diff --git a/404.html b/404.html index 31e5a86..7bd7310 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 index 390d087..5b2941e 100644 --- a/api/api.html +++ b/api/api.html @@ -6,10 +6,10 @@ mbcp | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
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 8eabb27..f4b318e 100644 --- a/api/index.html +++ b/api/index.html @@ -6,10 +6,10 @@ mbcp | MBCP 文档 - + - - + + @@ -19,7 +19,7 @@
MBCP 文档

简体中文

English
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简体中文

English
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繁體中文

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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/mp_math/angle.html b/api/mp_math/angle.html index 8b7be2b..c09d3ef 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) ​

def __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 ​
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):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def 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
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
 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
def 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
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
 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
def 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
func 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
def 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
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
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def 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
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
 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
def 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
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
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def 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
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
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def 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
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
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def 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
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
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def 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
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
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def 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
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
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def 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)
def __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
def 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)
def 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
def self / other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
@overload
+    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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other):
+    ...
func 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)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/const.html b/api/mp_math/const.html
index a3ba843..1af0d3e 100644
--- a/api/mp_math/const.html
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     mbcp.mp_math.const | MBCP 文档
     
     
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@@ -19,7 +19,7 @@
   
   
     
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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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diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html
index 128eedf..0304557 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 ​
def __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 ​
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):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
参数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码 或 在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
参数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码 或 在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         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

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diff --git a/api/mp_math/function.html b/api/mp_math/function.html
index f11399d..29a614b 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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+    
     
     
     
     
   
   
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mbcp.mp_math.function ​
说明: AAA
def 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 ​
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:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -34,7 +34,7 @@
     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)
def 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 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:
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
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 | MBCP 文档
     
     
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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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diff --git a/api/mp_math/line.html b/api/mp_math/line.html
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     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 ​
def __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 ​
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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
@@ -192,7 +192,7 @@
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/mp_math.html b/api/mp_math/mp_math.html
index 10177bc..25041fc 100644
--- a/api/mp_math/mp_math.html
+++ b/api/mp_math/mp_math.html
@@ -6,10 +6,10 @@
     mbcp.mp_math | 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
English
日本語
繁體中文
Appearance
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 a655e7c..8bea05d 100644
--- a/api/mp_math/mp_math_typing.html
+++ b/api/mp_math/mp_math_typing.html
@@ -6,10 +6,10 @@
     mbcp.mp_math.mp_math_typing | MBCP 文档
     
     
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@@ -19,7 +19,7 @@
   
   
     
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
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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
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html
index a5d7baf..91844cd 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 ​
def __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 ​
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):
     """
         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
def 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
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:
     """
         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
def 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
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':
     """
         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)}')
def 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)}')
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:
     """
         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)}')
def 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)}')
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':
     """
         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)
def 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)
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':
     """
         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))
def 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))
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def __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
func __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
def __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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:
     """
         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)
def __rand__(self, other: Line3) -> Point3 ​
源代码 或 在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.approx(other)
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

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diff --git a/api/mp_math/point.html b/api/mp_math/point.html
index 6f0ce09..183ae2d 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 ​
def __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):
+    
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):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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
def 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
func self + other: Vector3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         P - P -> V
 
@@ -70,7 +70,7 @@
         """
     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

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diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html
index bdef62d..3e45fed 100644
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+++ 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 ​
def __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 ​
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'):
     """
         三维空间中的线段。
         Args:
@@ -33,7 +33,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html
index 5da3fc6..e21a2f0 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
def 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 ​
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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    self.value = value
func __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
@@ -45,9 +45,9 @@
         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)
def 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)}')
def __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
-    return not self.__eq__(other)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -57,7 +57,7 @@
     Returns:
         [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -70,7 +70,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -87,7 +87,7 @@
         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

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diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html
index d33a5a4..cd122ec 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 ​
def __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 ​
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):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def 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
func 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
def 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
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
 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
def 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
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
 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
def __abs__(self) ​
源代码 或 在GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func self - other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func self * other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         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

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\ No newline at end of file
diff --git a/api/particle/index.html b/api/particle/index.html
index 5ef47ad..74a2f6b 100644
--- a/api/particle/index.html
+++ b/api/particle/index.html
@@ -6,10 +6,10 @@
     mbcp.particle | MBCP 文档
     
     
-    
+    
     
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-    
+    
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@@ -19,7 +19,7 @@
   
   
     
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diff --git a/api/particle/particle.html b/api/particle/particle.html
index a348987..392c032 100644
--- a/api/particle/particle.html
+++ b/api/particle/particle.html
@@ -6,10 +6,10 @@
     mbcp.particle | MBCP 文档
     
     
-    
+    
     
-    
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+    
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diff --git a/api/presets/index.html b/api/presets/index.html
index 10ab9da..d46bb5f 100644
--- a/api/presets/index.html
+++ b/api/presets/index.html
@@ -6,10 +6,10 @@
     mbcp.presets | MBCP 文档
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
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diff --git a/api/presets/model/index.html b/api/presets/model/index.html
index bb6be2e..6e2215a 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
def 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
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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
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diff --git a/api/presets/model/model.html b/api/presets/model/model.html
index 99f5c6e..eb31c87 100644
--- a/api/presets/model/model.html
+++ b/api/presets/model/model.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
def 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
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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
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diff --git a/api/presets/presets.html b/api/presets/presets.html
index 5739169..7c104da 100644
--- a/api/presets/presets.html
+++ b/api/presets/presets.html
@@ -6,10 +6,10 @@
     mbcp.presets | MBCP 文档
     
     
-    
+    
     
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+    
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@@ -19,7 +19,7 @@
   
   
     
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diff --git a/assets/api_mp_math_angle.md.3Na5IaYp.js b/assets/api_mp_math_angle.md.D0ius2dn.js
similarity index 61%
rename from assets/api_mp_math_angle.md.3Na5IaYp.js
rename to assets/api_mp_math_angle.md.D0ius2dn.js
index e2e4fa5..66a9b69 100644
--- a/assets/api_mp_math_angle.md.3Na5IaYp.js
+++ b/assets/api_mp_math_angle.md.D0ius2dn.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) ​
def __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):
+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:
  • 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
def 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
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
 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
def 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
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
 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
def 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
func 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
def 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
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
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def 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
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
 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
def 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
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
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def 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
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
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def 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
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
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def 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
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
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def 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
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
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def 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
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
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def 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)
def __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
def 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)
def 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
def self / other: float => AnyAngle ​
源代码 或 在GitHub上查看
python
@overload
+    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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self / other: AnyAngle => float ​
源代码 或 在GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
源代码 或 在GitHub上查看
python
def __truediv__(self, other):
+    ...
func 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,d,o,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c 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 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.3Na5IaYp.lean.js b/assets/api_mp_math_angle.md.D0ius2dn.lean.js
similarity index 86%
rename from assets/api_mp_math_angle.md.3Na5IaYp.lean.js
rename to assets/api_mp_math_angle.md.D0ius2dn.lean.js
index a2c29e4..5db2722 100644
--- a/assets/api_mp_math_angle.md.3Na5IaYp.lean.js
+++ b/assets/api_mp_math_angle.md.D0ius2dn.lean.js
@@ -1 +1 @@
-import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,d,o,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
+import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/angle.md","filePath":"zh/api/mp_math/angle.md"}'),t={name:"api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/api_mp_math_equation.md.z85zyCZL.js b/assets/api_mp_math_equation.md.D9gepkm-.js
similarity index 71%
rename from assets/api_mp_math_equation.md.z85zyCZL.js
rename to assets/api_mp_math_equation.md.D9gepkm-.js
index 84f5944..c81ecfd 100644
--- a/assets/api_mp_math_equation.md.z85zyCZL.js
+++ b/assets/api_mp_math_equation.md.D9gepkm-.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 ​
def __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 ​
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):
     """
         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
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
参数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码 或 在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
参数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码 或 在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -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,d,g){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(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};
diff --git a/assets/api_mp_math_equation.md.z85zyCZL.lean.js b/assets/api_mp_math_equation.md.D9gepkm-.lean.js
similarity index 86%
rename from assets/api_mp_math_equation.md.z85zyCZL.lean.js
rename to assets/api_mp_math_equation.md.D9gepkm-.lean.js
index 9c85f74..6be3a53 100644
--- a/assets/api_mp_math_equation.md.z85zyCZL.lean.js
+++ b/assets/api_mp_math_equation.md.D9gepkm-.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,g){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(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};
diff --git a/assets/api_mp_math_function.md.BhmJqpOo.js b/assets/api_mp_math_function.md.BhmJqpOo.js
deleted file mode 100644
index 48c44bc..0000000
--- a/assets/api_mp_math_function.md.BhmJqpOo.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
def 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),y=[c],u=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)
def 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,y)),u]),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.js b/assets/api_mp_math_function.md.DCuJC29A.js
new file mode 100644
index 0000000..f45ba9b
--- /dev/null
+++ b/assets/api_mp_math_function.md.DCuJC29A.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 ​
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_function.md.BhmJqpOo.lean.js b/assets/api_mp_math_function.md.DCuJC29A.lean.js
similarity index 95%
rename from assets/api_mp_math_function.md.BhmJqpOo.lean.js
rename to assets/api_mp_math_function.md.DCuJC29A.lean.js
index 17003ac..48b5568 100644
--- a/assets/api_mp_math_function.md.BhmJqpOo.lean.js
+++ b/assets/api_mp_math_function.md.DCuJC29A.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),e={name:"api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),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};
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),e={name:"api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/api_mp_math_line.md.Dovi6bdM.js b/assets/api_mp_math_line.md.ByGRRi0A.js
similarity index 60%
rename from assets/api_mp_math_line.md.Dovi6bdM.js
rename to assets/api_mp_math_line.md.ByGRRi0A.js
index 369c7ed..f408df4 100644
--- a/assets/api_mp_math_line.md.Dovi6bdM.js
+++ b/assets/api_mp_math_line.md.ByGRRi0A.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 ​
def __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":"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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
diff --git a/assets/api_mp_math_line.md.Dovi6bdM.lean.js b/assets/api_mp_math_line.md.ByGRRi0A.lean.js
similarity index 100%
rename from assets/api_mp_math_line.md.Dovi6bdM.lean.js
rename to assets/api_mp_math_line.md.ByGRRi0A.lean.js
diff --git a/assets/api_mp_math_plane.md.Dv-GWbJg.js b/assets/api_mp_math_plane.md.Ir4HtSn5.js
similarity index 72%
rename from assets/api_mp_math_plane.md.Dv-GWbJg.js
rename to assets/api_mp_math_plane.md.Ir4HtSn5.js
index 1cc8c7a..33c0d60 100644
--- a/assets/api_mp_math_plane.md.Dv-GWbJg.js
+++ b/assets/api_mp_math_plane.md.Ir4HtSn5.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.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 ​
def __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 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):
     """
         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 y
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def 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
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:
     """
         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 y
         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
def 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
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':
     """
         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 y
     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)}')
def 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)}')
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:
     """
         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 y
     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)}')
def 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)}')
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':
     """
         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 y
         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)
def 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)
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':
     """
         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 y
         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))
def 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))
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':
     """
         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 y
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def 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)
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def 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
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
 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
def 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
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
 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 y
         """
     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
def 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
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
 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 y
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def 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
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
 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 y
     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
def 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
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
 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 y
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __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
func __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
def __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源代码 或 在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __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):
+    ...
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):
     """
         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 y
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __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)}'")
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
def __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};
+    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};
diff --git a/assets/api_mp_math_plane.md.Dv-GWbJg.lean.js b/assets/api_mp_math_plane.md.Ir4HtSn5.lean.js
similarity index 69%
rename from assets/api_mp_math_plane.md.Dv-GWbJg.lean.js
rename to assets/api_mp_math_plane.md.Ir4HtSn5.lean.js
index 217bc99..aff7000 100644
--- a/assets/api_mp_math_plane.md.Dv-GWbJg.lean.js
+++ b/assets/api_mp_math_plane.md.Ir4HtSn5.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.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};
+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};
diff --git a/assets/api_mp_math_point.md.BvvrKTY8.js b/assets/api_mp_math_point.md.CIRBY4Zg.js
similarity index 57%
rename from assets/api_mp_math_point.md.BvvrKTY8.js
rename to assets/api_mp_math_point.md.CIRBY4Zg.js
index e469f51..c9710a1 100644
--- a/assets/api_mp_math_point.md.BvvrKTY8.js
+++ b/assets/api_mp_math_point.md.CIRBY4Zg.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 ​
def __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":"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):
     """
         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
def 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
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:
     """
         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
def 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
func self + other: Vector3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         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 e(p,k,o,r,d,g){return a(),i("div",null,h)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/api_mp_math_point.md.BvvrKTY8.lean.js b/assets/api_mp_math_point.md.CIRBY4Zg.lean.js
similarity index 72%
rename from assets/api_mp_math_point.md.BvvrKTY8.lean.js
rename to assets/api_mp_math_point.md.CIRBY4Zg.lean.js
index 2a6ff66..47771f4 100644
--- a/assets/api_mp_math_point.md.BvvrKTY8.lean.js
+++ b/assets/api_mp_math_point.md.CIRBY4Zg.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 e(p,k,o,r,d,g){return a(),i("div",null,h)}const y=s(n,[["render",e]]);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"},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};
diff --git a/assets/api_mp_math_segment.md._n__ViVt.js b/assets/api_mp_math_segment.md.DFwFkY98.js
similarity index 78%
rename from assets/api_mp_math_segment.md._n__ViVt.js
rename to assets/api_mp_math_segment.md.DFwFkY98.js
index a4b157f..d3a0a79 100644
--- a/assets/api_mp_math_segment.md._n__ViVt.js
+++ b/assets/api_mp_math_segment.md.DFwFkY98.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 ​
def __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 ​
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'):
     """
         三维空间中的线段。
         Args:
diff --git a/assets/api_mp_math_segment.md._n__ViVt.lean.js b/assets/api_mp_math_segment.md.DFwFkY98.lean.js
similarity index 100%
rename from assets/api_mp_math_segment.md._n__ViVt.lean.js
rename to assets/api_mp_math_segment.md.DFwFkY98.lean.js
diff --git a/assets/api_mp_math_utils.md.kW3A-lG9.js b/assets/api_mp_math_utils.md.CFXHDZgH.js
similarity index 58%
rename from assets/api_mp_math_utils.md.kW3A-lG9.js
rename to assets/api_mp_math_utils.md.CFXHDZgH.js
index fb79da9..5904472 100644
--- a/assets/api_mp_math_utils.md.kW3A-lG9.js
+++ b/assets/api_mp_math_utils.md.CFXHDZgH.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
def 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 ​
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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
源代码 或 在GitHub上查看
python
def __eq__(self, other):
+    self.value = value
func __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
@@ -25,9 +25,9 @@ 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)
def 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)}')
def __ne__(self, other) ​
源代码 或 在GitHub上查看
python
def __ne__(self, other):
-    return not self.__eq__(other)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源代码 或 在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -37,7 +37,7 @@ import{_ as s,c as i,o as a,a4 as t}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 abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -50,7 +50,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源代码 或 在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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 e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[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};
diff --git a/assets/api_mp_math_utils.md.kW3A-lG9.lean.js b/assets/api_mp_math_utils.md.CFXHDZgH.lean.js
similarity index 72%
rename from assets/api_mp_math_utils.md.kW3A-lG9.lean.js
rename to assets/api_mp_math_utils.md.CFXHDZgH.lean.js
index db5f944..38c2963 100644
--- a/assets/api_mp_math_utils.md.kW3A-lG9.lean.js
+++ b/assets/api_mp_math_utils.md.CFXHDZgH.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 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};
+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};
diff --git a/assets/api_mp_math_vector.md.mCFa4Azm.js b/assets/api_mp_math_vector.md.CuQ0WDoP.js
similarity index 65%
rename from assets/api_mp_math_vector.md.mCFa4Azm.js
rename to assets/api_mp_math_vector.md.CuQ0WDoP.js
index f126a2a..4a40469 100644
--- a/assets/api_mp_math_vector.md.mCFa4Azm.js
+++ b/assets/api_mp_math_vector.md.CuQ0WDoP.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"},e=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 ​
def __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"},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):
     """
         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
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         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
def 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
func 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
def 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
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
 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
def 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
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
 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
def __abs__(self) ​
源代码 或 在GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func self - other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self - other: Point3 => Point3 ​
源代码 或 在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func self * other: Vector3 => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
+    ...
@overload
func self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def self * other: RealNumber => Vector3 ​
源代码 或 在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         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),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/api_mp_math_vector.md.mCFa4Azm.lean.js b/assets/api_mp_math_vector.md.CuQ0WDoP.lean.js
similarity index 72%
rename from assets/api_mp_math_vector.md.mCFa4Azm.lean.js
rename to assets/api_mp_math_vector.md.CuQ0WDoP.lean.js
index d0f648e..bc7bcb5 100644
--- a/assets/api_mp_math_vector.md.mCFa4Azm.lean.js
+++ b/assets/api_mp_math_vector.md.CuQ0WDoP.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"},e=t("",138),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+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};
diff --git a/assets/api_presets_model_index.md.F2zeh9P2.js b/assets/api_presets_model_index.md.BcL7qpu8.js
similarity index 87%
rename from assets/api_presets_model_index.md.F2zeh9P2.js
rename to assets/api_presets_model_index.md.BcL7qpu8.js
index 813bb0b..5fc2697 100644
--- a/assets/api_presets_model_index.md.F2zeh9P2.js
+++ b/assets/api_presets_model_index.md.BcL7qpu8.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
def 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 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
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
diff --git a/assets/api_presets_model_index.md.F2zeh9P2.lean.js b/assets/api_presets_model_index.md.BcL7qpu8.lean.js
similarity index 100%
rename from assets/api_presets_model_index.md.F2zeh9P2.lean.js
rename to assets/api_presets_model_index.md.BcL7qpu8.lean.js
diff --git a/assets/api_presets_model_model.md.BoocA59j.js b/assets/api_presets_model_model.md.Ch05JNzT.js
similarity index 85%
rename from assets/api_presets_model_model.md.BoocA59j.js
rename to assets/api_presets_model_model.md.Ch05JNzT.js
index df608b8..0fb7911 100644
--- a/assets/api_presets_model_model.md.BoocA59j.js
+++ b/assets/api_presets_model_model.md.Ch05JNzT.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":"api/presets/model/model.md","filePath":"zh/api/presets/model/model.md"}'),n={name:"api/presets/model/model.md"},h=t(`
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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 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。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(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};
+    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.BoocA59j.lean.js b/assets/api_presets_model_model.md.Ch05JNzT.lean.js
similarity index 61%
rename from assets/api_presets_model_model.md.BoocA59j.lean.js
rename to assets/api_presets_model_model.md.Ch05JNzT.lean.js
index 11e6d76..9be95df 100644
--- a/assets/api_presets_model_model.md.BoocA59j.lean.js
+++ b/assets/api_presets_model_model.md.Ch05JNzT.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/model.md","filePath":"zh/api/presets/model/model.md"}'),n={name:"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 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/app.Dikvw3nD.js b/assets/app.CaA7Rfbk.js
similarity index 95%
rename from assets/app.Dikvw3nD.js
rename to assets/app.CaA7Rfbk.js
index 1e44e57..023a2c1 100644
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diff --git a/assets/chunks/theme.BIB25x10.js b/assets/chunks/theme.BhGtk3iD.js
similarity index 99%
rename from assets/chunks/theme.BIB25x10.js
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index a05a87e..fd17615 100644
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+++ b/assets/chunks/theme.BhGtk3iD.js
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diff --git a/assets/ja_api_mp_math_angle.md.CAq1hHov.js b/assets/en_api_mp_math_angle.md.DTo0bIGQ.js
similarity index 59%
rename from assets/ja_api_mp_math_angle.md.CAq1hHov.js
rename to assets/en_api_mp_math_angle.md.DTo0bIGQ.js
index a595c1c..195131e 100644
--- a/assets/ja_api_mp_math_angle.md.CAq1hHov.js
+++ b/assets/en_api_mp_math_angle.md.DTo0bIGQ.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) ​
def __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 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):
     """
         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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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)
def 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)
def __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)
def 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)
def 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
def 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)
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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
ソースコード または GitHubで表示
python
def __truediv__(self, other):
+    ...
func 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,d,o,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c 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{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.09R7pxw_.lean.js b/assets/en_api_mp_math_angle.md.DTo0bIGQ.lean.js
similarity index 72%
rename from assets/en_api_mp_math_angle.md.09R7pxw_.lean.js
rename to assets/en_api_mp_math_angle.md.DTo0bIGQ.lean.js
index 8f233a1..150c5ed 100644
--- a/assets/en_api_mp_math_angle.md.09R7pxw_.lean.js
+++ b/assets/en_api_mp_math_angle.md.DTo0bIGQ.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.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};
+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};
diff --git a/assets/zht_api_mp_math_equation.md.CNqNdo8e.js b/assets/en_api_mp_math_equation.md.NTcIjf_k.js
similarity index 68%
rename from assets/zht_api_mp_math_equation.md.CNqNdo8e.js
rename to assets/en_api_mp_math_equation.md.NTcIjf_k.js
index 1c6b67f..d8a1c2d 100644
--- a/assets/zht_api_mp_math_equation.md.CNqNdo8e.js
+++ b/assets/en_api_mp_math_equation.md.NTcIjf_k.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 ​
def __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":"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):
     """
         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
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
變數説明:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼 或 於GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
Arguments:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code or View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -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,d,g){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,c,d){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.DBXwIC0s.lean.js b/assets/en_api_mp_math_equation.md.NTcIjf_k.lean.js
similarity index 86%
rename from assets/en_api_mp_math_equation.md.DBXwIC0s.lean.js
rename to assets/en_api_mp_math_equation.md.NTcIjf_k.lean.js
index ec4bd2d..4358d3e 100644
--- a/assets/en_api_mp_math_equation.md.DBXwIC0s.lean.js
+++ b/assets/en_api_mp_math_equation.md.NTcIjf_k.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,c){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default};
+import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),t={name:"en/api/mp_math/equation.md"},l=n("",23),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};
diff --git a/assets/en_api_mp_math_function.md.BXNFIE6F.js b/assets/en_api_mp_math_function.md.BXNFIE6F.js
new file mode 100644
index 0000000..052be13
--- /dev/null
+++ b/assets/en_api_mp_math_function.md.BXNFIE6F.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 ​
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.nJ-E5W5r.lean.js b/assets/en_api_mp_math_function.md.BXNFIE6F.lean.js
similarity index 97%
rename from assets/en_api_mp_math_function.md.nJ-E5W5r.lean.js
rename to assets/en_api_mp_math_function.md.BXNFIE6F.lean.js
index 8b48bb7..d2c213a 100644
--- a/assets/en_api_mp_math_function.md.nJ-E5W5r.lean.js
+++ b/assets/en_api_mp_math_function.md.BXNFIE6F.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),e={name:"en/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 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),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),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};
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const V=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),e={name:"en/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const Z=l(e,[["render",x]]);export{V as __pageData,Z as default};
diff --git a/assets/en_api_mp_math_function.md.nJ-E5W5r.js b/assets/en_api_mp_math_function.md.nJ-E5W5r.js
deleted file mode 100644
index 034c018..0000000
--- a/assets/en_api_mp_math_function.md.nJ-E5W5r.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
def 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),y=[c],u=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)
def 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,y)),u]),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/ja_api_mp_math_line.md.BzytbSsM.js b/assets/en_api_mp_math_line.md.CxP-i4OT.js
similarity index 58%
rename from assets/ja_api_mp_math_line.md.BzytbSsM.js
rename to assets/en_api_mp_math_line.md.CxP-i4OT.js
index fc38906..aa92d9f 100644
--- a/assets/ja_api_mp_math_line.md.BzytbSsM.js
+++ b/assets/en_api_mp_math_line.md.CxP-i4OT.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 ​
def __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":"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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         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 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};
diff --git a/assets/en_api_mp_math_line.md.D0AfsxWD.lean.js b/assets/en_api_mp_math_line.md.CxP-i4OT.lean.js
similarity index 86%
rename from assets/en_api_mp_math_line.md.D0AfsxWD.lean.js
rename to assets/en_api_mp_math_line.md.CxP-i4OT.lean.js
index 0eaf12d..8a7176f 100644
--- a/assets/en_api_mp_math_line.md.D0AfsxWD.lean.js
+++ b/assets/en_api_mp_math_line.md.CxP-i4OT.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,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":"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};
diff --git a/assets/zht_api_mp_math_plane.md.Cbo0QRQD.js b/assets/en_api_mp_math_plane.md.BsgpTZdY.js
similarity index 70%
rename from assets/zht_api_mp_math_plane.md.Cbo0QRQD.js
rename to assets/en_api_mp_math_plane.md.BsgpTZdY.js
index 40b0940..666725f 100644
--- a/assets/zht_api_mp_math_plane.md.Cbo0QRQD.js
+++ b/assets/en_api_mp_math_plane.md.BsgpTZdY.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.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 ​
def __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 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):
     """
         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 y
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def 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
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:
     """
         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 y
         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
def 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
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':
     """
         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 y
     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)}')
def 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)}')
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:
     """
         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 y
     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)}')
def 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)}')
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':
     """
         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 y
         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)
def 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)
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':
     """
         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 y
         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))
def 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))
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':
     """
         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 y
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def 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)
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def 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
func 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
def 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
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
 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 y
         """
     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
def 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
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
 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 y
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def 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
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
 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 y
     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
def 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
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
 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 y
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __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
func __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __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):
+    ...
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):
     """
         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 y
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __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)}'")
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
def __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};
+    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};
diff --git a/assets/en_api_mp_math_plane.md.3xsZdWoR.lean.js b/assets/en_api_mp_math_plane.md.BsgpTZdY.lean.js
similarity index 54%
rename from assets/en_api_mp_math_plane.md.3xsZdWoR.lean.js
rename to assets/en_api_mp_math_plane.md.BsgpTZdY.lean.js
index 96be146..d91e863 100644
--- a/assets/en_api_mp_math_plane.md.3xsZdWoR.lean.js
+++ b/assets/en_api_mp_math_plane.md.BsgpTZdY.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.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/plane.md","filePath":"en/api/mp_math/plane.md"}'),l={name:"en/api/mp_math/plane.md"},t=n("",113),h=[t];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{y as __pageData,c as default};
+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/zht_api_mp_math_point.md.Ci0RyJlm.js b/assets/en_api_mp_math_point.md.DcGqVqiO.js
similarity index 56%
rename from assets/zht_api_mp_math_point.md.Ci0RyJlm.js
rename to assets/en_api_mp_math_point.md.DcGqVqiO.js
index 6df7f7c..e6a82a0 100644
--- a/assets/zht_api_mp_math_point.md.Ci0RyJlm.js
+++ b/assets/en_api_mp_math_point.md.DcGqVqiO.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 ​
def __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":"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):
     """
         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
def 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
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:
     """
         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
def 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
func self + other: Vector3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         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 e(p,k,o,r,d,g){return a(),i("div",null,h)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/en_api_mp_math_point.md.CxCgy181.lean.js b/assets/en_api_mp_math_point.md.DcGqVqiO.lean.js
similarity index 72%
rename from assets/en_api_mp_math_point.md.CxCgy181.lean.js
rename to assets/en_api_mp_math_point.md.DcGqVqiO.lean.js
index 8047eb5..1533944 100644
--- a/assets/en_api_mp_math_point.md.CxCgy181.lean.js
+++ b/assets/en_api_mp_math_point.md.DcGqVqiO.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),n={name:"en/api/mp_math/point.md"},e=t("",39),l=[e];function h(p,o,k,r,d,c){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const E=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","lastUpdated":false},"headers":[],"relativePath":"en/api/mp_math/point.md","filePath":"en/api/mp_math/point.md"}'),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};
diff --git a/assets/zht_api_mp_math_segment.md.D_xbGo8n.js b/assets/en_api_mp_math_segment.md.Cge1J0TK.js
similarity index 66%
rename from assets/zht_api_mp_math_segment.md.D_xbGo8n.js
rename to assets/en_api_mp_math_segment.md.Cge1J0TK.js
index fac510b..f6dc84f 100644
--- a/assets/zht_api_mp_math_segment.md.D_xbGo8n.js
+++ b/assets/en_api_mp_math_segment.md.Cge1J0TK.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 ​
def __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 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'):
     """
         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,o,E){return a(),i("div",null,h)}const F=s(t,[["render",l]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_segment.md.BevquOvV.lean.js b/assets/en_api_mp_math_segment.md.Cge1J0TK.lean.js
similarity index 53%
rename from assets/en_api_mp_math_segment.md.BevquOvV.lean.js
rename to assets/en_api_mp_math_segment.md.Cge1J0TK.lean.js
index f54225f..8e9289f 100644
--- a/assets/en_api_mp_math_segment.md.BevquOvV.lean.js
+++ b/assets/en_api_mp_math_segment.md.Cge1J0TK.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":"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};
+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};
diff --git a/assets/zht_api_mp_math_utils.md.BsNVdUjt.js b/assets/en_api_mp_math_utils.md.Bu0IGkds.js
similarity index 57%
rename from assets/zht_api_mp_math_utils.md.BsNVdUjt.js
rename to assets/en_api_mp_math_utils.md.Bu0IGkds.js
index c5f9ed3..dffb3c5 100644
--- a/assets/zht_api_mp_math_utils.md.BsNVdUjt.js
+++ b/assets/en_api_mp_math_utils.md.Bu0IGkds.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
def 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 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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    self.value = value
func __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
@@ -25,9 +25,9 @@ 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)
def 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)}')
def __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
-    return not self.__eq__(other)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -37,7 +37,7 @@ import{_ as s,c as i,o as a,a4 as t}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 abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -50,7 +50,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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 e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[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.lean.js b/assets/en_api_mp_math_utils.md.Bu0IGkds.lean.js
new file mode 100644
index 0000000..80d9fc9
--- /dev/null
+++ b/assets/en_api_mp_math_utils.md.Bu0IGkds.lean.js
@@ -0,0 +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.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.rVP-A71G.lean.js b/assets/en_api_mp_math_utils.md.rVP-A71G.lean.js
deleted file mode 100644
index c3c1302..0000000
--- a/assets/en_api_mp_math_utils.md.rVP-A71G.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","lastUpdated":false},"headers":[],"relativePath":"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 E=s(n,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/en_api_mp_math_vector.md.BEIFYOwe.js b/assets/en_api_mp_math_vector.md.DpvjNLj_.js
similarity index 66%
rename from assets/en_api_mp_math_vector.md.BEIFYOwe.js
rename to assets/en_api_mp_math_vector.md.DpvjNLj_.js
index cef3097..89b3469 100644
--- a/assets/en_api_mp_math_vector.md.BEIFYOwe.js
+++ b/assets/en_api_mp_math_vector.md.DpvjNLj_.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 ​
def __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 ​
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):
     """
         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
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         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
def np_array(self) -> np.ndarray ​
Return: np.ndarray: numpy数组
Source code or View on GitHub
python
@property
+    self.z /= length
@property
func 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
def 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
func 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
def 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
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
 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
def __abs__(self) ​
Source code or View on GitHub
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func self - other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func self * other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         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,g){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),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};
diff --git a/assets/en_api_mp_math_vector.md.BEIFYOwe.lean.js b/assets/en_api_mp_math_vector.md.DpvjNLj_.lean.js
similarity index 86%
rename from assets/en_api_mp_math_vector.md.BEIFYOwe.lean.js
rename to assets/en_api_mp_math_vector.md.DpvjNLj_.lean.js
index 0a3a5a2..12b0de0 100644
--- a/assets/en_api_mp_math_vector.md.BEIFYOwe.lean.js
+++ b/assets/en_api_mp_math_vector.md.DpvjNLj_.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,g){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),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};
diff --git a/assets/en_api_presets_model_index.md._hbR1U40.js b/assets/en_api_presets_model_index.md.BJWo1DBU.js
similarity index 87%
rename from assets/en_api_presets_model_index.md._hbR1U40.js
rename to assets/en_api_presets_model_index.md.BJWo1DBU.js
index f94ebdf..acf033b 100644
--- a/assets/en_api_presets_model_index.md._hbR1U40.js
+++ b/assets/en_api_presets_model_index.md.BJWo1DBU.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
def 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 ​
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。
diff --git a/assets/en_api_presets_model_index.md._hbR1U40.lean.js b/assets/en_api_presets_model_index.md.BJWo1DBU.lean.js
similarity index 100%
rename from assets/en_api_presets_model_index.md._hbR1U40.lean.js
rename to assets/en_api_presets_model_index.md.BJWo1DBU.lean.js
diff --git a/assets/en_api_presets_model_model.md.B9FfcMgc.js b/assets/en_api_presets_model_model.md.Cmq9KKw_.js
similarity index 87%
rename from assets/en_api_presets_model_model.md.B9FfcMgc.js
rename to assets/en_api_presets_model_model.md.Cmq9KKw_.js
index 1e2d7ff..e1b5d6c 100644
--- a/assets/en_api_presets_model_model.md.B9FfcMgc.js
+++ b/assets/en_api_presets_model_model.md.Cmq9KKw_.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/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
def 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/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。
diff --git a/assets/en_api_presets_model_model.md.B9FfcMgc.lean.js b/assets/en_api_presets_model_model.md.Cmq9KKw_.lean.js
similarity index 100%
rename from assets/en_api_presets_model_model.md.B9FfcMgc.lean.js
rename to assets/en_api_presets_model_model.md.Cmq9KKw_.lean.js
diff --git a/assets/zht_api_mp_math_angle.md.xBQ5jf2w.js b/assets/ja_api_mp_math_angle.md.DmogilJK.js
similarity index 61%
rename from assets/zht_api_mp_math_angle.md.xBQ5jf2w.js
rename to assets/ja_api_mp_math_angle.md.DmogilJK.js
index 25d4c95..56307b2 100644
--- a/assets/zht_api_mp_math_angle.md.xBQ5jf2w.js
+++ b/assets/ja_api_mp_math_angle.md.DmogilJK.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) ​
def __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":"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):
     """
         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
def 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
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
 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
def 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
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
 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
def 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
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
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def 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
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
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def 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
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
 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
def 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
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
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def 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
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
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def 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
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
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def 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
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
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def 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
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
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def 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
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
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def 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)
def __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
def 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)
def 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
def self / other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
@overload
+    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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func 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:
-    ...
def self / other ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other):
+    ...
func 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,d,o,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c 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 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.CAq1hHov.lean.js b/assets/ja_api_mp_math_angle.md.DmogilJK.lean.js
similarity index 86%
rename from assets/ja_api_mp_math_angle.md.CAq1hHov.lean.js
rename to assets/ja_api_mp_math_angle.md.DmogilJK.lean.js
index d5f4fc6..feff6a6 100644
--- a/assets/ja_api_mp_math_angle.md.CAq1hHov.lean.js
+++ b/assets/ja_api_mp_math_angle.md.DmogilJK.lean.js
@@ -1 +1 @@
-import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,d,o,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
+import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/angle.md","filePath":"ja/api/mp_math/angle.md"}'),t={name:"ja/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_equation.md.CwX1EUnA.js b/assets/ja_api_mp_math_equation.md.DuGNts4i.js
similarity index 71%
rename from assets/ja_api_mp_math_equation.md.CwX1EUnA.js
rename to assets/ja_api_mp_math_equation.md.DuGNts4i.js
index f9def83..723e7dd 100644
--- a/assets/ja_api_mp_math_equation.md.CwX1EUnA.js
+++ b/assets/ja_api_mp_math_equation.md.DuGNts4i.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 ​
def __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 ​
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):
     """
         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
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
引数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード または GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
引数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード または GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -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,d,g){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(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};
diff --git a/assets/ja_api_mp_math_equation.md.CwX1EUnA.lean.js b/assets/ja_api_mp_math_equation.md.DuGNts4i.lean.js
similarity index 73%
rename from assets/ja_api_mp_math_equation.md.CwX1EUnA.lean.js
rename to assets/ja_api_mp_math_equation.md.DuGNts4i.lean.js
index dde37b1..f4c7504 100644
--- a/assets/ja_api_mp_math_equation.md.CwX1EUnA.lean.js
+++ b/assets/ja_api_mp_math_equation.md.DuGNts4i.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,g){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(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};
diff --git a/assets/ja_api_mp_math_function.md.BpyLWMmS.js b/assets/ja_api_mp_math_function.md.BpyLWMmS.js
deleted file mode 100644
index 5555d81..0000000
--- a/assets/ja_api_mp_math_function.md.BpyLWMmS.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
def 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),y=[c],u=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)
def 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,y)),u]),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.js b/assets/ja_api_mp_math_function.md.DIn5uL0A.js
new file mode 100644
index 0000000..4bc4e78
--- /dev/null
+++ b/assets/ja_api_mp_math_function.md.DIn5uL0A.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 ​
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_function.md.BpyLWMmS.lean.js b/assets/ja_api_mp_math_function.md.DIn5uL0A.lean.js
similarity index 97%
rename from assets/ja_api_mp_math_function.md.BpyLWMmS.lean.js
rename to assets/ja_api_mp_math_function.md.DIn5uL0A.lean.js
index 3894173..e407719 100644
--- a/assets/ja_api_mp_math_function.md.BpyLWMmS.lean.js
+++ b/assets/ja_api_mp_math_function.md.DIn5uL0A.lean.js
@@ -1 +1 @@
-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("",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),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),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};
+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("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/en_api_mp_math_line.md.D0AfsxWD.js b/assets/ja_api_mp_math_line.md.Ber05s-D.js
similarity index 60%
rename from assets/en_api_mp_math_line.md.D0AfsxWD.js
rename to assets/ja_api_mp_math_line.md.Ber05s-D.js
index fa7aacb..0ad60c2 100644
--- a/assets/en_api_mp_math_line.md.D0AfsxWD.js
+++ b/assets/ja_api_mp_math_line.md.Ber05s-D.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 ​
def __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":"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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
diff --git a/assets/ja_api_mp_math_line.md.BzytbSsM.lean.js b/assets/ja_api_mp_math_line.md.Ber05s-D.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_line.md.BzytbSsM.lean.js
rename to assets/ja_api_mp_math_line.md.Ber05s-D.lean.js
diff --git a/assets/ja_api_mp_math_plane.md.Bw6ecTDW.js b/assets/ja_api_mp_math_plane.md.BlhqSUWq.js
similarity index 70%
rename from assets/ja_api_mp_math_plane.md.Bw6ecTDW.js
rename to assets/ja_api_mp_math_plane.md.BlhqSUWq.js
index b4ab779..113b075 100644
--- a/assets/ja_api_mp_math_plane.md.Bw6ecTDW.js
+++ b/assets/ja_api_mp_math_plane.md.BlhqSUWq.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.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 ​
def __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 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):
     """
         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 y
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def 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
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:
     """
         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 y
         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
def 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
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':
     """
         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 y
     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)}')
def 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)}')
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:
     """
         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 y
     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)}')
def 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)}')
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':
     """
         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 y
         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)
def 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)
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':
     """
         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 y
         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))
def 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))
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':
     """
         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 y
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def 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)
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def 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
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
 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
def 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
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
 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 y
         """
     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
def 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
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
 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 y
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def 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
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
 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 y
     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
def 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
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
 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 y
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __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
func __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
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func __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':
-    ...
def __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):
+    ...
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):
     """
         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 y
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __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)}'")
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
def __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};
+    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};
diff --git a/assets/ja_api_mp_math_plane.md.Bw6ecTDW.lean.js b/assets/ja_api_mp_math_plane.md.BlhqSUWq.lean.js
similarity index 68%
rename from assets/ja_api_mp_math_plane.md.Bw6ecTDW.lean.js
rename to assets/ja_api_mp_math_plane.md.BlhqSUWq.lean.js
index 8a72354..711844a 100644
--- a/assets/ja_api_mp_math_plane.md.Bw6ecTDW.lean.js
+++ b/assets/ja_api_mp_math_plane.md.BlhqSUWq.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.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};
+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};
diff --git a/assets/ja_api_mp_math_point.md.CFCWaCvm.js b/assets/ja_api_mp_math_point.md.Czyuzvxa.js
similarity index 58%
rename from assets/ja_api_mp_math_point.md.CFCWaCvm.js
rename to assets/ja_api_mp_math_point.md.Czyuzvxa.js
index c14faff..be1e367 100644
--- a/assets/ja_api_mp_math_point.md.CFCWaCvm.js
+++ b/assets/ja_api_mp_math_point.md.Czyuzvxa.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 ​
def __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"},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):
     """
         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
def 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
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:
     """
         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
def 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
func 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
def self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         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 e(p,k,o,r,d,g){return a(),i("div",null,h)}const y=s(n,[["render",e]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/ja_api_mp_math_point.md.CFCWaCvm.lean.js b/assets/ja_api_mp_math_point.md.Czyuzvxa.lean.js
similarity index 72%
rename from assets/ja_api_mp_math_point.md.CFCWaCvm.lean.js
rename to assets/ja_api_mp_math_point.md.Czyuzvxa.lean.js
index c6bf4a4..c278532 100644
--- a/assets/ja_api_mp_math_point.md.CFCWaCvm.lean.js
+++ b/assets/ja_api_mp_math_point.md.Czyuzvxa.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 e(p,k,o,r,d,g){return a(),i("div",null,h)}const y=s(n,[["render",e]]);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"},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};
diff --git a/assets/ja_api_mp_math_segment.md.cuLLXTSO.js b/assets/ja_api_mp_math_segment.md.DfoJ389C.js
similarity index 78%
rename from assets/ja_api_mp_math_segment.md.cuLLXTSO.js
rename to assets/ja_api_mp_math_segment.md.DfoJ389C.js
index 6f97ce1..be1679f 100644
--- a/assets/ja_api_mp_math_segment.md.cuLLXTSO.js
+++ b/assets/ja_api_mp_math_segment.md.DfoJ389C.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 ​
def __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 ​
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'):
     """
         三维空间中的线段。
         Args:
diff --git a/assets/ja_api_mp_math_segment.md.cuLLXTSO.lean.js b/assets/ja_api_mp_math_segment.md.DfoJ389C.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_segment.md.cuLLXTSO.lean.js
rename to assets/ja_api_mp_math_segment.md.DfoJ389C.lean.js
diff --git a/assets/ja_api_mp_math_utils.md.CrPKk6ui.js b/assets/ja_api_mp_math_utils.md.Dnl5rkoo.js
similarity index 58%
rename from assets/ja_api_mp_math_utils.md.CrPKk6ui.js
rename to assets/ja_api_mp_math_utils.md.Dnl5rkoo.js
index fd4c830..29d1c44 100644
--- a/assets/ja_api_mp_math_utils.md.CrPKk6ui.js
+++ b/assets/ja_api_mp_math_utils.md.Dnl5rkoo.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
def 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 ​
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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    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):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -25,9 +25,9 @@ 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)
def 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)}')
def __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)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -37,7 +37,7 @@ import{_ as s,c as i,o as a,a4 as t}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 abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -50,7 +50,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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 e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[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};
diff --git a/assets/ja_api_mp_math_utils.md.CrPKk6ui.lean.js b/assets/ja_api_mp_math_utils.md.Dnl5rkoo.lean.js
similarity index 68%
rename from assets/ja_api_mp_math_utils.md.CrPKk6ui.lean.js
rename to assets/ja_api_mp_math_utils.md.Dnl5rkoo.lean.js
index 935a7fb..48b11b3 100644
--- a/assets/ja_api_mp_math_utils.md.CrPKk6ui.lean.js
+++ b/assets/ja_api_mp_math_utils.md.Dnl5rkoo.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 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};
+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};
diff --git a/assets/ja_api_mp_math_vector.md.mfFeokXv.js b/assets/ja_api_mp_math_vector.md.CD5nfzHo.js
similarity index 65%
rename from assets/ja_api_mp_math_vector.md.mfFeokXv.js
rename to assets/ja_api_mp_math_vector.md.CD5nfzHo.js
index 7a056d3..3617bc2 100644
--- a/assets/ja_api_mp_math_vector.md.mfFeokXv.js
+++ b/assets/ja_api_mp_math_vector.md.CD5nfzHo.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"},e=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 ​
def __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"},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):
     """
         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
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def __abs__(self) ​
ソースコード または GitHubで表示
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func 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
def self - other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func 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
def self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def 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)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         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),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/ja_api_mp_math_vector.md.mfFeokXv.lean.js b/assets/ja_api_mp_math_vector.md.CD5nfzHo.lean.js
similarity index 72%
rename from assets/ja_api_mp_math_vector.md.mfFeokXv.lean.js
rename to assets/ja_api_mp_math_vector.md.CD5nfzHo.lean.js
index f1f838d..8a862f9 100644
--- a/assets/ja_api_mp_math_vector.md.mfFeokXv.lean.js
+++ b/assets/ja_api_mp_math_vector.md.CD5nfzHo.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"},e=t("",138),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+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};
diff --git a/assets/ja_api_presets_model_index.md.ub3RsBC9.js b/assets/ja_api_presets_model_index.md.D3Q5KLfq.js
similarity index 87%
rename from assets/ja_api_presets_model_index.md.ub3RsBC9.js
rename to assets/ja_api_presets_model_index.md.D3Q5KLfq.js
index d189d35..cf0be25 100644
--- a/assets/ja_api_presets_model_index.md.ub3RsBC9.js
+++ b/assets/ja_api_presets_model_index.md.D3Q5KLfq.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
def 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 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
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
diff --git a/assets/ja_api_presets_model_index.md.ub3RsBC9.lean.js b/assets/ja_api_presets_model_index.md.D3Q5KLfq.lean.js
similarity index 100%
rename from assets/ja_api_presets_model_index.md.ub3RsBC9.lean.js
rename to assets/ja_api_presets_model_index.md.D3Q5KLfq.lean.js
diff --git a/assets/ja_api_presets_model_model.md.Dw-6mfuk.js b/assets/ja_api_presets_model_model.md.vKB1wVU9.js
similarity index 85%
rename from assets/ja_api_presets_model_model.md.Dw-6mfuk.js
rename to assets/ja_api_presets_model_model.md.vKB1wVU9.js
index a7a440a..8d90f28 100644
--- a/assets/ja_api_presets_model_model.md.Dw-6mfuk.js
+++ b/assets/ja_api_presets_model_model.md.vKB1wVU9.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":"ja/api/presets/model/model.md","filePath":"ja/api/presets/model/model.md"}'),n={name:"ja/api/presets/model/model.md"},h=t(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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 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。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(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};
+    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.Dw-6mfuk.lean.js b/assets/ja_api_presets_model_model.md.vKB1wVU9.lean.js
similarity index 61%
rename from assets/ja_api_presets_model_model.md.Dw-6mfuk.lean.js
rename to assets/ja_api_presets_model_model.md.vKB1wVU9.lean.js
index ab3791c..1f52640 100644
--- a/assets/ja_api_presets_model_model.md.Dw-6mfuk.lean.js
+++ b/assets/ja_api_presets_model_model.md.vKB1wVU9.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/model.md","filePath":"ja/api/presets/model/model.md"}'),n={name:"ja/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 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/style.D-YKQyMb.css b/assets/style.D-YKQyMb.css
new file mode 100644
index 0000000..0e2e363
--- /dev/null
+++ b/assets/style.D-YKQyMb.css
@@ -0,0 +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: 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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div[class*=language-]{border-radius:8px!important}.excerpt-gradient-bottom[data-v-c74c0613]{position:absolute;bottom:-1px;left:0;width:100%;height:8px;background:linear-gradient(transparent,var(--vp-local-search-result-bg));z-index:1000}.excerpt-gradient-top[data-v-c74c0613]{position:absolute;top:-1px;left:0;width:100%;height:8px;background:linear-gradient(var(--vp-local-search-result-bg),transparent);z-index:1000}.result.selected .titles[data-v-c74c0613],.result.selected .title-icon[data-v-c74c0613]{color:var(--vp-c-brand-1)!important}.no-results[data-v-c74c0613]{font-size:.9rem;text-align:center;padding:12px}svg[data-v-c74c0613]{flex:none}
diff --git a/assets/style.UiSpMRXd.css b/assets/style.UiSpMRXd.css
deleted file mode 100644
index 5e755b7..0000000
--- a/assets/style.UiSpMRXd.css
+++ /dev/null
@@ -1 +0,0 @@
-:root{--vp-home-hero-name-color: transparent;--vp-home-hero-name-background: -webkit-linear-gradient(120deg, #bd34fe 30%, #41d1ff)}@media (min-width: 640px){:root{--vp-home-hero-image-filter: blur(56px)}}@media (min-width: 960px){:root{--vp-home-hero-image-filter: blur(68px)}}: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: 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diff --git a/assets/en_api_mp_math_angle.md.09R7pxw_.js b/assets/zht_api_mp_math_angle.md.CEIly6_X.js
similarity index 61%
rename from assets/en_api_mp_math_angle.md.09R7pxw_.js
rename to assets/zht_api_mp_math_angle.md.CEIly6_X.js
index bf5fd7c..b872440 100644
--- a/assets/en_api_mp_math_angle.md.09R7pxw_.js
+++ b/assets/zht_api_mp_math_angle.md.CEIly6_X.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.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) ​
def __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 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):
     """
         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 c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def 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
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
 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
def 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
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
 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
def 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
func 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
def 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
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
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def 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
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
 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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)
def 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)
def __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
def 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)
def 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
def self / other: float => AnyAngle ​
Source code or View on GitHub
python
@overload
+    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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
Source code or View on GitHub
python
def __truediv__(self, other):
+    ...
func 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 a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c 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 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.xBQ5jf2w.lean.js b/assets/zht_api_mp_math_angle.md.CEIly6_X.lean.js
similarity index 86%
rename from assets/zht_api_mp_math_angle.md.xBQ5jf2w.lean.js
rename to assets/zht_api_mp_math_angle.md.CEIly6_X.lean.js
index c0c9943..a629079 100644
--- a/assets/zht_api_mp_math_angle.md.xBQ5jf2w.lean.js
+++ b/assets/zht_api_mp_math_angle.md.CEIly6_X.lean.js
@@ -1 +1 @@
-import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,d,o,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
+import{_ as s,c as a,o as i,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/angle.md","filePath":"zht/api/mp_math/angle.md"}'),t={name:"zht/api/mp_math/angle.md"},e=n("",80),l=[e];function h(p,k,r,o,d,g){return i(),a("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_equation.md.DBXwIC0s.js b/assets/zht_api_mp_math_equation.md.BPMLYcpO.js
similarity index 72%
rename from assets/en_api_mp_math_equation.md.DBXwIC0s.js
rename to assets/zht_api_mp_math_equation.md.BPMLYcpO.js
index 1b7edf9..0f4d793 100644
--- a/assets/en_api_mp_math_equation.md.DBXwIC0s.js
+++ b/assets/zht_api_mp_math_equation.md.BPMLYcpO.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 ​
def __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":"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):
     """
         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
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
Arguments:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code or View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
變數説明:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼 或 於GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -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,d,c){return a(),i("div",null,p)}const o=s(t,[["render",h]]);export{u as __pageData,o as default};
+        raise ValueError('Invalid var type')
`,23),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};
diff --git a/assets/zht_api_mp_math_equation.md.CNqNdo8e.lean.js b/assets/zht_api_mp_math_equation.md.BPMLYcpO.lean.js
similarity index 73%
rename from assets/zht_api_mp_math_equation.md.CNqNdo8e.lean.js
rename to assets/zht_api_mp_math_equation.md.BPMLYcpO.lean.js
index a290646..593b902 100644
--- a/assets/zht_api_mp_math_equation.md.CNqNdo8e.lean.js
+++ b/assets/zht_api_mp_math_equation.md.BPMLYcpO.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as n}from"./chunks/framework.DpC1ZpOZ.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),t={name:"zht/api/mp_math/equation.md"},l=n("",23),p=[l];function h(e,k,r,E,d,g){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(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};
diff --git a/assets/zht_api_mp_math_function.md.BYw-sqJL.js b/assets/zht_api_mp_math_function.md.BYw-sqJL.js
deleted file mode 100644
index d66b819..0000000
--- a/assets/zht_api_mp_math_function.md.BYw-sqJL.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
def 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),y=[c],u=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)
def 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,y)),u]),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.js b/assets/zht_api_mp_math_function.md.D9y8K44X.js
new file mode 100644
index 0000000..1eab202
--- /dev/null
+++ b/assets/zht_api_mp_math_function.md.D9y8K44X.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 ​
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_function.md.BYw-sqJL.lean.js b/assets/zht_api_mp_math_function.md.D9y8K44X.lean.js
similarity index 97%
rename from assets/zht_api_mp_math_function.md.BYw-sqJL.lean.js
rename to assets/zht_api_mp_math_function.md.D9y8K44X.lean.js
index f9d5421..39dd29d 100644
--- a/assets/zht_api_mp_math_function.md.BYw-sqJL.lean.js
+++ b/assets/zht_api_mp_math_function.md.D9y8K44X.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),e={name:"zht/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),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};
+import{_ as l,c as t,j as s,a as n,a4 as a,o as i}from"./chunks/framework.DpC1ZpOZ.js";const Z=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","lastUpdated":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),e={name:"zht/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),u=[c],y=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,M,B,v){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,u)),y]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const V=l(e,[["render",x]]);export{Z as __pageData,V as default};
diff --git a/assets/zht_api_mp_math_line.md.BKWlVJmv.js b/assets/zht_api_mp_math_line.md.V0JKiMxX.js
similarity index 60%
rename from assets/zht_api_mp_math_line.md.BKWlVJmv.js
rename to assets/zht_api_mp_math_line.md.V0JKiMxX.js
index 7ab4604..8ba92ac 100644
--- a/assets/zht_api_mp_math_line.md.BKWlVJmv.js
+++ b/assets/zht_api_mp_math_line.md.V0JKiMxX.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 ​
def __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 ​
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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
diff --git a/assets/zht_api_mp_math_line.md.BKWlVJmv.lean.js b/assets/zht_api_mp_math_line.md.V0JKiMxX.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_line.md.BKWlVJmv.lean.js
rename to assets/zht_api_mp_math_line.md.V0JKiMxX.lean.js
diff --git a/assets/en_api_mp_math_plane.md.3xsZdWoR.js b/assets/zht_api_mp_math_plane.md.CKWKiFtm.js
similarity index 71%
rename from assets/en_api_mp_math_plane.md.3xsZdWoR.js
rename to assets/zht_api_mp_math_plane.md.CKWKiFtm.js
index f57c5f9..b4fffaf 100644
--- a/assets/en_api_mp_math_plane.md.3xsZdWoR.js
+++ b/assets/zht_api_mp_math_plane.md.CKWKiFtm.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.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 ​
def __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 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):
     """
         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 y
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def 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
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:
     """
         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 y
         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
def 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
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':
     """
         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 y
     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)}')
def 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)}')
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:
     """
         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 y
     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)}')
def 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)}')
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':
     """
         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 y
         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)
def 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)
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':
     """
         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 y
         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))
def 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))
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':
     """
         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 y
         Returns:
             [\`Plane3\`](./plane#class-plane3): 平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def 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)
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def 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
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
 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
def 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
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
 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 y
         """
     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
def 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
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
 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 y
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def 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
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
 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 y
     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
def 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
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
 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 y
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
+    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
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __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):
+    ...
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):
     """
         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 y
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __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)}'")
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:
     """
         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 y
         Returns:
             [\`bool\`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
-    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,113),h=[t];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const c=s(l,[["render",e]]);export{y as __pageData,c as default};
+    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};
diff --git a/assets/zht_api_mp_math_plane.md.Cbo0QRQD.lean.js b/assets/zht_api_mp_math_plane.md.CKWKiFtm.lean.js
similarity index 67%
rename from assets/zht_api_mp_math_plane.md.Cbo0QRQD.lean.js
rename to assets/zht_api_mp_math_plane.md.CKWKiFtm.lean.js
index 43a9b72..00a9c41 100644
--- a/assets/zht_api_mp_math_plane.md.Cbo0QRQD.lean.js
+++ b/assets/zht_api_mp_math_plane.md.CKWKiFtm.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.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};
+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};
diff --git a/assets/en_api_mp_math_point.md.CxCgy181.js b/assets/zht_api_mp_math_point.md.D7bOx2HI.js
similarity index 61%
rename from assets/en_api_mp_math_point.md.CxCgy181.js
rename to assets/zht_api_mp_math_point.md.D7bOx2HI.js
index 14d07b0..2f6fe97 100644
--- a/assets/en_api_mp_math_point.md.CxCgy181.js
+++ b/assets/zht_api_mp_math_point.md.D7bOx2HI.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"},e=t(`
mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
def __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":"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):
     """
         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
def 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
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:
     """
         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
def 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
func self + other: Vector3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         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),l=[e];function h(p,o,k,r,d,c){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/zht_api_mp_math_point.md.Ci0RyJlm.lean.js b/assets/zht_api_mp_math_point.md.D7bOx2HI.lean.js
similarity index 72%
rename from assets/zht_api_mp_math_point.md.Ci0RyJlm.lean.js
rename to assets/zht_api_mp_math_point.md.D7bOx2HI.lean.js
index c875422..54ef0dc 100644
--- a/assets/zht_api_mp_math_point.md.Ci0RyJlm.lean.js
+++ b/assets/zht_api_mp_math_point.md.D7bOx2HI.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 e(p,k,o,r,d,g){return a(),i("div",null,h)}const y=s(n,[["render",e]]);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"},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};
diff --git a/assets/en_api_mp_math_segment.md.BevquOvV.js b/assets/zht_api_mp_math_segment.md.pWjtiCkV.js
similarity index 80%
rename from assets/en_api_mp_math_segment.md.BevquOvV.js
rename to assets/zht_api_mp_math_segment.md.pWjtiCkV.js
index cc6747c..515bbfd 100644
--- a/assets/en_api_mp_math_segment.md.BevquOvV.js
+++ b/assets/zht_api_mp_math_segment.md.pWjtiCkV.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":"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 ​
def __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":"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'):
     """
         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 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};
+    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};
diff --git a/assets/zht_api_mp_math_segment.md.D_xbGo8n.lean.js b/assets/zht_api_mp_math_segment.md.pWjtiCkV.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_segment.md.D_xbGo8n.lean.js
rename to assets/zht_api_mp_math_segment.md.pWjtiCkV.lean.js
diff --git a/assets/en_api_mp_math_utils.md.rVP-A71G.js b/assets/zht_api_mp_math_utils.md.DIDbd5be.js
similarity index 63%
rename from assets/en_api_mp_math_utils.md.rVP-A71G.js
rename to assets/zht_api_mp_math_utils.md.DIDbd5be.js
index d9f58a2..00d94e8 100644
--- a/assets/en_api_mp_math_utils.md.rVP-A71G.js
+++ b/assets/zht_api_mp_math_utils.md.DIDbd5be.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":"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 ​
Description: 本模块定义了一些常用的工具函数
def 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":"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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([\`RealNumber\`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
+    self.value = value
func __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
@@ -25,9 +25,9 @@ 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)
def 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)}')
def __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
-    return not self.__eq__(other)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -37,7 +37,7 @@ import{_ as s,c as i,o as a,a4 as t}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 abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([\`float\`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -50,7 +50,7 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const F
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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 e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(n,[["render",e]]);export{F as __pageData,E as default};
+        return ''
`,38),h=[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};
diff --git a/assets/zht_api_mp_math_utils.md.BsNVdUjt.lean.js b/assets/zht_api_mp_math_utils.md.DIDbd5be.lean.js
similarity index 67%
rename from assets/zht_api_mp_math_utils.md.BsNVdUjt.lean.js
rename to assets/zht_api_mp_math_utils.md.DIDbd5be.lean.js
index 24b504f..ce79bcd 100644
--- a/assets/zht_api_mp_math_utils.md.BsNVdUjt.lean.js
+++ b/assets/zht_api_mp_math_utils.md.DIDbd5be.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 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};
+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};
diff --git a/assets/zht_api_mp_math_vector.md.vRujd3bN.js b/assets/zht_api_mp_math_vector.md.4G7-2lGN.js
similarity index 66%
rename from assets/zht_api_mp_math_vector.md.vRujd3bN.js
rename to assets/zht_api_mp_math_vector.md.4G7-2lGN.js
index f3580dd..094f149 100644
--- a/assets/zht_api_mp_math_vector.md.vRujd3bN.js
+++ b/assets/zht_api_mp_math_vector.md.4G7-2lGN.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"},e=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 ​
def __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"},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):
     """
         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
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         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
def 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
func 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
def 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
func 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
def 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
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
 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
def __abs__(self) ​
源碼 或 於GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func self - other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func self * other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         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),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+    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};
diff --git a/assets/zht_api_mp_math_vector.md.vRujd3bN.lean.js b/assets/zht_api_mp_math_vector.md.4G7-2lGN.lean.js
similarity index 73%
rename from assets/zht_api_mp_math_vector.md.vRujd3bN.lean.js
rename to assets/zht_api_mp_math_vector.md.4G7-2lGN.lean.js
index 4ec8288..0cc6efe 100644
--- a/assets/zht_api_mp_math_vector.md.vRujd3bN.lean.js
+++ b/assets/zht_api_mp_math_vector.md.4G7-2lGN.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"},e=t("",138),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{E as __pageData,y as default};
+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};
diff --git a/assets/zht_api_presets_model_index.md.a46BvX0I.js b/assets/zht_api_presets_model_index.md.BMgFAAtM.js
similarity index 85%
rename from assets/zht_api_presets_model_index.md.a46BvX0I.js
rename to assets/zht_api_presets_model_index.md.BMgFAAtM.js
index f0d8967..32b7ff7 100644
--- a/assets/zht_api_presets_model_index.md.a46BvX0I.js
+++ b/assets/zht_api_presets_model_index.md.BMgFAAtM.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/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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 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。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(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};
+    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.a46BvX0I.lean.js b/assets/zht_api_presets_model_index.md.BMgFAAtM.lean.js
similarity index 63%
rename from assets/zht_api_presets_model_index.md.a46BvX0I.lean.js
rename to assets/zht_api_presets_model_index.md.BMgFAAtM.lean.js
index 51a0c5b..971fa91 100644
--- a/assets/zht_api_presets_model_index.md.a46BvX0I.lean.js
+++ b/assets/zht_api_presets_model_index.md.BMgFAAtM.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a4 as t}from"./chunks/framework.DpC1ZpOZ.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","lastUpdated":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t("",10),l=[h];function p(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 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.C8PKDM2B.js b/assets/zht_api_presets_model_model.md.hVmtKMyB.js
similarity index 87%
rename from assets/zht_api_presets_model_model.md.C8PKDM2B.js
rename to assets/zht_api_presets_model_model.md.hVmtKMyB.js
index a7ba29e..26da939 100644
--- a/assets/zht_api_presets_model_model.md.C8PKDM2B.js
+++ b/assets/zht_api_presets_model_model.md.hVmtKMyB.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
def 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/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
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
diff --git a/assets/zht_api_presets_model_model.md.C8PKDM2B.lean.js b/assets/zht_api_presets_model_model.md.hVmtKMyB.lean.js
similarity index 100%
rename from assets/zht_api_presets_model_model.md.C8PKDM2B.lean.js
rename to assets/zht_api_presets_model_model.md.hVmtKMyB.lean.js
diff --git a/demo/best-practice.html b/demo/best-practice.html
index de67b8b..279bd0e 100644
--- a/demo/best-practice.html
+++ b/demo/best-practice.html
@@ -6,10 +6,10 @@
     最佳实践 | MBCP 文档
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/demo/index.html b/demo/index.html
index 69c7815..2c679f8 100644
--- a/demo/index.html
+++ b/demo/index.html
@@ -6,10 +6,10 @@
     demo | MBCP 文档
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
demo ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/api.html b/en/api/api.html
index 327cc23..43630fc 100644
--- a/en/api/api.html
+++ b/en/api/api.html
@@ -6,10 +6,10 @@
     mbcp | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/index.html b/en/api/index.html
index 59941f2..e2a73d9 100644
--- a/en/api/index.html
+++ b/en/api/index.html
@@ -6,10 +6,10 @@
     mbcp | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index c77d99a..817111f 100644
--- a/en/api/mp_math/angle.html
+++ b/en/api/mp_math/angle.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.angle | MBCP docs
     
     
-    
+    
     
-    
-    
+    
+    
     
-    
+    
     
     
     
     
   
   
-    
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.angle ​
Description: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
def __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
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.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):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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)
def 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)
def __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
def 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)
def 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
def self / other: float => AnyAngle ​
Source code or View on GitHub
python
@overload
+    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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self / other: AnyAngle => float ​
Source code or View on GitHub
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
Source code or View on GitHub
python
def __truediv__(self, other):
+    ...
func 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

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diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html
index b770d9b..9a5d92b 100644
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+++ b/en/api/mp_math/const.html
@@ -6,10 +6,10 @@
     mbcp.mp_math.const | MBCP docs
     
     
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MBCP docs
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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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diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html
index 24df0d9..e3a8a47 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.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 ​
def __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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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):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
Arguments:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code or View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
Arguments:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code or View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html
index 429e6cc..dc5b900 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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mbcp.mp_math.function ​
Description: AAA
def 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:
+    
MBCP docs
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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:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -34,7 +34,7 @@
     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)
def 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 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:
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html
index a887067..a816b0b 100644
--- a/en/api/mp_math/index.html
+++ b/en/api/mp_math/index.html
@@ -6,10 +6,10 @@
     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

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diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html
index dd704b1..351eca9 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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English
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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 ​
def __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 ​
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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
@@ -192,7 +192,7 @@
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/mp_math.html b/en/api/mp_math/mp_math.html
index 95e3007..62bba41 100644
--- a/en/api/mp_math/mp_math.html
+++ b/en/api/mp_math/mp_math.html
@@ -6,10 +6,10 @@
     mbcp.mp_math | MBCP docs
     
     
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@@ -19,7 +19,7 @@
   
   
     
MBCP docs
English
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日本語
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English
简体中文
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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 5b14004..e2c2c0f 100644
--- a/en/api/mp_math/mp_math_typing.html
+++ b/en/api/mp_math/mp_math_typing.html
@@ -6,10 +6,10 @@
     mbcp.mp_math.mp_math_typing | MBCP docs
     
     
-    
+    
     
-    
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+    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
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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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diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html
index ceb6b6a..667402d 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 docs
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日本語
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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 ​
def __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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简体中文
日本語
繁體中文
English
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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):
     """
         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
def 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
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:
     """
         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
def 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
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':
     """
         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)}')
def 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)}')
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:
     """
         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)}')
def 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)}')
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':
     """
         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)
def 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)
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':
     """
         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))
def 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))
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':
     """
         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)
def 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)
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:
     """
         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
def 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
func 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def __and__(self, other: Line3) -> Point3 | None ​
Source code or View on GitHub
python
@overload
+    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
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
Source code or View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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:
     """
         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)
def __rand__(self, other: Line3) -> Point3 ​
Source code or View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    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

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diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html
index 424e701..5f38a1b 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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mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
def __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 ​
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):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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
def 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
func self + other: Vector3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         P - P -> V
 
@@ -70,7 +70,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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+    
     
   
 
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diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html
index 30ab545..7f39923 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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+    
     
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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 ​
def __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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日本語
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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'):
     """
         三维空间中的线段。
         Args:
@@ -33,7 +33,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html
index 5dab145..95731c8 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
     
     
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mbcp.mp_math.utils ​
Description: 本模块定义了一些常用的工具函数
def 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:
+    
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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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
Source code or View on GitHub
python
def __eq__(self, other):
+    self.value = value
func __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
@@ -45,9 +45,9 @@
         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)
def 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)}')
def __ne__(self, other) ​
Source code or View on GitHub
python
def __ne__(self, other):
-    return not self.__eq__(other)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
Return: bool: 是否近似相等
Source code or View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -57,7 +57,7 @@
     Returns:
         [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -70,7 +70,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
Return: str: 符号 + - ""
Source code or View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -87,7 +87,7 @@
         return f'-{abs(x)}'
     else:
         return ''
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html
index 82039b0..2f46eda 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
     
     
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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.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 ​
def __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
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.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):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Return: np.ndarray: numpy数组
Source code or View on GitHub
python
@property
+    self.z /= length
@property
func 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
def 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
func 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
def 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
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
 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
def __abs__(self) ​
Source code or View on GitHub
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func self - other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self - other: Point3 => Point3 ​
Source code or View on GitHub
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func self * other: Vector3 => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
+    ...
@overload
func self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def self * other: RealNumber => Vector3 ​
Source code or View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         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

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index 01afd36..233cd34 100644
--- a/en/api/particle/index.html
+++ b/en/api/particle/index.html
@@ -6,10 +6,10 @@
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index 934dba2..8c0a05c 100644
--- a/en/api/particle/particle.html
+++ b/en/api/particle/particle.html
@@ -6,10 +6,10 @@
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diff --git a/en/api/presets/index.html b/en/api/presets/index.html
index 013181d..c81424c 100644
--- a/en/api/presets/index.html
+++ b/en/api/presets/index.html
@@ -6,10 +6,10 @@
     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 838e136..ccbb1c8 100644
--- a/en/api/presets/model/index.html
+++ b/en/api/presets/model/index.html
@@ -6,19 +6,19 @@
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mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
def 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
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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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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English
简体中文
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mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
def 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
简体中文
日本語
繁體中文
Appearance
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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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开始不了一点 ​
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Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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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

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index aa3ac8d..a691228 100644
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MBCP docs
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Reference ​
help us to improve the documentation
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开始不了一点 ​
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AAA ​
BBB ​
C ​
ddd ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/hashmap.json b/hashmap.json
index 7039ee1..458fb13 100644
--- a/hashmap.json
+++ b/hashmap.json
@@ -1 +1 @@
-{"api_api.md":"rnPOv6-O","api_index.md":"qnrSd__i","api_mp_math_angle.md":"3Na5IaYp","api_mp_math_const.md":"O6cTulwX","api_mp_math_equation.md":"z85zyCZL","api_mp_math_function.md":"BhmJqpOo","api_mp_math_index.md":"DHhPNV6R","api_mp_math_line.md":"Dovi6bdM","api_mp_math_mp_math.md":"mVabZTHd","api_mp_math_mp_math_typing.md":"CEryCREV","api_mp_math_plane.md":"Dv-GWbJg","api_mp_math_point.md":"BvvrKTY8","api_mp_math_segment.md":"_n__ViVt","api_mp_math_utils.md":"kW3A-lG9","api_mp_math_vector.md":"mCFa4Azm","api_particle_index.md":"BxLVuqry","api_particle_particle.md":"CioLG9Ab","api_presets_index.md":"C7sBj6Q8","api_presets_model_index.md":"F2zeh9P2","api_presets_model_model.md":"BoocA59j","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":"09R7pxw_","en_api_mp_math_const.md":"DjbxFoGO","en_api_mp_math_equation.md":"DBXwIC0s","en_api_mp_math_function.md":"nJ-E5W5r","en_api_mp_math_index.md":"ypHGEnmb","en_api_mp_math_line.md":"D0AfsxWD","en_api_mp_math_mp_math.md":"5IisTIt3","en_api_mp_math_mp_math_typing.md":"DWjztCj6","en_api_mp_math_plane.md":"3xsZdWoR","en_api_mp_math_point.md":"CxCgy181","en_api_mp_math_segment.md":"BevquOvV","en_api_mp_math_utils.md":"rVP-A71G","en_api_mp_math_vector.md":"BEIFYOwe","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":"_hbR1U40","en_api_presets_model_model.md":"B9FfcMgc","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":"CAq1hHov","ja_api_mp_math_const.md":"CACmM3Q4","ja_api_mp_math_equation.md":"CwX1EUnA","ja_api_mp_math_function.md":"BpyLWMmS","ja_api_mp_math_index.md":"B_UDRWJp","ja_api_mp_math_line.md":"BzytbSsM","ja_api_mp_math_mp_math.md":"DGl-Yqoj","ja_api_mp_math_mp_math_typing.md":"BANGfx9Q","ja_api_mp_math_plane.md":"Bw6ecTDW","ja_api_mp_math_point.md":"CFCWaCvm","ja_api_mp_math_segment.md":"cuLLXTSO","ja_api_mp_math_utils.md":"CrPKk6ui","ja_api_mp_math_vector.md":"mfFeokXv","ja_api_particle_index.md":"SXvJHpqE","ja_api_particle_particle.md":"DpDqAPA7","ja_api_presets_index.md":"DrJ0aeZq","ja_api_presets_model_index.md":"ub3RsBC9","ja_api_presets_model_model.md":"Dw-6mfuk","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":"xBQ5jf2w","zht_api_mp_math_const.md":"DhnGo46u","zht_api_mp_math_equation.md":"CNqNdo8e","zht_api_mp_math_function.md":"BYw-sqJL","zht_api_mp_math_index.md":"C-ytwIT_","zht_api_mp_math_line.md":"BKWlVJmv","zht_api_mp_math_mp_math.md":"WAo96wsQ","zht_api_mp_math_mp_math_typing.md":"2475K9x4","zht_api_mp_math_plane.md":"Cbo0QRQD","zht_api_mp_math_point.md":"Ci0RyJlm","zht_api_mp_math_segment.md":"D_xbGo8n","zht_api_mp_math_utils.md":"BsNVdUjt","zht_api_mp_math_vector.md":"vRujd3bN","zht_api_particle_index.md":"C8wv1sGB","zht_api_particle_particle.md":"DLxDzJsb","zht_api_presets_index.md":"CKWpXp08","zht_api_presets_model_index.md":"a46BvX0I","zht_api_presets_model_model.md":"C8PKDM2B","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_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"}
diff --git a/index.html b/index.html
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MBCP 文档
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MBCP
更多基础变换粒子
用于几何运算和Minecraft粒子制作的库
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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mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
def __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):
+    
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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):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def 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
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
 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
def 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
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
 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
def 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
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
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def 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
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
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def 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
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
 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
def 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
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
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def 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
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
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def 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
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
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def 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
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
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def 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
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
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def 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
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
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def 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)
def __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)
def 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)
def 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
def 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)
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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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:
-    ...
def self / other ​
ソースコード または GitHubで表示
python
def __truediv__(self, other):
+    ...
func 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)
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/const.html b/ja/api/mp_math/const.html
index d5a417e..63f2ceb 100644
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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
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/equation.html b/ja/api/mp_math/equation.html
index 029ebcb..efeac0f 100644
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+++ b/ja/api/mp_math/equation.html
@@ -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 ​
def __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 ​
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):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
引数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード または GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
引数:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード または GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
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diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html
index 4c3e5bd..c173582 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
def 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 ​
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:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -34,7 +34,7 @@
     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)
def 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 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:
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
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     mbcp.mp_math | 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：
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.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 ​
def __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 ​
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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
@@ -192,7 +192,7 @@
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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@@ -6,10 +6,10 @@
     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：
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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@@ -6,10 +6,10 @@
     mbcp.mp_math.mp_math_typing | 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.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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index bfa9e6e..ef74bc9 100644
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+++ b/ja/api/mp_math/plane.html
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     mbcp.mp_math.plane | 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.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __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 ​
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):
     """
         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
def 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
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:
     """
         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
def 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
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':
     """
         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)}')
def 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)}')
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:
     """
         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)}')
def 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)}')
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':
     """
         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)
def 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)
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':
     """
         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))
def 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))
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def __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
func __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
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func __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':
-    ...
def __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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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:
     """
         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)
def __rand__(self, other: Line3) -> Point3 ​
ソースコード または GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.approx(other)
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)
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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index c1a83b8..755a30e 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 ​
def __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 ​
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):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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
def 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
func 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
def self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         P - P -> V
 
@@ -70,7 +70,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html
index 6cb21b1..b36ea46 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 ​
def __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 ​
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'):
     """
         三维空间中的线段。
         Args:
@@ -33,7 +33,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html
index 2876ec2..092ef15 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
def 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 ​
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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
ソースコード または GitHubで表示
python
def __eq__(self, other):
+    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):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -45,9 +45,9 @@
         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)
def 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)}')
def __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)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
戻り値: bool: 是否近似相等
ソースコード または GitHubで表示
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -57,7 +57,7 @@
     Returns:
         [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -70,7 +70,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
戻り値: str: 符号 + - ""
ソースコード または GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -87,7 +87,7 @@
         return f'-{abs(x)}'
     else:
         return ''
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
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diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html
index 6d343f2..4e316f8 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
     
     
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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 ​
def __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):
+    
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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):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def 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
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
 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
def 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
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
 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
def 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
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
 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
def __abs__(self) ​
ソースコード または GitHubで表示
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func 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
def self - other: Point3 => Point3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func 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
def self * other: RealNumber => Vector3 ​
ソースコード または GitHubで表示
python
@overload
+    ...
@overload
func 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':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def 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)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • タイプ: Vector3
  • デフォルト: Vector3(0, 0, 1)
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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index be16ae6..dde6619 100644
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+++ b/ja/api/particle/index.html
@@ -6,10 +6,10 @@
     mbcp.particle | MBCP ドキュメント
     
     
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index 9e21d0b..f2c25b8 100644
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@@ -6,10 +6,10 @@
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index c03edd3..b2ed878 100644
--- a/ja/api/presets/index.html
+++ b/ja/api/presets/index.html
@@ -6,10 +6,10 @@
     mbcp.presets | MBCP ドキュメント
     
     
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diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html
index 8a9fae5..68faea3 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.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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 ​
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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
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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index fb5d010..55b5a1e 100644
--- a/ja/api/presets/model/model.html
+++ b/ja/api/presets/model/model.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP ドキュメント
     
     
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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
+    
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.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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
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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index 7516c9b..542f607 100644
--- a/ja/api/presets/presets.html
+++ b/ja/api/presets/presets.html
@@ -6,10 +6,10 @@
     mbcp.presets | MBCP ドキュメント
     
     
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index 634bc04..c1f044e 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 95568fc..a7f2f68 100644
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+++ b/ja/guide/index.html
@@ -6,10 +6,10 @@
     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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开始不了一点 ​
∫12x111
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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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

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index 86ef534..ea798ef 100644
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@@ -6,10 +6,10 @@
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Reference ​
Help us to improve the documentation
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@@ -6,10 +6,10 @@
     柯里化 | MBCP 文档
     
     
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Reference ​
Help us to improve the documentation
文档由 VitePress 构建 | API引用由 litedoc 生成
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diff --git a/zht/api/api.html b/zht/api/api.html
index 1437afc..351f60b 100644
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diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html
index d77474c..d660f46 100644
--- a/zht/api/mp_math/angle.html
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     mbcp.mp_math.angle | MBCP 文檔
     
     
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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) ​
def __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):
+    
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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):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def 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
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
 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
def 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
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
 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
def 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
func 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
def 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
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
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def 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
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
 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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
def 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
func 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)
def 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)
def __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
def 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)
def 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
def self / other: float => AnyAngle ​
源碼 或 於GitHub上查看
python
@overload
+    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
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self / other: AnyAngle => float ​
源碼 或 於GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
源碼 或 於GitHub上查看
python
def __truediv__(self, other):
+    ...
func 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

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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.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 ​
def __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 ​
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):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __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
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, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
變數説明:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼 或 於GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
func get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
變數説明:
  • func (MultiVarsFunc): N元函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼 或 於GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.mp_math.function ​
説明: AAA
def 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 ​
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:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -34,7 +34,7 @@
     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)
def 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 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:
@@ -60,7 +60,7 @@
         """@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

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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.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
def __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 ​
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'):
     """
         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
def 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
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:
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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.')
def 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.')
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':
     """
         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
def 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
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':
     """
         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))
def 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))
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':
     """
         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
def 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
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]:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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)
def 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)
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:
     """
         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
def 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
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):
     """
         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
def 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
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
 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)
def __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)
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':
     """
         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)
def __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)
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:
     """
         判断两条直线是否等价。
 
@@ -192,7 +192,7 @@
             [`bool`](https%3A//docs.python.org/3/library/functions.html#bool): 是否等价
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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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.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.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __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 ​
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):
     """
         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
def 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
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:
     """
         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
def 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
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':
     """
         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)}')
def 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)}')
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:
     """
         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)}')
def 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)}')
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':
     """
         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)
def 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)
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':
     """
         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))
def 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))
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def 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
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
 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
def __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
func __and__(self, other: Line3) -> Point3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func __and__(self, other: Plane3) -> Line3 | None ​
源碼 或 於GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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:
     """
         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)
def __rand__(self, other: Line3) -> Point3 ​
源碼 或 於GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    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

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+++ b/zht/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP 文檔
     
     
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+    
+    
     
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+    
     
     
     
     
   
   
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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 ​
def __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 ​
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):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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
def 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
func self + other: Vector3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)
def __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)
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):
     """
         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)
def 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)
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':
     """
         P - P -> V
 
@@ -70,7 +70,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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@@ -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 ​
def __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'):
+    
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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'):
     """
         三维空间中的线段。
         Args:
@@ -33,7 +33,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html
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--- 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
def 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 ​
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:
     """
     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 ​
def __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 ​
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):
     """
         用于近似比较对象
         Args:
             value ([`RealNumber`](./mp_math_typing#realnumber)): 实数
         """
-    self.value = value
def __eq__(self, other) ​
源碼 或 於GitHub上查看
python
def __eq__(self, other):
+    self.value = value
func __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
@@ -45,9 +45,9 @@
         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)
def 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)}')
def __ne__(self, other) ​
源碼 或 於GitHub上查看
python
def __ne__(self, other):
-    return not self.__eq__(other)
def 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:
+            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):
+    return not self.__eq__(other)
func approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
變數説明:
  • x (float): 数1
  • y (float): 数2
  • epsilon (float): 误差
返回: bool: 是否近似相等
源碼 或 於GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -57,7 +57,7 @@
     Returns:
         [`bool`](https://docs.python.org/3/library/functions.html#bool): 是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x ([`float`](https://docs.python.org/3/library/functions.html#float)): 数
@@ -70,7 +70,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x (float): 数
  • only_neg (bool): 是否只返回负数的符号
返回: str: 符号 + - ""
源碼 或 於GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -87,7 +87,7 @@
         return f'-{abs(x)}'
     else:
         return ''
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html
index 0666646..087a15a 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
     
     
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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 ​
def __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):
+    
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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):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def 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
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:
     """
         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])
def 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])
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':
     """
         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)
def 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)
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':
     """
         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)
def 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)
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:
     """
         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
def 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
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:
     """
         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)
def 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)
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):
     """
         将向量归一化。
 
@@ -92,33 +92,33 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def 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
func 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
def 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
func 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
def 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
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
 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
def __abs__(self) ​
源碼 或 於GitHub上查看
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    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
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self + other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}'")
def __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)}'")
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):
     """
         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)
def 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)
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':
     """
         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
def 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
func self - other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self - other: Point3 => Point3 ​
源碼 或 於GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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):
+    ...
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):
     """
         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)}"')
def 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)}"')
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'):
     """
         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
def 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
func self * other: Vector3 => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
+    ...
@overload
func self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def 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':
+    ...
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':
     """
         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)}'")
def self * other: RealNumber => Vector3 ​
源碼 或 於GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
def 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)}'")
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':
     """
         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
def 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)
def - 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
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':
     """
         取负。
         Returns:
             [`Vector3`](#class-vector3): 负向量
         """
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 ​
  • 説明: 零向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 0)
var x_axis ​
  • 説明: x轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(1, 0, 0)
var y_axis ​
  • 説明: y轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 1, 0)
var z_axis ​
  • 説明: z轴单位向量
  • 類型: Vector3
  • 默認值: Vector3(0, 0, 1)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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index ac9c60c..4d59034 100644
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index aaa432e..2fe2757 100644
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@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP 文檔
     
     
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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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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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def 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
繁體中文
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English
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繁體中文
简体中文
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。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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开始不了一点 ​
∫12x111
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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
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高度易用
通過簡單的接口，實現了大部分幾何運算及粒子製作的需求
📦
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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index ccfa113..14963a0 100644
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Reference ​
Help us to improve the documentation
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