または GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction ([`Vector3`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other (Line3): 另一条直线
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other (Line3): 另一条直线
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -43,7 +43,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -65,7 +65,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other (Line3): 另一条直线
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other (Line3): 另一条直线
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -80,7 +80,7 @@
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
戻り値: Line3: 垂线
ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
戻り値: Line3: 垂线
ソースコード または GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -88,7 +88,7 @@
         Returns:
             [`Line3`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
戻り値: Point3: 点
ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
戻り値: Point3: 点
ソースコード または GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -96,13 +96,13 @@
         Returns:
             [`Point3`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
ソースコード または GitHubで表示
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -111,7 +111,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -119,7 +119,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
戻り値: bool: 是否共线
ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
戻り値: bool: 是否共线
ソースコード または GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -127,7 +127,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
戻り値: bool: 是否在直线上
ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
戻り値: bool: 是否在直线上
ソースコード または GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -135,7 +135,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
戻り値: bool: 是否共面
ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
戻り値: bool: 是否共面
ソースコード または GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -144,7 +144,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード または GitHubで表示
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード または GitHubで表示
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -157,7 +157,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
戻り値: Line3: 直线
ソースコード または GitHubで表示
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
戻り値: Line3: 直线
ソースコード または GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -168,7 +168,7 @@
             [`Line3`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other (Line3): 另一条直线
戻り値: Line3 | Point3 | None: 交集
ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other (Line3): 另一条直线
戻り値: Line3 | Point3 | None: 交集
ソースコード または GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -181,7 +181,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other (Line3): 另一条直线
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other (Line3): 另一条直线
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -191,8 +191,8 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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-    
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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diff --git a/ja/api/mp_math/mp_math.html b/ja/api/mp_math/mp_math.html
deleted file mode 100644
index d84968a..0000000
--- a/ja/api/mp_math/mp_math.html
+++ /dev/null
@@ -1,25 +0,0 @@
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-    mbcp.mp_math | MBCP ドキュメント
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MBCP ドキュメント
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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
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diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html
index 9cb2edd..7ca735d 100644
--- a/ja/api/mp_math/mp_math_typing.html
+++ b/ja/api/mp_math/mp_math_typing.html
@@ -6,20 +6,20 @@
     mbcp.mp_math.mp_math_typing | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
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MBCP ドキュメント
日本語
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mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • タイプ: TypeAlias
  • デフォルト: int | float
var Number ​
  • 説明: 数
  • タイプ: TypeAlias
  • デフォルト: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • デフォルト: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • タイプ: TypeAlias
  • デフォルト: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • タイプ: TypeAlias
  • デフォルト: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • タイプ: TypeAlias
  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • タイプ: TypeAlias
  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • タイプ: TypeAlias
  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
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-    
+    
MBCP ドキュメント
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mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • タイプ: TypeAlias
  • デフォルト: int | float
var Number ​
  • 説明: 数
  • タイプ: TypeAlias
  • デフォルト: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • デフォルト: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • デフォルト: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • タイプ: TypeAlias
  • デフォルト: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • タイプ: TypeAlias
  • デフォルト: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • タイプ: TypeAlias
  • デフォルト: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • タイプ: TypeAlias
  • デフォルト: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • タイプ: TypeAlias
  • デフォルト: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • タイプ: TypeAlias
  • デフォルト: MultiSingleVarsFunc | MultiArraysFunc
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
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diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html
index ef74bc9..db5b994 100644
--- a/ja/api/mp_math/plane.html
+++ b/ja/api/mp_math/plane.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.plane | MBCP ドキュメント
     
     
-    
+    
     
-    
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+    
+    
     
-    
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mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
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mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
ソースコード または GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
戻り値: AnyAngle: 夹角
例外:
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
戻り値: AnyAngle: 夹角
例外:
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
戻り値: float: 距离
例外:
ソースコード または GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other (Plane3): 另一个平面
戻り値: Line3: 交线
例外:
ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other (Plane3): 另一个平面
戻り値: Line3: 交线
例外:
ソースコード または GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -104,7 +104,7 @@
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
戻り値: Point3: 交点
例外:
ソースコード または GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +118,7 @@
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +126,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +134,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: Vector3: 法向量
ソースコード または GitHubで表示
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: Vector3: 法向量
ソースコード または GitHubで表示
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
戻り値: Plane3: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +153,7 @@
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +167,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +181,7 @@
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
戻り値: 平面
ソースコード または GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +191,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
ソースコード または GitHubで表示
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
戻り値: Line3 | Point3 | None: 交集
例外:
ソースコード または GitHubで表示
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
戻り値: Line3 | Point3 | None: 交集
例外:
ソースコード または GitHubで表示
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +214,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
引数:
  • other (Plane3): 另一个平面
戻り値: bool: 是否等价
ソースコード または GitHubで表示
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +222,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
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-    
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html
index 755a30e..f5ea891 100644
--- a/ja/api/mp_math/point.html
+++ b/ja/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
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mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
+    
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mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
ソースコード または GitHubで表示
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 または GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: P + V -> P P + P -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,7 +50,7 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -58,7 +58,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
引数:
戻り値: Vector3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
引数:
戻り値: Vector3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,8 +69,8 @@
             [`Vector3`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
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-    
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html
index b36ea46..3e9dfa8 100644
--- a/ja/api/mp_math/segment.html
+++ b/ja/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
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mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
引数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
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mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
引数:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
ソースコード または GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -32,8 +32,8 @@
     '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)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html
index 092ef15..1bcd397 100644
--- a/ja/api/mp_math/utils.html
+++ b/ja/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
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mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
引数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
戻り値: float: 限定在区间内的值
ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
引数:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
戻り値: float: 限定在区间内的值
ソースコード または GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,13 +29,13 @@
     Returns:
         `float`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
引数:
ソースコード または GitHubで表示
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
引数:
ソースコード または GitHubで表示
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -45,8 +45,8 @@
         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)
func raise_type_error(self, other) ​
ソースコード または GitHubで表示
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
ソースコード または GitHubで表示
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード または GitHubで表示
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード または GitHubで表示
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -86,8 +86,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        return ''
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html
index 4e316f8..1141169 100644
--- a/ja/api/mp_math/vector.html
+++ b/ja/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP ドキュメント
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
ソースコード または GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
戻り値: AnyAngle: 夹角
ソースコード または GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
戻り値: Vector3: 叉乘结果
ソースコード または GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
戻り値: Vector3: 叉乘结果
ソースコード または GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
戻り値: bool: 是否近似平行
ソースコード または GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
戻り値: bool: 是否平行
ソースコード または GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード または GitHubで表示
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード または GitHubで表示
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
戻り値: np.ndarray: numpy数组
ソースコード または GitHubで表示
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
戻り値: np.ndarray: numpy数组
ソースコード または GitHubで表示
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
説明: 向量的模。
戻り値: float: 模
ソースコード または GitHubで表示
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
説明: 向量的模。
戻り値: float: 模
ソースコード または GitHubで表示
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: Vector3: 单位向量
ソースコード または GitHubで表示
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: Vector3: 单位向量
ソースコード または GitHubで表示
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
ソースコード または GitHubで表示
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    return self / self.length
method __abs__(self) ​
ソースコード または GitHubで表示
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: V + P -> P
V + V -> V
引数:
戻り値: Vector3 | Point3: 新的向量或点
ソースコード または GitHubで表示
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
戻り値: Vector3 | Point3: 新的向量或点
ソースコード または GitHubで表示
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -133,7 +133,7 @@
     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)}'")
func __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
戻り値: bool: 是否相等
ソースコード または GitHubで表示
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +141,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -151,11 +151,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
説明: V - P -> P
V - V -> V
引数:
戻り値: Vector3 | Point3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
戻り値: Vector3 | Point3: 新的向量
ソースコード または GitHubで表示
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -170,7 +170,7 @@
     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)}"')
func self - other: Point3 ​
説明: P - V -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
戻り値: Point3: 新的点
ソースコード または GitHubで表示
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -181,11 +181,11 @@
     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
func self * other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
戻り値: Vector3: 数组运算结果
ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
戻り値: Vector3: 数组运算结果
ソースコード または GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +198,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
func self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
戻り値: float: 点乘结果
ソースコード または GitHubで表示
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
戻り値: float: 点乘结果
ソースコード または GitHubで表示
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -207,15 +207,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
説明: 取负。
戻り値: Vector3: 负向量
ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
説明: 取负。
戻り値: Vector3: 负向量
ソースコード または GitHubで表示
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 1)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 1)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html
index dde6619..4c68c5a 100644
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+++ b/ja/api/particle/index.html
@@ -6,20 +6,20 @@
     mbcp.particle | MBCP ドキュメント
     
     
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+++ /dev/null
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diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html
index b2ed878..a1192a0 100644
--- a/ja/api/presets/index.html
+++ b/ja/api/presets/index.html
@@ -6,20 +6,20 @@
     mbcp.presets | MBCP ドキュメント
     
     
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diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html
index 68faea3..2b1df4f 100644
--- a/ja/api/presets/model/index.html
+++ b/ja/api/presets/model/index.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP ドキュメント
     
     
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MBCP ドキュメント
日本語
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
+    
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mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,8 +35,8 @@
     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)]
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
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diff --git a/ja/api/presets/model/model.html b/ja/api/presets/model/model.html
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+++ /dev/null
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MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード または GitHubで表示
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    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)]
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diff --git a/ja/api/presets/presets.html b/ja/api/presets/presets.html
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index 542f607..0000000
--- a/ja/api/presets/presets.html
+++ /dev/null
@@ -1,25 +0,0 @@
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-    mbcp.presets | MBCP ドキュメント
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diff --git a/ja/demo/best-practice.html b/ja/demo/best-practice.html
index c1f044e..0e17a2c 100644
--- a/ja/demo/best-practice.html
+++ b/ja/demo/best-practice.html
@@ -6,10 +6,10 @@
     ベストプラクティス | MBCP ドキュメント
     
     
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index a7f2f68..3c931e3 100644
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     开始不了一点 | MBCP ドキュメント
     
     
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MBCP ドキュメント
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English
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开始不了一点 ​
∫12x111
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
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开始不了一点 ​
∫12x111
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/index.html b/ja/index.html
index 227265d..254bc47 100644
--- a/ja/index.html
+++ b/ja/index.html
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     MBCP ドキュメント
     
     
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MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
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MBCP
More basic change particle
ジオメトリ演算とパーティクル作成のためのライブラリ
はじめる
API リファレンス
ベストプラクティス
MBCP logo
🛠️
高可用性
シンプルなインターフェースを通じて、ほとんどのジオメトリ演算とパーティクル作成のニーズを実現しました
📦
高集積度
numpy、scipy、およびsympyをラップして統合し、Geogebraを使用するように簡単にスクリプトを作成できます
🧊
組み込みプリセット
多くのプリセットを提供しており、一般的なジオメトリ図形やパーティクル効果など、迅速に作成できます
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
MBCP
More basic change particle
ジオメトリ演算とパーティクル作成のためのライブラリ
はじめる
API リファレンス
ベストプラクティス
MBCP logo
🛠️
高可用性
シンプルなインターフェースを通じて、ほとんどのジオメトリ演算とパーティクル作成のニーズを実現しました
📦
高集積度
numpy、scipy、およびsympyをラップして統合し、Geogebraを使用するように簡単にスクリプトを作成できます
🧊
組み込みプリセット
多くのプリセットを提供しており、一般的なジオメトリ図形やパーティクル効果など、迅速に作成できます
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
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diff --git a/ja/refer/index.html b/ja/refer/index.html
index ea798ef..9837c6d 100644
--- a/ja/refer/index.html
+++ b/ja/refer/index.html
@@ -6,10 +6,10 @@
     Reference | MBCP ドキュメント
     
     
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MBCP ドキュメント
日本語
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Reference ​
Help us to improve the documentation
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP ドキュメント
日本語
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English
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Reference ​
Help us to improve the documentation
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/refer/function/curry.html b/refer/function/curry.html
index 5f7a4fd..6c7c03c 100644
--- a/refer/function/curry.html
+++ b/refer/function/curry.html
@@ -6,10 +6,10 @@
     柯里化 | MBCP 文档
     
     
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MBCP 文档
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日本語
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简体中文
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-    
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MBCP 文档
简体中文
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简体中文
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文档由 VitePress 构建 | API引用由 litedoc 生成
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diff --git a/refer/function/function.html b/refer/function/function.html
index faf69a1..26c1a85 100644
--- a/refer/function/function.html
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     函数 | MBCP 文档
     
     
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MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
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文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP 文档
简体中文
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日本語
繁體中文
简体中文
English
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文档由 VitePress 构建 | API引用由 litedoc 生成
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diff --git a/refer/index.html b/refer/index.html
index 37d8d41..05db968 100644
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     参考 | MBCP 文档
     
     
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MBCP 文档
简体中文
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简体中文
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Reference ​
Help us to improve the documentation
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-    
+    
MBCP 文档
简体中文
English
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繁體中文
简体中文
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Reference ​
Help us to improve the documentation
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diff --git a/sitemap.xml b/sitemap.xml
index d4567e7..bb915ee 100644
--- a/sitemap.xml
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     mbcp | MBCP 文檔
     
     
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MBCP 文檔
繁體中文
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日本語
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简体中文
English
日本語
Appearance
mbcp ​
本模块是主模块，提供了一些工具 可导入
mbcp.mp_math：数学工具
mbcp.particle：粒子生成工具
mbcp.presets：预设
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
func __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP 文檔
繁體中文
简体中文
English
日本語
繁體中文
简体中文
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日本語
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mbcp.mp_math.angle ​
本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼 或 於GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
func complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼 或 於GitHub上查看
python
@property
+        self.radian = value * PI / 180
@property
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼 或 於GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
func supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼 或 於GitHub上查看
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼 或 於GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
func degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
func minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼 或 於GitHub上查看
python
@property
+    return self.radian * 180 / PI
@property
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼 或 於GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
func maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼 或 於GitHub上查看
python
@property
+    return AnyAngle(self.radian % (2 * PI))
@property
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼 或 於GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
func sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
func cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼 或 於GitHub上查看
python
@property
+    return math.sin(self.radian)
@property
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼 或 於GitHub上查看
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
func tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼 或 於GitHub上查看
python
@property
+    return math.cos(self.radian)
@property
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼 或 於GitHub上查看
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
func cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼 或 於GitHub上查看
python
@property
+    return math.tan(self.radian)
@property
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼 或 於GitHub上查看
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
func sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
func csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
func self + other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
func __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
func self - other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
func self * other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload
func self / other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
@overload
+    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
method self / other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
func self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
func self / other ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other):
+    ...
method self / other ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return AnyAngle(self.radian / other, is_radian=True)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • 默認值: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • 默認值: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • 默認值: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • 默認值: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • 默認值: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • 默認值: 0.001
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.mp_math.const ​
本模块定义了一些常用的常量
var PI ​
  • 説明: 常量 π
  • 默認值: math.pi
var E ​
  • 説明: 自然对数的底 exp(1)
  • 默認值: math.e
var GOLDEN_RATIO ​
  • 説明: 黄金分割比
  • 默認值: (1 + math.sqrt(5)) / 2
var GAMMA ​
  • 説明: 欧拉常数
  • 默認值: 0.5772156649015329
var EPSILON ​
  • 説明: 精度误差
  • 默認值: 0.0001
var APPROX ​
  • 説明: 约等于判定误差
  • 默認值: 0.001
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html
index 19e0c3b..350525e 100644
--- a/zht/api/mp_math/equation.html
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@@ -6,19 +6,19 @@
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mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
func __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
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mbcp.mp_math.equation ​
本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
func __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼 或 於GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼 或 於GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -82,8 +82,8 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        raise ValueError('Invalid var type')
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/function.html b/zht/api/mp_math/function.html
index fdf936e..dcb7787 100644
--- a/zht/api/mp_math/function.html
+++ b/zht/api/mp_math/function.html
@@ -6,19 +6,19 @@
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mbcp.mp_math.function ​
説明: AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
變數説明:
返回: 梯度
源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
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mbcp.mp_math.function ​
AAA
func cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
變數説明:
返回: 梯度
源碼 或 於GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -59,8 +59,8 @@
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return curried_func
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html
index 1255371..91a83e0 100644
--- a/zht/api/mp_math/index.html
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@@ -6,20 +6,20 @@
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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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MBCP 文檔
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简体中文
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繁體中文
简体中文
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mbcp.mp_math ​
本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html
index 0e45ecc..98318fd 100644
--- a/zht/api/mp_math/line.html
+++ b/zht/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP 文檔
     
     
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mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
func __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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mbcp.mp_math.line ​
本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point (Point3): 直线上的一点
  • direction (Vector3): 方向向量
源碼 或 於GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction ([`Vector3`](./vector#class-vector3)): 方向向量
         """
     self.point = point
-    self.direction = direction
func approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
func cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other (Line3): 另一条直线
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -43,7 +43,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return self.direction.cal_angle(other.direction)
func cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -65,7 +65,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
func cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other (Line3): 另一条直线
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other (Line3): 另一条直线
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -80,7 +80,7 @@
         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
func cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
返回: Line3: 垂线
源碼 或 於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
返回: Line3: 垂线
源碼 或 於GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -88,7 +88,7 @@
         Returns:
             [`Line3`](./line#class-line3): 垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
func get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
返回: Point3: 点
源碼 或 於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
返回: Point3: 点
源碼 或 於GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -96,13 +96,13 @@
         Returns:
             [`Point3`](./point#class-point3): 点
         """
-    return self.point + t * self.direction
func get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源碼 或 於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]: 参数方程
源碼 或 於GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             [`tuple`](https%3A//docs.python.org/3/library/stdtypes.html#tuple)[[`OneSingleVarFunc`](./mp_math_typing#var-onesinglevarfunc), `OneSingleVarFunc`, `OneSingleVarFunc`]: 参数方程
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
func is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other (Line3): 另一条直线
  • epsilon (float): 误差
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -111,7 +111,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
func is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -119,7 +119,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.direction.is_parallel(other.direction)
func is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
返回: bool: 是否共线
源碼 或 於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
返回: bool: 是否共线
源碼 或 於GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -127,7 +127,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
func is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
返回: bool: 是否在直线上
源碼 或 於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
返回: bool: 是否在直线上
源碼 或 於GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -135,7 +135,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
func is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
返回: bool: 是否共面
源碼 或 於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
返回: bool: 是否共面
源碼 或 於GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -144,7 +144,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
func simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼 或 於GitHub上查看
python
def simplify(self):
+    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼 或 於GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -157,7 +157,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
func from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
返回: Line3: 直线
源碼 或 於GitHub上查看
python
@classmethod
+        self.point.z = 0
@classmethod
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
返回: Line3: 直线
源碼 或 於GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -168,7 +168,7 @@
             [`Line3`](./line#class-line3): 直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
func __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other (Line3): 另一条直线
返回: Line3 | Point3 | None: 交集
源碼 或 於GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -181,7 +181,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
func __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
+        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other (Line3): 另一条直线
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -191,8 +191,8 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html
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--- a/zht/api/mp_math/mp_math_typing.html
+++ b/zht/api/mp_math/mp_math_typing.html
@@ -6,20 +6,20 @@
     mbcp.mp_math.mp_math_typing | MBCP 文檔
     
     
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mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • 類型: TypeAlias
  • 默認值: int | float
var Number ​
  • 説明: 数
  • 類型: TypeAlias
  • 默認值: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • 默認值: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • 類型: TypeAlias
  • 默認值: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • 類型: TypeAlias
  • 默認值: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • 類型: TypeAlias
  • 默認值: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • 類型: TypeAlias
  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • 類型: TypeAlias
  • 默認值: MultiSingleVarsFunc | MultiArraysFunc
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.mp_math.mp_math_typing ​
本模块用于内部类型提示
var RealNumber ​
  • 説明: 实数
  • 類型: TypeAlias
  • 默認值: int | float
var Number ​
  • 説明: 数
  • 類型: TypeAlias
  • 默認值: RealNumber | complex
var SingleVar ​
  • 説明: 单变量
  • 默認值: TypeVar('SingleVar', bound=Number)
var ArrayVar ​
  • 説明: 数组变量
  • 默認值: TypeVar('ArrayVar', bound=Iterable[Number])
var Var ​
  • 説明: 变量
  • 類型: TypeAlias
  • 默認值: SingleVar | ArrayVar
var OneSingleVarFunc ​
  • 説明: 一元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar], SingleVar]
var OneArrayFunc ​
  • 説明: 一元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar], ArrayVar]
var OneVarFunc ​
  • 説明: 一元函数
  • 類型: TypeAlias
  • 默認值: OneSingleVarFunc | OneArrayFunc
var TwoSingleVarsFunc ​
  • 説明: 二元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar], SingleVar]
var TwoArraysFunc ​
  • 説明: 二元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar], ArrayVar]
var TwoVarsFunc ​
  • 説明: 二元函数
  • 類型: TypeAlias
  • 默認值: TwoSingleVarsFunc | TwoArraysFunc
var ThreeSingleVarsFunc ​
  • 説明: 三元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[[SingleVar, SingleVar, SingleVar], SingleVar]
var ThreeArraysFunc ​
  • 説明: 三元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar]
var ThreeVarsFunc ​
  • 説明: 三元函数
  • 類型: TypeAlias
  • 默認值: ThreeSingleVarsFunc | ThreeArraysFunc
var MultiSingleVarsFunc ​
  • 説明: 多元单变量函数
  • 類型: TypeAlias
  • 默認值: Callable[..., SingleVar]
var MultiArraysFunc ​
  • 説明: 多元数组函数
  • 類型: TypeAlias
  • 默認值: Callable[..., ArrayVar]
var MultiVarsFunc ​
  • 説明: 多元函数
  • 類型: TypeAlias
  • 默認值: MultiSingleVarsFunc | MultiArraysFunc
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html
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--- a/zht/api/mp_math/plane.html
+++ b/zht/api/mp_math/plane.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.plane | MBCP 文檔
     
     
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mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
func __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
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mbcp.mp_math.plane ​
本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a (float): x系数
  • b (float): y系数
  • c (float): z系数
  • d (float): 常数项
源碼 或 於GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
func approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         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
func cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
返回: AnyAngle: 夹角
抛出:
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     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)}')
func cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
返回: float: 距离
抛出:
源碼 或 於GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     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)}')
func cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other (Plane3): 另一个平面
返回: Line3: 交线
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other (Plane3): 另一个平面
返回: Line3: 交线
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -104,7 +104,7 @@
         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)
func cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
返回: Point3: 交点
抛出:
源碼 或 於GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -118,7 +118,7 @@
         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))
func cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -126,7 +126,7 @@
         Returns:
             [`Plane3`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
func is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -134,14 +134,14 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
func normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: Vector3: 法向量
源碼 或 於GitHub上查看
python
@property
+    return self.normal.is_parallel(other.normal)
@property
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: Vector3: 法向量
源碼 或 於GitHub上查看
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             [`Vector3`](./vector#class-vector3): 法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod
func from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
變數説明:
返回: Plane3: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -153,7 +153,7 @@
         """
     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
func from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1 (Point3): 点1
  • p2 (Point3): 点2
  • p3 (Point3): 点3
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -167,7 +167,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
func from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1 (Line3): 直线
  • l2 (Line3): 直线
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -181,7 +181,7 @@
     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
func from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
返回: 平面
源碼 或 於GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -191,11 +191,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
func __and__(self, other: Line3) -> Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
method __and__(self, other: Line3) -> Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
func __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
返回: Line3 | Point3 | None: 交集
抛出:
源碼 或 於GitHub上查看
python
def __and__(self, other):
+    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
返回: Line3 | Point3 | None: 交集
抛出:
源碼 或 於GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -214,7 +214,7 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
func __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
説明: 判断两个平面是否等价。
變數説明:
  • other (Plane3): 另一个平面
返回: bool: 是否等价
源碼 或 於GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两个平面是否等价。
         Args:
@@ -222,9 +222,9 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
func __rand__(self, other: Line3) -> Point3 ​
源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html
index a0cf2ec..e40f559 100644
--- a/zht/api/mp_math/point.html
+++ b/zht/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP 文檔
     
     
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mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+    
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mbcp.mp_math.point ​
本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x (float): x 坐标
  • y (float): y 坐标
  • z (float): z 坐标
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
func self + other: Vector3 => Point3 ​
源碼 或 於GitHub上查看
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 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: P + V -> P P + P -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,7 +50,7 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
func __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
@@ -58,7 +58,7 @@
         Returns:
             [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
變數説明:
返回: Vector3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 Vector3 中实现
變數説明:
返回: Vector3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,8 +69,8 @@
             [`Vector3`](./vector#class-vector3): 新的向量
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
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diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html
index 353205a..0526f0a 100644
--- a/zht/api/mp_math/segment.html
+++ b/zht/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP 文檔
     
     
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mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
func __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
變數説明:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP 文檔
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mbcp.mp_math.segment ​
本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。
變數説明:
  • p1 (Point3): 线段的一个端点
  • p2 (Point3): 线段的另一个端点
源碼 或 於GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         Args:
@@ -32,8 +32,8 @@
     '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)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html
index 4c21b76..9b548b4 100644
--- a/zht/api/mp_math/utils.html
+++ b/zht/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP 文檔
     
     
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mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
變數説明:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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mbcp.mp_math.utils ​
本模块定义了一些常用的工具函数
func clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
變數説明:
  • x (float): 值
  • min_ (float): 最小值
  • max_ (float): 最大值
返回: float: 限定在区间内的值
源碼 或 於GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,13 +29,13 @@
     Returns:
         `float`: 限定在区间内的值
     """
-    return max(min(x, max_), min_)
class Approx ​
func __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, value: RealNumber):
+    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
説明: 用于近似比较对象
變數説明:
源碼 或 於GitHub上查看
python
def __init__(self, value: RealNumber):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
func __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    self.value = value
method __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -45,8 +45,8 @@
         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)
func raise_type_error(self, other) ​
源碼 或 於GitHub上查看
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
func __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
+            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼 或 於GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
     return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
@@ -86,8 +86,8 @@
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+        return ''
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html
index 087a15a..7454431 100644
--- a/zht/api/mp_math/vector.html
+++ b/zht/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP 文檔
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
MBCP 文檔
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
func __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP 文檔
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.vector ​
本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x (float): x轴分量
  • y (float): y轴分量
  • z (float): z轴分量
源碼 或 於GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
func approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
func cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
返回: AnyAngle: 夹角
源碼 或 於GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             [`AnyAngle`](./angle#class-anyangle): 夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
func cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
返回: Vector3: 叉乘结果
源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
返回: Vector3: 叉乘结果
源碼 或 於GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             [`Vector3`](#class-vector3): 叉乘结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
func is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
返回: bool: 是否近似平行
源碼 或 於GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否近似平行
         """
-    return self.cross(other).length < epsilon
func is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
返回: bool: 是否平行
源碼 或 於GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.cross(other).approx(zero_vector3)
func normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼 或 於GitHub上查看
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼 或 於GitHub上查看
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
func np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源碼 或 於GitHub上查看
python
@property
+    self.z /= length
@property
method np_array(self) -> np.ndarray ​
返回: np.ndarray: numpy数组
源碼 或 於GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
             [`np.ndarray`](https%3A//numpy.org/doc/stable/reference/generated/numpy.ndarray.html): numpy数组
         """
-    return np.array([self.x, self.y, self.z])
@property
func length(self) -> float ​
説明: 向量的模。
返回: float: 模
源碼 或 於GitHub上查看
python
@property
+    return np.array([self.x, self.y, self.z])
@property
method length(self) -> float ​
説明: 向量的模。
返回: float: 模
源碼 或 於GitHub上查看
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
func unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源碼 或 於GitHub上查看
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: Vector3: 单位向量
源碼 或 於GitHub上查看
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             [`Vector3`](#class-vector3): 单位向量
         """
-    return self / self.length
func __abs__(self) ​
源碼 或 於GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
func self + other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    return self / self.length
method __abs__(self) ​
源碼 或 於GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
method self + other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
func self + other ​
説明: V + P -> P
V + V -> V
變數説明:
返回: Vector3 | Point3: 新的向量或点
源碼 或 於GitHub上查看
python
def __add__(self, other):
+    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
返回: Vector3 | Point3: 新的向量或点
源碼 或 於GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -133,7 +133,7 @@
     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)}'")
func __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
返回: bool: 是否相等
源碼 或 於GitHub上查看
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -141,7 +141,7 @@
         Returns:
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
func self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -151,11 +151,11 @@
         Returns:
             [`Point3`](./point#class-point3): 新的点
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
func self - other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
method self - other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
func self - other ​
説明: V - P -> P
V - V -> V
變數説明:
返回: Vector3 | Point3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other):
+    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
返回: Vector3 | Point3: 新的向量
源碼 或 於GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -170,7 +170,7 @@
     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)}"')
func self - other: Point3 ​
説明: P - V -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
返回: Point3: 新的点
源碼 或 於GitHub上查看
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -181,11 +181,11 @@
     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
func self * other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
method self * other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
func self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
method self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
func self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
返回: Vector3: 数组运算结果
源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
返回: Vector3: 数组运算结果
源碼 或 於GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -198,8 +198,8 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
func self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
func self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
返回: float: 点乘结果
源碼 或 於GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
返回: float: 点乘结果
源碼 或 於GitHub上查看
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
@@ -207,15 +207,15 @@
         Returns:
             [`float`](https%3A//docs.python.org/3/library/functions.html#float): 点乘结果
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
func self / other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
func - self => Vector3 ​
説明: 取负。
返回: Vector3: 负向量
源碼 或 於GitHub上查看
python
def __neg__(self) -> 'Vector3':
+    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
method - self => Vector3 ​
説明: 取负。
返回: Vector3: 负向量
源碼 或 於GitHub上查看
python
def __neg__(self) -> 'Vector3':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 1)
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 1)
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diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html
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     mbcp.presets.model | MBCP 文檔
     
     
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
+    
MBCP 文檔
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繁體中文
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mbcp.presets.model ​
几何模型点集
class GeometricModels ​
@staticmethod
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,8 +35,8 @@
     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)]
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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English
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
func sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼 或 於GitHub上查看
python
@staticmethod
-def sphere(radius: float, density: float):
-    """
-        生成球体上的点集。
-        Args:
-            radius:
-            density:
-        Returns:
-            List[Point3]: 球体上的点集。
-        """
-    area = 4 * np.pi * radius ** 2
-    num = int(area * density)
-    phi_list = np.arccos([clamp(-1 + (2.0 * _ - 1.0) / num, -1, 1) for _ in range(num)])
-    theta_list = np.sqrt(num * np.pi) * phi_list
-    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)]
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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Appearance
开始不了一点 ​
∫12x111
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开始不了一点 ​
∫12x111
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MBCP 文檔
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简体中文
English
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MBCP
更多基礎變化粒子
用於幾何運算和 當個創世神 粒子製作的軟體庫
跟隨引導
API文檔
最佳實踐
MBCP logo
🛠️
高度易用
通過簡單的接口，實現了大部分幾何運算及粒子製作的需求
📦
高度集成
對numpy、scipy及sympy進行了封裝和集成，使腳本編寫像使用Geogebra一樣easy
🧊
內置預設
提供了大量的預設，包括常見的幾何圖形、粒子效果等，便於快速生產
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP 文檔
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
MBCP
更多基礎變化粒子
用於幾何運算和 當個創世神 粒子製作的軟體庫
跟隨引導
API文檔
最佳實踐
MBCP logo
🛠️
高度易用
通過簡單的接口，實現了大部分幾何運算及粒子製作的需求
📦
高度集成
對numpy、scipy及sympy進行了封裝和集成，使腳本編寫像使用Geogebra一樣easy
🧊
內置預設
提供了大量的預設，包括常見的幾何圖形、粒子效果等，便於快速生產
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/refer/index.html b/zht/refer/index.html
index 14963a0..0d3395b 100644
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MBCP 文檔
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Appearance
Reference ​
Help us to improve the documentation
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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MBCP 文檔
繁體中文
简体中文
English
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繁體中文
简体中文
English
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Appearance
Reference ​
Help us to improve the documentation
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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