diff --git a/404.html b/404.html index 13d4be0..6e6b349 100644 --- a/404.html +++ b/404.html @@ -15,7 +15,7 @@
- + \ No newline at end of file diff --git a/api/index.html b/api/index.html index cffb79b..b8c878f 100644 --- a/api/index.html +++ b/api/index.html @@ -17,8 +17,8 @@ -
MBCP docs

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp ​

说明: 本模块塞了一些预设的粒子生成器

文档由 VitePress 构建 | API引用由 litedoc 生成

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

- +
MBCP docs

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp ​

说明: 本模块塞了一些预设的粒子生成器

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 8231900..ae4b06b 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -12,12 +12,12 @@ - + -
MBCP docs

简体中文

English
日本語
繁體中文

简体中文

English
日本語
繁體中文

Appearance

mbcp.mp_math.angle ​

说明: 本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

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

说明: 任意角度。

参数:

  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码
python
@property
+        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
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码
python
@property
+    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
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
python
@property
+    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
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
源代码
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
源代码
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源代码
python
def __truediv__(self, other):
+    ...
def self / other ​
源代码
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
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/const.html b/api/mp_math/const.html
index 1d59785..493c095 100644
--- a/api/mp_math/const.html
+++ b/api/mp_math/const.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.const ​
说明: 本模块定义了一些常用的常量
var PI = math.pi ​
  • 说明: 常量 π
var E = math.e ​
  • 说明: 自然对数的底 exp(1)
var GOLDEN_RATIO = (1 + math.sqrt(5)) / 2 ​
  • 说明: 黄金分割比
var GAMMA = 0.5772156649015329 ​
  • 说明: 欧拉常数
var EPSILON = 0.0001 ​
  • 说明: 精度误差
var APPROX = 0.001 ​
  • 说明: 约等于判定误差
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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

+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html
index 522b9bb..db33f59 100644
--- a/api/mp_math/equation.html
+++ b/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -39,7 +39,7 @@
     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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -81,7 +81,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源代码
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源代码
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -97,7 +97,7 @@
         """@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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/function.html b/api/mp_math/function.html
index 428cce7..7ba5e11 100644
--- a/api/mp_math/function.html
+++ b/api/mp_math/function.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源代码
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源代码
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 @@
     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)
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/index.html b/api/mp_math/index.html
index 37d6d9b..dee8923 100644
--- a/api/mp_math/index.html
+++ b/api/mp_math/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/line.html b/api/mp_math/line.html
index 8599ff3..efbed45 100644
--- a/api/mp_math/line.html
+++ b/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.line ​
说明: 本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
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: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
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:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
  • p1: 点1
  • p2: 点2
返回: 直线
源代码
python
@classmethod
+        self.point.z = 0
@classmethod
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:
  • p1: 点1
  • p2: 点2
返回: 直线
源代码
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
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: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
+        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:
源代码
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
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 55660ca..7bf6888 100644
--- a/api/mp_math/mp_math_typing.html
+++ b/api/mp_math/mp_math_typing.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.mp_math_typing ​
说明: 本模块用于内部类型提示
var RealNumber = int | float ​
  • 类型: TypeAlias
  • 说明: 实数
var Number = RealNumber | complex ​
  • 类型: TypeAlias
  • 说明: 数
var SingleVar = TypeVar('SingleVar', bound=Number) ​
  • 说明: 单变量
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
  • 说明: 数组变量
var Var = SingleVar | ArrayVar ​
  • 类型: TypeAlias
  • 说明: 变量
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • 类型: TypeAlias
  • 说明: 一元单变量函数
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 一元数组函数
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • 类型: TypeAlias
  • 说明: 一元函数
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • 类型: TypeAlias
  • 说明: 二元单变量函数
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 二元数组函数
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • 类型: TypeAlias
  • 说明: 二元函数
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • 类型: TypeAlias
  • 说明: 三元单变量函数
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 三元数组函数
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • 类型: TypeAlias
  • 说明: 三元函数
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • 类型: TypeAlias
  • 说明: 多元单变量函数
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 多元数组函数
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • 类型: TypeAlias
  • 说明: 多元函数
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.mp_math_typing ​
说明: 本模块用于内部类型提示
var RealNumber = int | float ​
  • 类型: TypeAlias
  • 说明: 实数
var Number = RealNumber | complex ​
  • 类型: TypeAlias
  • 说明: 数
var SingleVar = TypeVar('SingleVar', bound=Number) ​
  • 说明: 单变量
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
  • 说明: 数组变量
var Var = SingleVar | ArrayVar ​
  • 类型: TypeAlias
  • 说明: 变量
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • 类型: TypeAlias
  • 说明: 一元单变量函数
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 一元数组函数
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • 类型: TypeAlias
  • 说明: 一元函数
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • 类型: TypeAlias
  • 说明: 二元单变量函数
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 二元数组函数
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • 类型: TypeAlias
  • 说明: 二元函数
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • 类型: TypeAlias
  • 说明: 三元单变量函数
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 三元数组函数
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • 类型: TypeAlias
  • 说明: 三元函数
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • 类型: TypeAlias
  • 说明: 多元单变量函数
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • 类型: TypeAlias
  • 说明: 多元数组函数
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • 类型: TypeAlias
  • 说明: 多元函数
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html
index 9b51a98..db97c97 100644
--- a/api/mp_math/plane.html
+++ b/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.plane ​
说明: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回: 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
def approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回: 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
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:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源代码
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源代码
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • other:
返回: 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • other:
返回: 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/point.html b/api/mp_math/point.html
index bc74f54..1755b52 100644
--- a/api/mp_math/point.html
+++ b/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.point ​
说明: 本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源代码
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
def self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
def __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html
index 4ccd97f..10a2794 100644
--- a/api/mp_math/segment.html
+++ b/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.mp_math.segment ​
说明: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html
index a698fa7..ad2f2cd 100644
--- a/api/mp_math/utils.html
+++ b/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,8 +28,8 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源代码
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -39,9 +39,9 @@
         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)
method raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源代码
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -51,7 +51,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -64,7 +64,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
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: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -81,7 +81,7 @@
         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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/mp_math/vector.html b/api/mp_math/vector.html
index 42fc7fb..5402d2f 100644
--- a/api/mp_math/vector.html
+++ b/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源代码
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
def __abs__(self) ​
源代码
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
def self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • other:
返回: 是否相等
源代码
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • other:
返回: 是否相等
源代码
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    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。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
源代码
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源代码
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
+    ...
def self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> '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:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源代码
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/particle/index.html b/api/particle/index.html
index 2478857..44eab28 100644
--- a/api/particle/index.html
+++ b/api/particle/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
-    
+    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/index.html b/api/presets/index.html
index acc2501..3fa76e6 100644
--- a/api/presets/index.html
+++ b/api/presets/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets ​
说明: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets ​
说明: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/model/index.html b/api/presets/model/index.html
index f2e63e5..4a87dfc 100644
--- a/api/presets/model/index.html
+++ b/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/assets/en_api_mp_math_angle.md.DI0aMl64.js b/assets/api_mp_math_angle.md.vKQLLqTS.js
similarity index 56%
rename from assets/en_api_mp_math_angle.md.DI0aMl64.js
rename to assets/api_mp_math_angle.md.vKQLLqTS.js
index f2fd506..31fd76e 100644
--- a/assets/en_api_mp_math_angle.md.DI0aMl64.js
+++ b/assets/api_mp_math_angle.md.vKQLLqTS.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
+        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
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
python
@property
+    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
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
+    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
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
源代码
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
源代码
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
Source code
python
def __truediv__(self, other):
+    ...
def self / other ​
源代码
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,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,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_angle.md.iDErkOWa.lean.js b/assets/api_mp_math_angle.md.vKQLLqTS.lean.js
similarity index 86%
rename from assets/api_mp_math_angle.md.iDErkOWa.lean.js
rename to assets/api_mp_math_angle.md.vKQLLqTS.lean.js
index d242364..9e9de3c 100644
--- a/assets/api_mp_math_angle.md.iDErkOWa.lean.js
+++ b/assets/api_mp_math_angle.md.vKQLLqTS.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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 a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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 a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_equation.md.Bx4R1cWT.js b/assets/api_mp_math_equation.md.DpRfW_6Z.js
similarity index 68%
rename from assets/ja_api_mp_math_equation.md.Bx4R1cWT.js
rename to assets/api_mp_math_equation.md.DpRfW_6Z.js
index 26eeafe..c9e00a8 100644
--- a/assets/ja_api_mp_math_equation.md.Bx4R1cWT.js
+++ b/assets/api_mp_math_equation.md.DpRfW_6Z.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n(`
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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
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,a2 as n}from"./chunks/framework.C94oF1kp.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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,7 +62,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
戻り値: 柯里化后的函数
ソースコード
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源代码
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
diff --git a/assets/api_mp_math_equation.md.Di7kIkyq.lean.js b/assets/api_mp_math_equation.md.DpRfW_6Z.lean.js
similarity index 100%
rename from assets/api_mp_math_equation.md.Di7kIkyq.lean.js
rename to assets/api_mp_math_equation.md.DpRfW_6Z.lean.js
diff --git a/assets/api_mp_math_function.md.Cj4FyaYl.js b/assets/api_mp_math_function.md.Cj4FyaYl.js
new file mode 100644
index 0000000..e994972
--- /dev/null
+++ b/assets/api_mp_math_function.md.Cj4FyaYl.js
@@ -0,0 +1,17 @@
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),l={name:"api/mp_math/function.md"},n=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
参数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源代码
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: 三元函数
+        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/api_mp_math_function.md.roDde0nH.lean.js b/assets/api_mp_math_function.md.Cj4FyaYl.lean.js
similarity index 94%
rename from assets/api_mp_math_function.md.roDde0nH.lean.js
rename to assets/api_mp_math_function.md.Cj4FyaYl.lean.js
index c77d22b..9b33d81 100644
--- a/assets/api_mp_math_function.md.roDde0nH.lean.js
+++ b/assets/api_mp_math_function.md.Cj4FyaYl.lean.js
@@ -1 +1 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),n={name:"api/mp_math/function.md"},l=a("",4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a("",4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),l={name:"api/mp_math/function.md"},n=a("",4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a("",4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/api_mp_math_function.md.roDde0nH.js b/assets/api_mp_math_function.md.roDde0nH.js
deleted file mode 100644
index 8437b8c..0000000
--- a/assets/api_mp_math_function.md.roDde0nH.js
+++ /dev/null
@@ -1,17 +0,0 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"api/mp_math/function.md","filePath":"zh/api/mp_math/function.md"}'),n={name:"api/mp_math/function.md"},l=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
参数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源代码
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: 三元函数
-        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/en_api_mp_math_line.md.BI7jrk5A.js b/assets/api_mp_math_line.md.DPWL9O-M.js
similarity index 63%
rename from assets/en_api_mp_math_line.md.BI7jrk5A.js
rename to assets/api_mp_math_line.md.DPWL9O-M.js
index 05b7bb9..c39f908 100644
--- a/assets/en_api_mp_math_line.md.BI7jrk5A.js
+++ b/assets/api_mp_math_line.md.DPWL9O-M.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=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: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
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: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
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:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return: 直线
Source code
python
@classmethod
+        self.point.z = 0
@classmethod
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:
  • p1: 点1
  • p2: 点2
返回: 直线
源代码
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
+        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:
源代码
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),e=[l];function h(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",h]]);export{E as __pageData,c as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),p=[t];function e(h,k,r,o,d,g){return a(),i("div",null,p)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_line.md.DbfheWE4.lean.js b/assets/api_mp_math_line.md.DPWL9O-M.lean.js
similarity index 57%
rename from assets/api_mp_math_line.md.DbfheWE4.lean.js
rename to assets/api_mp_math_line.md.DPWL9O-M.lean.js
index 5f010ab..29f45da 100644
--- a/assets/api_mp_math_line.md.DbfheWE4.lean.js
+++ b/assets/api_mp_math_line.md.DPWL9O-M.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),t={name:"api/mp_math/line.md"},l=n("",107),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"api/mp_math/line.md","filePath":"zh/api/mp_math/line.md"}'),l={name:"api/mp_math/line.md"},t=n("",107),p=[t];function e(h,k,r,o,d,g){return a(),i("div",null,p)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_plane.md.C6JEigTz.js b/assets/api_mp_math_plane.md.DTAJAb0P.js
similarity index 72%
rename from assets/en_api_mp_math_plane.md.C6JEigTz.js
rename to assets/api_mp_math_plane.md.DTAJAb0P.js
index ca9c8b8..a3869df 100644
--- a/assets/en_api_mp_math_plane.md.C6JEigTz.js
+++ b/assets/api_mp_math_plane.md.DTAJAb0P.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":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 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return: 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
+    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: 另一个平面
返回: 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
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:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Return: 平面
Source code
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源代码
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • other:
返回: 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,105),h=[t];function p(e,k,r,d,o,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,105),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DLuC3Mxh.lean.js b/assets/api_mp_math_plane.md.DTAJAb0P.lean.js
similarity index 100%
rename from assets/api_mp_math_plane.md.DLuC3Mxh.lean.js
rename to assets/api_mp_math_plane.md.DTAJAb0P.lean.js
diff --git a/assets/api_mp_math_point.md.DAQFtNol.js b/assets/api_mp_math_point.md.vtgIded6.js
similarity index 64%
rename from assets/api_mp_math_point.md.DAQFtNol.js
rename to assets/api_mp_math_point.md.vtgIded6.js
index 8d71459..0929386 100644
--- a/assets/api_mp_math_point.md.DAQFtNol.js
+++ b/assets/api_mp_math_point.md.vtgIded6.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t(`
mbcp.mp_math.point ​
说明: 本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源代码
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
def self + other ​
说明: P + V -> P P + P -> P
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
说明: 判断两个点是否相等。
参数:
  • other:
源代码
python
def __eq__(self, other):
+    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:
  • other:
源代码
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
说明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
参数:
  • other:
源代码
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_point.md.DAQFtNol.lean.js b/assets/api_mp_math_point.md.vtgIded6.lean.js
similarity index 72%
rename from assets/api_mp_math_point.md.DAQFtNol.lean.js
rename to assets/api_mp_math_point.md.vtgIded6.lean.js
index 0322ca7..f1c7b94 100644
--- a/assets/api_mp_math_point.md.DAQFtNol.lean.js
+++ b/assets/api_mp_math_point.md.vtgIded6.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},h=t("",36),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":false},"headers":[],"relativePath":"api/mp_math/point.md","filePath":"zh/api/mp_math/point.md"}'),n={name:"api/mp_math/point.md"},l=t("",36),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_segment.md.CQz_FDoI.js b/assets/api_mp_math_segment.md.D-8aRB8W.js
similarity index 77%
rename from assets/api_mp_math_segment.md.CQz_FDoI.js
rename to assets/api_mp_math_segment.md.D-8aRB8W.js
index 69e900d..858fe2f 100644
--- a/assets/api_mp_math_segment.md.CQz_FDoI.js
+++ b/assets/api_mp_math_segment.md.D-8aRB8W.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n(`
mbcp.mp_math.segment ​
说明: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":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。 :param p1: :param p2:
源代码
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.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)
`,6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{F as __pageData,y as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,6),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/api_mp_math_segment.md.CQz_FDoI.lean.js b/assets/api_mp_math_segment.md.D-8aRB8W.lean.js
similarity index 58%
rename from assets/api_mp_math_segment.md.CQz_FDoI.lean.js
rename to assets/api_mp_math_segment.md.D-8aRB8W.lean.js
index a3483a7..411b9f3 100644
--- a/assets/api_mp_math_segment.md.CQz_FDoI.lean.js
+++ b/assets/api_mp_math_segment.md.D-8aRB8W.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},h=n("",6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"api/mp_math/segment.md","filePath":"zh/api/mp_math/segment.md"}'),t={name:"api/mp_math/segment.md"},p=n("",6),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/api_mp_math_utils.md.C2moaW8N.js b/assets/api_mp_math_utils.md.DaaoR634.js
similarity index 63%
rename from assets/api_mp_math_utils.md.C2moaW8N.js
rename to assets/api_mp_math_utils.md.DaaoR634.js
index 52e1927..515a6f5 100644
--- a/assets/api_mp_math_utils.md.C2moaW8N.js
+++ b/assets/api_mp_math_utils.md.DaaoR634.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,8 +9,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源代码
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源代码
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -20,9 +20,9 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源代码
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源代码
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源代码
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
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: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源代码
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -61,4 +61,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,35),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_utils.md.C2moaW8N.lean.js b/assets/api_mp_math_utils.md.DaaoR634.lean.js
similarity index 86%
rename from assets/api_mp_math_utils.md.C2moaW8N.lean.js
rename to assets/api_mp_math_utils.md.DaaoR634.lean.js
index 8ce45d9..aa06c91 100644
--- a/assets/api_mp_math_utils.md.C2moaW8N.lean.js
+++ b/assets/api_mp_math_utils.md.DaaoR634.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n("",35),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),l={name:"api/mp_math/utils.md"},t=n("",35),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_vector.md.BIkkuu3D.js b/assets/api_mp_math_vector.md.BTnPeAKR.js
similarity index 64%
rename from assets/ja_api_mp_math_vector.md.BIkkuu3D.js
rename to assets/api_mp_math_vector.md.BTnPeAKR.js
index 92128df..a376927 100644
--- a/assets/ja_api_mp_math_vector.md.BIkkuu3D.js
+++ b/assets/api_mp_math_vector.md.BTnPeAKR.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t(`
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 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),t={name:"api/mp_math/vector.md"},l=n(`
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: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
+    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
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源代码
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
+    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: 单位向量
源代码
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return self / self.length
def __abs__(self) ​
源代码
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
def self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • other:
戻り値: 是否相等
ソースコード
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • other:
返回: 是否相等
源代码
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    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。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
源代码
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源代码
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
+    ...
def self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> '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:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
`,127),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源代码
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
`,127),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_vector.md.BTnPeAKR.lean.js b/assets/api_mp_math_vector.md.BTnPeAKR.lean.js
new file mode 100644
index 0000000..43fec61
--- /dev/null
+++ b/assets/api_mp_math_vector.md.BTnPeAKR.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),t={name:"api/mp_math/vector.md"},l=n("",127),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_vector.md.BiNus8y5.lean.js b/assets/api_mp_math_vector.md.BiNus8y5.lean.js
deleted file mode 100644
index e586017..0000000
--- a/assets/api_mp_math_vector.md.BiNus8y5.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=t("",127),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/api_presets_model_index.md.CJMO-ffZ.js b/assets/api_presets_model_index.md.gO0Notp6.js
similarity index 84%
rename from assets/api_presets_model_index.md.CJMO-ffZ.js
rename to assets/api_presets_model_index.md.gO0Notp6.js
index 11bb8bb..6293b88 100644
--- a/assets/api_presets_model_index.md.CJMO-ffZ.js
+++ b/assets/api_presets_model_index.md.gO0Notp6.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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 ​
method sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/assets/api_presets_model_index.md.CJMO-ffZ.lean.js b/assets/api_presets_model_index.md.gO0Notp6.lean.js
similarity index 64%
rename from assets/api_presets_model_index.md.CJMO-ffZ.lean.js
rename to assets/api_presets_model_index.md.gO0Notp6.lean.js
index 1c76908..fdc554c 100644
--- a/assets/api_presets_model_index.md.CJMO-ffZ.lean.js
+++ b/assets/api_presets_model_index.md.gO0Notp6.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"api/presets/model/index.md","filePath":"zh/api/presets/model/index.md"}'),t={name:"api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/assets/api_mp_math_angle.md.iDErkOWa.js b/assets/en_api_mp_math_angle.md.Bu07wjnV.js
similarity index 61%
rename from assets/api_mp_math_angle.md.iDErkOWa.js
rename to assets/en_api_mp_math_angle.md.Bu07wjnV.js
index 51df1f0..3965a1b 100644
--- a/assets/api_mp_math_angle.md.iDErkOWa.js
+++ b/assets/en_api_mp_math_angle.md.Bu07wjnV.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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) ​
method __init__(self, value: float, is_radian: bool = False) ​
说明: 任意角度。
参数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源代码
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n(`
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
说明: 余角：两角的和为90°。
返回: 余角
源代码
python
@property
+        self.radian = value * PI / 180
@property
def complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
python
@property
+    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源代码
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源代码
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源代码
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源代码
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源代码
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
Source code
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
Source code
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源代码
python
def __truediv__(self, other):
+    ...
def self / other ​
Source code
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_angle.md.DI0aMl64.lean.js b/assets/en_api_mp_math_angle.md.Bu07wjnV.lean.js
similarity index 58%
rename from assets/en_api_mp_math_angle.md.DI0aMl64.lean.js
rename to assets/en_api_mp_math_angle.md.Bu07wjnV.lean.js
index 1a9c359..b67133d 100644
--- a/assets/en_api_mp_math_angle.md.DI0aMl64.lean.js
+++ b/assets/en_api_mp_math_angle.md.Bu07wjnV.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":false},"headers":[],"relativePath":"en/api/mp_math/angle.md","filePath":"en/api/mp_math/angle.md"}'),e={name:"en/api/mp_math/angle.md"},t=n("",80),l=[t];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(e,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/en_api_mp_math_equation.md.CFa2gNNX.js b/assets/en_api_mp_math_equation.md.DqlD6s-6.js
similarity index 71%
rename from assets/en_api_mp_math_equation.md.CFa2gNNX.js
rename to assets/en_api_mp_math_equation.md.DqlD6s-6.js
index 5a4e5e5..e6a66b1 100644
--- a/assets/en_api_mp_math_equation.md.CFa2gNNX.js
+++ b/assets/en_api_mp_math_equation.md.DqlD6s-6.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
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,a2 as n}from"./chunks/framework.C94oF1kp.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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,7 +62,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
Return: 柯里化后的函数
Source code
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
Return: 柯里化后的函数
Source code
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
diff --git a/assets/en_api_mp_math_equation.md.CFa2gNNX.lean.js b/assets/en_api_mp_math_equation.md.DqlD6s-6.lean.js
similarity index 100%
rename from assets/en_api_mp_math_equation.md.CFa2gNNX.lean.js
rename to assets/en_api_mp_math_equation.md.DqlD6s-6.lean.js
diff --git a/assets/en_api_mp_math_function.md.Bgn-YygZ.js b/assets/en_api_mp_math_function.md.Bgn-YygZ.js
new file mode 100644
index 0000000..af447d5
--- /dev/null
+++ b/assets/en_api_mp_math_function.md.Bgn-YygZ.js
@@ -0,0 +1,17 @@
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),n={name:"en/api/mp_math/function.md"},l=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
Arguments:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
Return: 梯度
Source code
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: 三元函数
+        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/en_api_mp_math_function.md.D5HNykIX.lean.js b/assets/en_api_mp_math_function.md.Bgn-YygZ.lean.js
similarity index 100%
rename from assets/en_api_mp_math_function.md.D5HNykIX.lean.js
rename to assets/en_api_mp_math_function.md.Bgn-YygZ.lean.js
diff --git a/assets/en_api_mp_math_function.md.D5HNykIX.js b/assets/en_api_mp_math_function.md.D5HNykIX.js
deleted file mode 100644
index e1fab56..0000000
--- a/assets/en_api_mp_math_function.md.D5HNykIX.js
+++ /dev/null
@@ -1,17 +0,0 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"en/api/mp_math/function.md","filePath":"en/api/mp_math/function.md"}'),n={name:"en/api/mp_math/function.md"},l=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
Arguments:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
Return: 梯度
Source code
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: 三元函数
-        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/ja_api_mp_math_line.md.CUb8HcBw.js b/assets/en_api_mp_math_line.md.BGq09mco.js
similarity index 61%
rename from assets/ja_api_mp_math_line.md.CUb8HcBw.js
rename to assets/en_api_mp_math_line.md.BGq09mco.js
index 281c949..c6d7568 100644
--- a/assets/ja_api_mp_math_line.md.CUb8HcBw.js
+++ b/assets/en_api_mp_math_line.md.BGq09mco.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),l={name:"en/api/mp_math/line.md"},t=n(`
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: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
def cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
  • p1: 点1
  • p2: 点2
戻り値: 直线
ソースコード
python
@classmethod
+        self.point.z = 0
@classmethod
def from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return: 直线
Source code
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
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: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
+        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:
Source code
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),e=[t];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const c=s(l,[["render",p]]);export{E as __pageData,c as default};
diff --git a/assets/en_api_mp_math_line.md.BI7jrk5A.lean.js b/assets/en_api_mp_math_line.md.BGq09mco.lean.js
similarity index 58%
rename from assets/en_api_mp_math_line.md.BI7jrk5A.lean.js
rename to assets/en_api_mp_math_line.md.BGq09mco.lean.js
index 57a3677..9841c6a 100644
--- a/assets/en_api_mp_math_line.md.BI7jrk5A.lean.js
+++ b/assets/en_api_mp_math_line.md.BGq09mco.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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("",107),e=[l];function h(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",h]]);export{E as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"en/api/mp_math/line.md","filePath":"en/api/mp_math/line.md"}'),l={name:"en/api/mp_math/line.md"},t=n("",107),e=[t];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const c=s(l,[["render",p]]);export{E as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_plane.md.CzPHp-i-.js b/assets/en_api_mp_math_plane.md.C3KPGKE4.js
similarity index 72%
rename from assets/ja_api_mp_math_plane.md.CzPHp-i-.js
rename to assets/en_api_mp_math_plane.md.C3KPGKE4.js
index 161ca85..5a2f8ed 100644
--- a/assets/ja_api_mp_math_plane.md.CzPHp-i-.js
+++ b/assets/en_api_mp_math_plane.md.C3KPGKE4.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n(`
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
def approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return: 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
  • point: 平面上的一点
  • normal: 法向量
戻り値: 平面
ソースコード
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
Return: 平面
Source code
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
-    return self.cal_intersection_point3(other)
`,105),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,105),h=[t];function p(k,e,r,d,E,o){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_plane.md.C6JEigTz.lean.js b/assets/en_api_mp_math_plane.md.C3KPGKE4.lean.js
similarity index 86%
rename from assets/en_api_mp_math_plane.md.C6JEigTz.lean.js
rename to assets/en_api_mp_math_plane.md.C3KPGKE4.lean.js
index 921f178..7a6f73a 100644
--- a/assets/en_api_mp_math_plane.md.C6JEigTz.lean.js
+++ b/assets/en_api_mp_math_plane.md.C3KPGKE4.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":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("",105),h=[t];function p(e,k,r,d,o,E){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":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("",105),h=[t];function p(k,e,r,d,E,o){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_point.md.DgKVopYL.js b/assets/en_api_mp_math_point.md.D7ZdR7VM.js
similarity index 63%
rename from assets/en_api_mp_math_point.md.DgKVopYL.js
rename to assets/en_api_mp_math_point.md.D7ZdR7VM.js
index 1a81585..60064a4 100644
--- a/assets/en_api_mp_math_point.md.DgKVopYL.js
+++ b/assets/en_api_mp_math_point.md.D7ZdR7VM.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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 ​
def __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const c
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    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:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const c
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
Source code
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
def self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const c
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
+    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:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const c
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const y=s(n,[["render",e]]);export{c as __pageData,y as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),e=[l];function h(p,k,o,r,d,E){return a(),i("div",null,e)}const c=s(n,[["render",h]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_mp_math_point.md.DgKVopYL.lean.js b/assets/en_api_mp_math_point.md.D7ZdR7VM.lean.js
similarity index 55%
rename from assets/en_api_mp_math_point.md.DgKVopYL.lean.js
rename to assets/en_api_mp_math_point.md.D7ZdR7VM.lean.js
index 1b6dad3..8b54859 100644
--- a/assets/en_api_mp_math_point.md.DgKVopYL.lean.js
+++ b/assets/en_api_mp_math_point.md.D7ZdR7VM.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const c=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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("",36),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const y=s(n,[["render",e]]);export{c as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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("",36),e=[l];function h(p,k,o,r,d,E){return a(),i("div",null,e)}const c=s(n,[["render",h]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_segment.md.BZQVMFnu.js b/assets/en_api_mp_math_segment.md.DMW-YUfw.js
similarity index 81%
rename from assets/zht_api_mp_math_segment.md.BZQVMFnu.js
rename to assets/en_api_mp_math_segment.md.DMW-YUfw.js
index d4c23d6..bc304eb 100644
--- a/assets/zht_api_mp_math_segment.md.BZQVMFnu.js
+++ b/assets/en_api_mp_math_segment.md.DMW-YUfw.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n(`
mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":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。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.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)
`,6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{F as __pageData,y as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,6),h=[p];function e(l,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",e]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_segment.md.GweOoNT9.lean.js b/assets/en_api_mp_math_segment.md.DMW-YUfw.lean.js
similarity index 72%
rename from assets/en_api_mp_math_segment.md.GweOoNT9.lean.js
rename to assets/en_api_mp_math_segment.md.DMW-YUfw.lean.js
index cfa19a5..0053b23 100644
--- a/assets/en_api_mp_math_segment.md.GweOoNT9.lean.js
+++ b/assets/en_api_mp_math_segment.md.DMW-YUfw.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n("",6),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",e]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":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("",6),h=[p];function e(l,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",e]]);export{F as __pageData,y as default};
diff --git a/assets/en_api_mp_math_utils.md.VHDSe3i2.js b/assets/en_api_mp_math_utils.md.B3i5gz_2.js
similarity index 61%
rename from assets/en_api_mp_math_utils.md.VHDSe3i2.js
rename to assets/en_api_mp_math_utils.md.B3i5gz_2.js
index 8b7cd19..1bf53b6 100644
--- a/assets/en_api_mp_math_utils.md.VHDSe3i2.js
+++ b/assets/en_api_mp_math_utils.md.B3i5gz_2.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":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: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return: 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),l={name:"en/api/mp_math/utils.md"},t=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return: 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,8 +9,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
Source code
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -20,9 +20,9 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
Source code
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: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -61,4 +61,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[t];function e(p,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_utils.md.VHDSe3i2.lean.js b/assets/en_api_mp_math_utils.md.B3i5gz_2.lean.js
similarity index 58%
rename from assets/en_api_mp_math_utils.md.VHDSe3i2.lean.js
rename to assets/en_api_mp_math_utils.md.B3i5gz_2.lean.js
index d52826c..d363c07 100644
--- a/assets/en_api_mp_math_utils.md.VHDSe3i2.lean.js
+++ b/assets/en_api_mp_math_utils.md.B3i5gz_2.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":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("",35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"en/api/mp_math/utils.md","filePath":"en/api/mp_math/utils.md"}'),l={name:"en/api/mp_math/utils.md"},t=n("",35),h=[t];function e(p,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/en_api_mp_math_vector.md.BlzUS0V3.lean.js b/assets/en_api_mp_math_vector.md.BlzUS0V3.lean.js
deleted file mode 100644
index 960c528..0000000
--- a/assets/en_api_mp_math_vector.md.BlzUS0V3.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t("",127),e=[h];function l(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_mp_math_vector.md.BlzUS0V3.js b/assets/en_api_mp_math_vector.md.CgtIoM4A.js
similarity index 65%
rename from assets/en_api_mp_math_vector.md.BlzUS0V3.js
rename to assets/en_api_mp_math_vector.md.CgtIoM4A.js
index be30ddf..a4afb99 100644
--- a/assets/en_api_mp_math_vector.md.BlzUS0V3.js
+++ b/assets/en_api_mp_math_vector.md.CgtIoM4A.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),n={name:"en/api/mp_math/vector.md"},h=t(`
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 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),t={name:"en/api/mp_math/vector.md"},e=n(`
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: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    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:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
+    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
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Source code
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
def __abs__(self) ​
Source code
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
def self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • other:
Return: 是否相等
Source code
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • other:
Return: 是否相等
Source code
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
Source code
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
Source code
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
+    ...
def self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> '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:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
`,127),e=[h];function l(p,k,r,o,d,g){return a(),i("div",null,e)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
Source code
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
`,127),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_vector.md.CgtIoM4A.lean.js b/assets/en_api_mp_math_vector.md.CgtIoM4A.lean.js
new file mode 100644
index 0000000..041914c
--- /dev/null
+++ b/assets/en_api_mp_math_vector.md.CgtIoM4A.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"en/api/mp_math/vector.md","filePath":"en/api/mp_math/vector.md"}'),t={name:"en/api/mp_math/vector.md"},e=n("",127),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_presets_model_index.md.BOZde1R5.js b/assets/en_api_presets_model_index.md.pbEu-669.js
similarity index 86%
rename from assets/en_api_presets_model_index.md.BOZde1R5.js
rename to assets/en_api_presets_model_index.md.pbEu-669.js
index 208d48d..7409381 100644
--- a/assets/en_api_presets_model_index.md.BOZde1R5.js
+++ b/assets/en_api_presets_model_index.md.pbEu-669.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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 ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_presets_model_index.md.BOZde1R5.lean.js b/assets/en_api_presets_model_index.md.pbEu-669.lean.js
similarity index 87%
rename from assets/en_api_presets_model_index.md.BOZde1R5.lean.js
rename to assets/en_api_presets_model_index.md.pbEu-669.lean.js
index 59631d6..38a796b 100644
--- a/assets/en_api_presets_model_index.md.BOZde1R5.lean.js
+++ b/assets/en_api_presets_model_index.md.pbEu-669.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n("",10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"en/api/presets/model/index.md","filePath":"en/api/presets/model/index.md"}'),t={name:"en/api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,g){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_mp_math_angle.md.BHWp5-Wz.js b/assets/ja_api_mp_math_angle.md.DTK1PNuJ.js
similarity index 64%
rename from assets/zht_api_mp_math_angle.md.BHWp5-Wz.js
rename to assets/ja_api_mp_math_angle.md.DTK1PNuJ.js
index 2b3ca5c..3a65e80 100644
--- a/assets/zht_api_mp_math_angle.md.BHWp5-Wz.js
+++ b/assets/ja_api_mp_math_angle.md.DTK1PNuJ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼
python
@property
+        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
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼
python
@property
+    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
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼
python
@property
+    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
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
+    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
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
+    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
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
+    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
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
+    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
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
+    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
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
ソースコード
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
ソースコード
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源碼
python
def __truediv__(self, other):
+    ...
def self / other ​
ソースコード
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_angle.md.mNl1_TuR.lean.js b/assets/ja_api_mp_math_angle.md.DTK1PNuJ.lean.js
similarity index 82%
rename from assets/ja_api_mp_math_angle.md.mNl1_TuR.lean.js
rename to assets/ja_api_mp_math_angle.md.DTK1PNuJ.lean.js
index adc42fe..c63a8a6 100644
--- a/assets/ja_api_mp_math_angle.md.mNl1_TuR.lean.js
+++ b/assets/ja_api_mp_math_angle.md.DTK1PNuJ.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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 a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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 a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_equation.md.Di7kIkyq.js b/assets/ja_api_mp_math_equation.md.Bt8bfjRZ.js
similarity index 73%
rename from assets/api_mp_math_equation.md.Di7kIkyq.js
rename to assets/ja_api_mp_math_equation.md.Bt8bfjRZ.js
index 61c68a0..ed705c0 100644
--- a/assets/api_mp_math_equation.md.Di7kIkyq.js
+++ b/assets/ja_api_mp_math_equation.md.Bt8bfjRZ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":false},"headers":[],"relativePath":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),l={name:"api/mp_math/equation.md"},t=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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),l={name:"ja/api/mp_math/equation.md"},t=n(`
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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
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,a2 as n}from"./chunks/framework.C94oF1kp.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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
引发:
  • ValueError 无效变量类型
源代码
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,7 +62,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源代码
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
戻り値: 柯里化后的函数
ソースコード
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
diff --git a/assets/ja_api_mp_math_equation.md.Bx4R1cWT.lean.js b/assets/ja_api_mp_math_equation.md.Bt8bfjRZ.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_equation.md.Bx4R1cWT.lean.js
rename to assets/ja_api_mp_math_equation.md.Bt8bfjRZ.lean.js
diff --git a/assets/ja_api_mp_math_function.md.Bx9H66-W.js b/assets/ja_api_mp_math_function.md.Bx9H66-W.js
new file mode 100644
index 0000000..556bda8
--- /dev/null
+++ b/assets/ja_api_mp_math_function.md.Bx9H66-W.js
@@ -0,0 +1,17 @@
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),l={name:"ja/api/mp_math/function.md"},n=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
引数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
戻り値: 梯度
ソースコード
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: 三元函数
+        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/ja_api_mp_math_function.md.D1A2lXjy.lean.js b/assets/ja_api_mp_math_function.md.Bx9H66-W.lean.js
similarity index 95%
rename from assets/ja_api_mp_math_function.md.D1A2lXjy.lean.js
rename to assets/ja_api_mp_math_function.md.Bx9H66-W.lean.js
index ef9c878..6b86c70 100644
--- a/assets/ja_api_mp_math_function.md.D1A2lXjy.lean.js
+++ b/assets/ja_api_mp_math_function.md.Bx9H66-W.lean.js
@@ -1 +1 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),n={name:"ja/api/mp_math/function.md"},l=a("",4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a("",4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),l={name:"ja/api/mp_math/function.md"},n=a("",4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a("",4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/ja_api_mp_math_function.md.D1A2lXjy.js b/assets/ja_api_mp_math_function.md.D1A2lXjy.js
deleted file mode 100644
index 79abebd..0000000
--- a/assets/ja_api_mp_math_function.md.D1A2lXjy.js
+++ /dev/null
@@ -1,17 +0,0 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/function.md","filePath":"ja/api/mp_math/function.md"}'),n={name:"ja/api/mp_math/function.md"},l=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
引数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
戻り値: 梯度
ソースコード
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: 三元函数
-        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/api_mp_math_line.md.DbfheWE4.js b/assets/ja_api_mp_math_line.md.DYJV4KNE.js
similarity index 76%
rename from assets/api_mp_math_line.md.DbfheWE4.js
rename to assets/ja_api_mp_math_line.md.DYJV4KNE.js
index 5a9b352..6782857 100644
--- a/assets/api_mp_math_line.md.DbfheWE4.js
+++ b/assets/ja_api_mp_math_line.md.DYJV4KNE.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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 ​
method __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n(`
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: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源代码
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
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: 另一条直线
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 另一条直线
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
说明: 计算直线和直线或点之间的距离。
参数:
  • other: 平行直线或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
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:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 另一条直线
返回: 交点
引发:
  • ValueError 直线平行
  • ValueError 直线不共面
源代码
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • point: 指定点
返回: 垂线
源代码
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
  • t: 参数t
返回: 点
源代码
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源代码
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    return self.point + t * self.direction
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
说明: 判断两条直线是否近似平行。
参数:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • other: 另一条直线
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • other: 另一条直线
返回: 是否共线
源代码
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • point: 点
返回: 是否在直线上
源代码
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
返回: 是否共面
源代码
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
  • p1: 点1
  • p2: 点2
返回: 直线
源代码
python
@classmethod
+        self.point.z = 0
@classmethod
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:
  • p1: 点1
  • p2: 点2
戻り値: 直线
ソースコード
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other: 另一条直线
返回: 交点
源代码
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
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: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
源代码
python
def __eq__(self, other) -> bool:
+        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:
ソースコード
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),p=[t];function e(h,k,r,o,d,g){return a(),i("div",null,p)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_line.md.CUb8HcBw.lean.js b/assets/ja_api_mp_math_line.md.DYJV4KNE.lean.js
similarity index 58%
rename from assets/ja_api_mp_math_line.md.CUb8HcBw.lean.js
rename to assets/ja_api_mp_math_line.md.DYJV4KNE.lean.js
index 69f2dae..5fb9a23 100644
--- a/assets/ja_api_mp_math_line.md.CUb8HcBw.lean.js
+++ b/assets/ja_api_mp_math_line.md.DYJV4KNE.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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("",107),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/line.md","filePath":"ja/api/mp_math/line.md"}'),l={name:"ja/api/mp_math/line.md"},t=n("",107),p=[t];function e(h,k,r,o,d,g){return a(),i("div",null,p)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DLuC3Mxh.js b/assets/ja_api_mp_math_plane.md.D-yHaxP-.js
similarity index 77%
rename from assets/api_mp_math_plane.md.DLuC3Mxh.js
rename to assets/ja_api_mp_math_plane.md.D-yHaxP-.js
index 0911194..9872d64 100644
--- a/assets/api_mp_math_plane.md.DLuC3Mxh.js
+++ b/assets/ja_api_mp_math_plane.md.D-yHaxP-.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":false},"headers":[],"relativePath":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n(`
mbcp.mp_math.plane ​
说明: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 另一个平面
返回: 是否近似相等
源代码
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
def approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • other: 另一个平面
返回: 夹角弧度
引发:
  • TypeError 不支持的类型
源代码
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
  • other: 另一个平面或点
返回: 距离
引发:
  • TypeError 不支持的类型
源代码
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
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:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 另一个平面
返回: 两平面的交线
源代码
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • other: 不与平面平行或在平面上的直线
返回: 交点
引发:
  • ValueError 平面与直线平行或重合
源代码
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
  • point: 指定点
返回: 所求平面
源代码
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 另一个平面
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 法向量
源代码
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
说明: 工厂函数 由点和法向量构造平面(点法式构造)。
参数:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源代码
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源代码
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源代码
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源代码
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • other:
返回: 不平行平面的交线，平面平行返回None
源代码
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源代码
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源代码
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
`,105),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_plane.md.CzPHp-i-.lean.js b/assets/ja_api_mp_math_plane.md.D-yHaxP-.lean.js
similarity index 100%
rename from assets/ja_api_mp_math_plane.md.CzPHp-i-.lean.js
rename to assets/ja_api_mp_math_plane.md.D-yHaxP-.lean.js
diff --git a/assets/ja_api_mp_math_point.md.1OBHSorb.js b/assets/ja_api_mp_math_point.md.DjHRkHI5.js
similarity index 62%
rename from assets/ja_api_mp_math_point.md.1OBHSorb.js
rename to assets/ja_api_mp_math_point.md.DjHRkHI5.js
index 10a18fa..b9735ff 100644
--- a/assets/ja_api_mp_math_point.md.1OBHSorb.js
+++ b/assets/ja_api_mp_math_point.md.DjHRkHI5.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
ソースコード
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
def self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
  • other:
ソースコード
python
def __eq__(self, other):
+    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:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_point.md.1OBHSorb.lean.js b/assets/ja_api_mp_math_point.md.DjHRkHI5.lean.js
similarity index 86%
rename from assets/ja_api_mp_math_point.md.1OBHSorb.lean.js
rename to assets/ja_api_mp_math_point.md.DjHRkHI5.lean.js
index ceb0b23..83beb8b 100644
--- a/assets/ja_api_mp_math_point.md.1OBHSorb.lean.js
+++ b/assets/ja_api_mp_math_point.md.DjHRkHI5.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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("",36),h=[l];function e(p,k,o,r,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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("",36),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_segment.md.Elu4YWS-.js b/assets/ja_api_mp_math_segment.md.37V8kAc1.js
similarity index 78%
rename from assets/ja_api_mp_math_segment.md.Elu4YWS-.js
rename to assets/ja_api_mp_math_segment.md.37V8kAc1.js
index ab70f79..2a61ac7 100644
--- a/assets/ja_api_mp_math_segment.md.Elu4YWS-.js
+++ b/assets/ja_api_mp_math_segment.md.37V8kAc1.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n(`
mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":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。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.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)
`,6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{F as __pageData,y as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,6),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_segment.md.Elu4YWS-.lean.js b/assets/ja_api_mp_math_segment.md.37V8kAc1.lean.js
similarity index 59%
rename from assets/ja_api_mp_math_segment.md.Elu4YWS-.lean.js
rename to assets/ja_api_mp_math_segment.md.37V8kAc1.lean.js
index 5a2fd16..399c379 100644
--- a/assets/ja_api_mp_math_segment.md.Elu4YWS-.lean.js
+++ b/assets/ja_api_mp_math_segment.md.37V8kAc1.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/segment.md","filePath":"ja/api/mp_math/segment.md"}'),t={name:"ja/api/mp_math/segment.md"},h=n("",6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":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("",6),h=[p];function l(e,k,r,d,E,g){return a(),i("div",null,h)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_utils.md.CAphuB0R.js b/assets/ja_api_mp_math_utils.md.BbdhM1tp.js
similarity index 66%
rename from assets/zht_api_mp_math_utils.md.CAphuB0R.js
rename to assets/ja_api_mp_math_utils.md.BbdhM1tp.js
index 5100857..7c674b7 100644
--- a/assets/zht_api_mp_math_utils.md.CAphuB0R.js
+++ b/assets/ja_api_mp_math_utils.md.BbdhM1tp.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),t={name:"zht/api/mp_math/utils.md"},l=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,8 +9,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -20,9 +20,9 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
ソースコード
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: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
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: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -61,4 +61,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_utils.md.DdUJsEiD.lean.js b/assets/ja_api_mp_math_utils.md.BbdhM1tp.lean.js
similarity index 86%
rename from assets/ja_api_mp_math_utils.md.DdUJsEiD.lean.js
rename to assets/ja_api_mp_math_utils.md.BbdhM1tp.lean.js
index 9543877..f674376 100644
--- a/assets/ja_api_mp_math_utils.md.DdUJsEiD.lean.js
+++ b/assets/ja_api_mp_math_utils.md.BbdhM1tp.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n("",35),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n("",35),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_vector.md.BiNus8y5.js b/assets/ja_api_mp_math_vector.md.BBVnCwJa.js
similarity index 67%
rename from assets/api_mp_math_vector.md.BiNus8y5.js
rename to assets/ja_api_mp_math_vector.md.BBVnCwJa.js
index 029bd4a..386905a 100644
--- a/assets/api_mp_math_vector.md.BiNus8y5.js
+++ b/assets/ja_api_mp_math_vector.md.BBVnCwJa.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"api/mp_math/vector.md","filePath":"zh/api/mp_math/vector.md"}'),n={name:"api/mp_math/vector.md"},h=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 ​
method __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),t={name:"ja/api/mp_math/vector.md"},l=n(`
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: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
  • other:
  • epsilon:
返回: 是否近似相等
源代码
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • other: 另一个向量
返回: 夹角
源代码
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
返回: 行列式的结果
源代码
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似平行。
参数:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源代码
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • other: 另一个向量
返回: 是否平行
源代码
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
python
def normalize(self):
+    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
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
ソースコード
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
说明: 向量的模。
返回: 模
源代码
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
说明: 获取该向量的单位向量。
返回: 单位向量
源代码
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
def __abs__(self) ​
ソースコード
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
说明: V + P -> P
V + V -> V
参数:
  • other:
源代码
python
def __add__(self, other):
+    ...
def self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • other:
返回: 是否相等
源代码
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • other:
戻り値: 是否相等
ソースコード
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :param other: :return:
源代码
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    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。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源代码
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
说明: V - P -> P
V - V -> V
参数:
  • other:
源代码
python
def __sub__(self, other):
+    ...
def self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
说明: P - V -> P
参数:
  • other:
源代码
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源代码
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • other:
源代码
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
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:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源代码
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源代码
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源代码
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 类型: Vector3
  • 说明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 类型: Vector3
  • 说明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 类型: Vector3
  • 说明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 类型: Vector3
  • 说明: z轴单位向量
`,127),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
ソースコード
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
`,127),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_vector.md.BBVnCwJa.lean.js b/assets/ja_api_mp_math_vector.md.BBVnCwJa.lean.js
new file mode 100644
index 0000000..1e17985
--- /dev/null
+++ b/assets/ja_api_mp_math_vector.md.BBVnCwJa.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),t={name:"ja/api/mp_math/vector.md"},l=n("",127),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_vector.md.BIkkuu3D.lean.js b/assets/ja_api_mp_math_vector.md.BIkkuu3D.lean.js
deleted file mode 100644
index d1736cc..0000000
--- a/assets/ja_api_mp_math_vector.md.BIkkuu3D.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/vector.md","filePath":"ja/api/mp_math/vector.md"}'),n={name:"ja/api/mp_math/vector.md"},h=t("",127),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_presets_model_index.md.DGIEt4ke.js b/assets/ja_api_presets_model_index.md.C-Ypf-qh.js
similarity index 84%
rename from assets/ja_api_presets_model_index.md.DGIEt4ke.js
rename to assets/ja_api_presets_model_index.md.C-Ypf-qh.js
index 5d13f5f..4ff335d 100644
--- a/assets/ja_api_presets_model_index.md.DGIEt4ke.js
+++ b/assets/ja_api_presets_model_index.md.C-Ypf-qh.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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 ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/assets/ja_api_presets_model_index.md.DGIEt4ke.lean.js b/assets/ja_api_presets_model_index.md.C-Ypf-qh.lean.js
similarity index 64%
rename from assets/ja_api_presets_model_index.md.DGIEt4ke.lean.js
rename to assets/ja_api_presets_model_index.md.C-Ypf-qh.lean.js
index 2a8e5fd..17ebf41 100644
--- a/assets/ja_api_presets_model_index.md.DGIEt4ke.lean.js
+++ b/assets/ja_api_presets_model_index.md.C-Ypf-qh.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"ja/api/presets/model/index.md","filePath":"ja/api/presets/model/index.md"}'),t={name:"ja/api/presets/model/index.md"},h=n("",10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_angle.md.mNl1_TuR.js b/assets/zht_api_mp_math_angle.md.lzcXwnW6.js
similarity index 58%
rename from assets/ja_api_mp_math_angle.md.mNl1_TuR.js
rename to assets/zht_api_mp_math_angle.md.lzcXwnW6.js
index f1764e4..9003c28 100644
--- a/assets/ja_api_mp_math_angle.md.mNl1_TuR.js
+++ b/assets/zht_api_mp_math_angle.md.lzcXwnW6.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード
python
def __init__(self, value: float, is_radian: bool=False):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード
python
@property
+        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
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード
python
@property
+    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
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード
python
@property
+    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
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
ソースコード
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
源碼
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
源碼
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
def self / other ​
源碼
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_angle.md.BHWp5-Wz.lean.js b/assets/zht_api_mp_math_angle.md.lzcXwnW6.lean.js
similarity index 82%
rename from assets/zht_api_mp_math_angle.md.BHWp5-Wz.lean.js
rename to assets/zht_api_mp_math_angle.md.lzcXwnW6.lean.js
index ecf0ccf..07adbfd 100644
--- a/assets/zht_api_mp_math_angle.md.BHWp5-Wz.lean.js
+++ b/assets/zht_api_mp_math_angle.md.lzcXwnW6.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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 a(),i("div",null,l)}const c=s(t,[["render",h]]);export{F as __pageData,c as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.angle","description":"","frontmatter":{"title":"mbcp.mp_math.angle","editLink":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 a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_equation.md.Da-XfzS0.js b/assets/zht_api_mp_math_equation.md.Bn6MiQ1c.js
similarity index 70%
rename from assets/zht_api_mp_math_equation.md.Da-XfzS0.js
rename to assets/zht_api_mp_math_equation.md.Bn6MiQ1c.js
index 3952e8c..893d175 100644
--- a/assets/zht_api_mp_math_equation.md.Da-XfzS0.js
+++ b/assets/zht_api_mp_math_equation.md.Bn6MiQ1c.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n(`
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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
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,a2 as n}from"./chunks/framework.C94oF1kp.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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,7 +62,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源碼
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源碼
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -77,4 +77,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,30),p=[l];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
+    return curried_func
`,30),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(l,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_equation.md.Da-XfzS0.lean.js b/assets/zht_api_mp_math_equation.md.Bn6MiQ1c.lean.js
similarity index 60%
rename from assets/zht_api_mp_math_equation.md.Da-XfzS0.lean.js
rename to assets/zht_api_mp_math_equation.md.Bn6MiQ1c.lean.js
index 6dbb689..6da5510 100644
--- a/assets/zht_api_mp_math_equation.md.Da-XfzS0.lean.js
+++ b/assets/zht_api_mp_math_equation.md.Bn6MiQ1c.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":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("",30),p=[l];function h(k,e,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,a2 as n}from"./chunks/framework.C94oF1kp.js";const u=JSON.parse('{"title":"mbcp.mp_math.equation","description":"","frontmatter":{"title":"mbcp.mp_math.equation","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/equation.md","filePath":"zht/api/mp_math/equation.md"}'),l={name:"zht/api/mp_math/equation.md"},t=n("",30),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(l,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_function.md.C6pPUbwO.js b/assets/zht_api_mp_math_function.md.C6pPUbwO.js
new file mode 100644
index 0000000..21aa198
--- /dev/null
+++ b/assets/zht_api_mp_math_function.md.C6pPUbwO.js
@@ -0,0 +1,17 @@
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),l={name:"zht/api/mp_math/function.md"},n=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
變數説明:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源碼
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: 三元函数
+        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/zht_api_mp_math_function.md.CFVTTeOW.lean.js b/assets/zht_api_mp_math_function.md.C6pPUbwO.lean.js
similarity index 95%
rename from assets/zht_api_mp_math_function.md.CFVTTeOW.lean.js
rename to assets/zht_api_mp_math_function.md.C6pPUbwO.lean.js
index 99228b7..b3cc230 100644
--- a/assets/zht_api_mp_math_function.md.CFVTTeOW.lean.js
+++ b/assets/zht_api_mp_math_function.md.C6pPUbwO.lean.js
@@ -1 +1 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),n={name:"zht/api/mp_math/function.md"},l=a("",4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a("",4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
+import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),l={name:"zht/api/mp_math/function.md"},n=a("",4),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a("",1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a("",4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[n,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(l,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/zht_api_mp_math_function.md.CFVTTeOW.js b/assets/zht_api_mp_math_function.md.CFVTTeOW.js
deleted file mode 100644
index 9480db4..0000000
--- a/assets/zht_api_mp_math_function.md.CFVTTeOW.js
+++ /dev/null
@@ -1,17 +0,0 @@
-import{_ as i,c as s,j as t,a as T,a2 as a,o as Q}from"./chunks/framework.C94oF1kp.js";const v=JSON.parse('{"title":"mbcp.mp_math.function","description":"","frontmatter":{"title":"mbcp.mp_math.function","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/function.md","filePath":"zht/api/mp_math/function.md"}'),n={name:"zht/api/mp_math/function.md"},l=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),e={class:"tip custom-block github-alert"},h=t("p",{class:"custom-block-title"},"TIP",-1),r={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},d={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},p=a('',1),o=[p],m=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("mi",null,"x"),t("mo",null,","),t("mi",null,"y"),t("mo",null,","),t("mi",null,"z"),t("mo",{stretchy:"false"},")")])],-1),k={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},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=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")")])],-1),f={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},E={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],w=t("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[t("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[t("mi",{mathvariant:"normal"},"∇"),t("mi",null,"f"),t("mo",{stretchy:"false"},"("),t("msub",null,[t("mi",null,"x"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"y"),t("mn",null,"0")]),t("mo",null,","),t("msub",null,[t("mi",null,"z"),t("mn",null,"0")]),t("mo",{stretchy:"false"},")"),t("mo",null,"="),t("mrow",{"data-mjx-texclass":"INNER"},[t("mo",{"data-mjx-texclass":"OPEN"},"("),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"x")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"y")])]),t("mo",null,","),t("mfrac",null,[t("mrow",null,[t("mi",null,"∂"),t("mi",null,"f")]),t("mrow",null,[t("mi",null,"∂"),t("mi",null,"z")])]),t("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),x=a(`
變數説明:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源碼
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: 三元函数
-        p: 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)
`,4);function L(C,H,M,Z,b,D){return Q(),s("div",null,[l,t("div",e,[h,t("p",null,[T("已知一个函数"),t("mjx-container",r,[(Q(),s("svg",d,o)),m]),T("，则其在点"),t("mjx-container",k,[(Q(),s("svg",g,y)),u]),T("处的梯度向量为: "),t("mjx-container",f,[(Q(),s("svg",E,_)),w])])]),x])}const V=i(n,[["render",L]]);export{v as __pageData,V as default};
diff --git a/assets/zht_api_mp_math_line.md.CERQpbvD.js b/assets/zht_api_mp_math_line.md.DX62bgjZ.js
similarity index 63%
rename from assets/zht_api_mp_math_line.md.CERQpbvD.js
rename to assets/zht_api_mp_math_line.md.DX62bgjZ.js
index 8113729..8038235 100644
--- a/assets/zht_api_mp_math_line.md.CERQpbvD.js
+++ b/assets/zht_api_mp_math_line.md.DX62bgjZ.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n(`
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: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
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: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
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: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -25,7 +25,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
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:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -48,7 +48,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
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:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -71,7 +71,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -79,13 +79,13 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -94,7 +94,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -102,7 +102,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -110,7 +110,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -118,7 +118,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -127,7 +127,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -140,7 +140,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
  • p1: 点1
  • p2: 点2
返回: 直线
源碼
python
@classmethod
+        self.point.z = 0
@classmethod
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:
  • p1: 点1
  • p2: 点2
返回: 直线
源碼
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -151,7 +151,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -164,7 +164,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
+        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:
源碼
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -175,4 +175,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         Returns:
 
         """
-    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),p=[t];function e(h,k,r,o,d,g){return a(),i("div",null,p)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_line.md.CERQpbvD.lean.js b/assets/zht_api_mp_math_line.md.DX62bgjZ.lean.js
similarity index 58%
rename from assets/zht_api_mp_math_line.md.CERQpbvD.lean.js
rename to assets/zht_api_mp_math_line.md.DX62bgjZ.lean.js
index 297756a..55a0c8a 100644
--- a/assets/zht_api_mp_math_line.md.CERQpbvD.lean.js
+++ b/assets/zht_api_mp_math_line.md.DX62bgjZ.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":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("",107),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.line","description":"","frontmatter":{"title":"mbcp.mp_math.line","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/line.md","filePath":"zht/api/mp_math/line.md"}'),l={name:"zht/api/mp_math/line.md"},t=n("",107),p=[t];function e(h,k,r,o,d,g){return a(),i("div",null,p)}const y=s(l,[["render",e]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.8lFm9uJ1.js b/assets/zht_api_mp_math_plane.md.DJ_9NQFz.js
similarity index 73%
rename from assets/zht_api_mp_math_plane.md.8lFm9uJ1.js
rename to assets/zht_api_mp_math_plane.md.DJ_9NQFz.js
index 157e98d..9046d88 100644
--- a/assets/zht_api_mp_math_plane.md.8lFm9uJ1.js
+++ b/assets/zht_api_mp_math_plane.md.DJ_9NQFz.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n(`
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.plane","description":"","frontmatter":{"title":"mbcp.mp_math.plane","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other: 另一个平面
返回: 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
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: 另一个平面
返回: 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
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:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
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:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -83,7 +83,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -97,7 +97,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -105,7 +105,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -113,14 +113,14 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源碼
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源碼
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -132,7 +132,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -160,7 +160,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -170,11 +170,11 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -191,6 +191,6 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
`,105),t=[h];function p(k,e,r,d,E,o){return a(),i("div",null,t)}const y=s(l,[["render",p]]);export{F as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.8lFm9uJ1.lean.js b/assets/zht_api_mp_math_plane.md.DJ_9NQFz.lean.js
similarity index 100%
rename from assets/zht_api_mp_math_plane.md.8lFm9uJ1.lean.js
rename to assets/zht_api_mp_math_plane.md.DJ_9NQFz.lean.js
diff --git a/assets/zht_api_mp_math_point.md.CH6HpvMW.js b/assets/zht_api_mp_math_point.md.D1nAiRP0.js
similarity index 62%
rename from assets/zht_api_mp_math_point.md.CH6HpvMW.js
rename to assets/zht_api_mp_math_point.md.D1nAiRP0.js
index c1ab724..006128b 100644
--- a/assets/zht_api_mp_math_point.md.CH6HpvMW.js
+++ b/assets/zht_api_mp_math_point.md.D1nAiRP0.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},h=t(`
mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -18,11 +18,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源碼
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
def self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -30,14 +30,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
+    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:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -48,4 +48,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
 
         """
     from .vector import Vector3
-    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_point.md.CH6HpvMW.lean.js b/assets/zht_api_mp_math_point.md.D1nAiRP0.lean.js
similarity index 72%
rename from assets/zht_api_mp_math_point.md.CH6HpvMW.lean.js
rename to assets/zht_api_mp_math_point.md.D1nAiRP0.lean.js
index f80dac1..6468bc9 100644
--- a/assets/zht_api_mp_math_point.md.CH6HpvMW.lean.js
+++ b/assets/zht_api_mp_math_point.md.D1nAiRP0.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/point.md","filePath":"zht/api/mp_math/point.md"}'),n={name:"zht/api/mp_math/point.md"},h=t("",36),l=[h];function e(p,k,o,r,d,E){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.point","description":"","frontmatter":{"title":"mbcp.mp_math.point","editLink":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("",36),h=[l];function e(p,k,r,o,d,E){return a(),i("div",null,h)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_segment.md.GweOoNT9.js b/assets/zht_api_mp_math_segment.md.CMRey-MG.js
similarity index 71%
rename from assets/en_api_mp_math_segment.md.GweOoNT9.js
rename to assets/zht_api_mp_math_segment.md.CMRey-MG.js
index c04bd2a..0e722a3 100644
--- a/assets/en_api_mp_math_segment.md.GweOoNT9.js
+++ b/assets/zht_api_mp_math_segment.md.CMRey-MG.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"en/api/mp_math/segment.md","filePath":"en/api/mp_math/segment.md"}'),t={name:"en/api/mp_math/segment.md"},h=n(`
mbcp.mp_math.segment ​
Description: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n(`
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。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -11,4 +11,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.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)
`,6),p=[h];function e(l,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",e]]);export{F as __pageData,y as default};
+    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_segment.md.BZQVMFnu.lean.js b/assets/zht_api_mp_math_segment.md.CMRey-MG.lean.js
similarity index 73%
rename from assets/zht_api_mp_math_segment.md.BZQVMFnu.lean.js
rename to assets/zht_api_mp_math_segment.md.CMRey-MG.lean.js
index 6a4431d..e6d60ae 100644
--- a/assets/zht_api_mp_math_segment.md.BZQVMFnu.lean.js
+++ b/assets/zht_api_mp_math_segment.md.CMRey-MG.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n("",6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{F as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.mp_math.segment","description":"","frontmatter":{"title":"mbcp.mp_math.segment","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/segment.md","filePath":"zht/api/mp_math/segment.md"}'),t={name:"zht/api/mp_math/segment.md"},h=n("",6),p=[h];function l(e,k,r,d,E,g){return a(),i("div",null,p)}const y=s(t,[["render",l]]);export{o as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_utils.md.DdUJsEiD.js b/assets/zht_api_mp_math_utils.md.BDpW2Fd4.js
similarity index 61%
rename from assets/ja_api_mp_math_utils.md.DdUJsEiD.js
rename to assets/zht_api_mp_math_utils.md.BDpW2Fd4.js
index 7bdfe21..d351925 100644
--- a/assets/ja_api_mp_math_utils.md.DdUJsEiD.js
+++ b/assets/zht_api_mp_math_utils.md.BDpW2Fd4.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"ja/api/mp_math/utils.md","filePath":"ja/api/mp_math/utils.md"}'),l={name:"ja/api/mp_math/utils.md"},t=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n(`
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -9,8 +9,8 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源碼
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -20,9 +20,9 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
method raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源碼
python
def __ne__(self, other):
+    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -32,7 +32,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -45,7 +45,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
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: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -61,4 +61,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
     elif x < 0:
         return f'-{abs(x)}'
     else:
-        return ''
`,35),h=[t];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_utils.md.CAphuB0R.lean.js b/assets/zht_api_mp_math_utils.md.BDpW2Fd4.lean.js
similarity index 58%
rename from assets/zht_api_mp_math_utils.md.CAphuB0R.lean.js
rename to assets/zht_api_mp_math_utils.md.BDpW2Fd4.lean.js
index 0997936..e56152e 100644
--- a/assets/zht_api_mp_math_utils.md.CAphuB0R.lean.js
+++ b/assets/zht_api_mp_math_utils.md.BDpW2Fd4.lean.js
@@ -1 +1 @@
-import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),t={name:"zht/api/mp_math/utils.md"},l=n("",35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E=JSON.parse('{"title":"mbcp.mp_math.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/utils.md","filePath":"zht/api/mp_math/utils.md"}'),l={name:"zht/api/mp_math/utils.md"},t=n("",35),h=[t];function p(e,k,r,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_vector.md.B57rC4-I.lean.js b/assets/zht_api_mp_math_vector.md.B57rC4-I.lean.js
deleted file mode 100644
index 344491f..0000000
--- a/assets/zht_api_mp_math_vector.md.B57rC4-I.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t("",127),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_vector.md.B57rC4-I.js b/assets/zht_api_mp_math_vector.md.DGVOQo3Y.js
similarity index 67%
rename from assets/zht_api_mp_math_vector.md.B57rC4-I.js
rename to assets/zht_api_mp_math_vector.md.DGVOQo3Y.js
index cefe23c..49dab6e 100644
--- a/assets/zht_api_mp_math_vector.md.B57rC4-I.js
+++ b/assets/zht_api_mp_math_vector.md.DGVOQo3Y.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),n={name:"zht/api/mp_math/vector.md"},h=t(`
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 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),t={name:"zht/api/mp_math/vector.md"},l=n(`
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: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
+    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
python
def normalize(self):
     """
         将向量归一化。
 
@@ -72,32 +72,32 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源碼
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
def __abs__(self) ​
源碼
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
def self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • other:
返回: 是否相等
源碼
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • other:
返回: 是否相等
源碼
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -120,7 +120,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    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。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -128,11 +128,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
源碼
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源碼
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
+    ...
def self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -157,11 +157,11 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> '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:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
-    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
`,127),l=[h];function e(p,k,r,o,d,g){return a(),i("div",null,l)}const F=s(n,[["render",e]]);export{y as __pageData,F as default};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源碼
python
def __neg__(self):
+    return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
`,127),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_vector.md.DGVOQo3Y.lean.js b/assets/zht_api_mp_math_vector.md.DGVOQo3Y.lean.js
new file mode 100644
index 0000000..dd2cd98
--- /dev/null
+++ b/assets/zht_api_mp_math_vector.md.DGVOQo3Y.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.mp_math.vector","description":"","frontmatter":{"title":"mbcp.mp_math.vector","editLink":false},"headers":[],"relativePath":"zht/api/mp_math/vector.md","filePath":"zht/api/mp_math/vector.md"}'),t={name:"zht/api/mp_math/vector.md"},l=n("",127),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const F=s(t,[["render",e]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.D2Dc7np7.js b/assets/zht_api_presets_model_index.md.BJWX_k6K.js
similarity index 83%
rename from assets/zht_api_presets_model_index.md.D2Dc7np7.js
rename to assets/zht_api_presets_model_index.md.BJWX_k6K.js
index 879cc9e..2b61760 100644
--- a/assets/zht_api_presets_model_index.md.D2Dc7np7.js
+++ b/assets/zht_api_presets_model_index.md.BJWX_k6K.js
@@ -1,4 +1,4 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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 ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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
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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.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,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.BJWX_k6K.lean.js b/assets/zht_api_presets_model_index.md.BJWX_k6K.lean.js
new file mode 100644
index 0000000..664af76
--- /dev/null
+++ b/assets/zht_api_presets_model_index.md.BJWX_k6K.lean.js
@@ -0,0 +1 @@
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":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,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{o as __pageData,F as default};
diff --git a/assets/zht_api_presets_model_index.md.D2Dc7np7.lean.js b/assets/zht_api_presets_model_index.md.D2Dc7np7.lean.js
deleted file mode 100644
index 13a4beb..0000000
--- a/assets/zht_api_presets_model_index.md.D2Dc7np7.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y=JSON.parse('{"title":"mbcp.presets.model","description":"","frontmatter":{"title":"mbcp.presets.model","editLink":false,"collapsed":true},"headers":[],"relativePath":"zht/api/presets/model/index.md","filePath":"zht/api/presets/model/index.md"}'),n={name:"zht/api/presets/model/index.md"},h=t("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(n,[["render",p]]);export{y as __pageData,c as default};
diff --git a/demo/index.html b/demo/index.html
index 8f0caf0..ab81d17 100644
--- a/demo/index.html
+++ b/demo/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
demo ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
demo ​
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/en/api/index.html b/en/api/index.html
index 44a40ab..4d927c0 100644
--- a/en/api/index.html
+++ b/en/api/index.html
@@ -18,7 +18,7 @@
   
   
     
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
Appearance
mbcp ​
Description: 本模块塞了一些预设的粒子生成器
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index c9dc1c7..4d30d87 100644
--- a/en/api/mp_math/angle.html
+++ b/en/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.angle ​
Description: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code
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) ​
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
+        self.radian = value * PI / 180
@property
def complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
python
@property
+    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
+    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
+    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
+    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
Source code
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
Source code
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
Source code
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
Source code
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
Source code
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
Source code
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
Source code
python
def __truediv__(self, other):
+    ...
def self / other ​
Source code
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html
index cb13e4d..67de2e8 100644
--- a/en/api/mp_math/const.html
+++ b/en/api/mp_math/const.html
@@ -18,7 +18,7 @@
   
   
     
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
Appearance
mbcp.mp_math.const ​
Description: 本模块定义了一些常用的常量
var PI = math.pi ​
  • Description: 常量 π
var E = math.e ​
  • Description: 自然对数的底 exp(1)
var GOLDEN_RATIO = (1 + math.sqrt(5)) / 2 ​
  • Description: 黄金分割比
var GAMMA = 0.5772156649015329 ​
  • Description: 欧拉常数
var EPSILON = 0.0001 ​
  • Description: 精度误差
var APPROX = 0.001 ​
  • Description: 约等于判定误差
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html
index 33d6292..f80fc8d 100644
--- a/en/api/mp_math/equation.html
+++ b/en/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
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.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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -39,7 +39,7 @@
     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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
Return: 偏导函数
Raises:
  • ValueError 无效变量类型
Source code
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -81,7 +81,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
Return: 柯里化后的函数
Source code
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
Return: 柯里化后的函数
Source code
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -97,7 +97,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html
index 67619ec..6afaf93 100644
--- a/en/api/mp_math/function.html
+++ b/en/api/mp_math/function.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
Return: 梯度
Source code
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
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.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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
Return: 梯度
Source code
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 @@
     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)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html
index 56c9efa..18a459a 100644
--- a/en/api/mp_math/index.html
+++ b/en/api/mp_math/index.html
@@ -18,7 +18,7 @@
   
   
     
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
Appearance
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html
index 98f8802..d10eef1 100644
--- a/en/api/mp_math/line.html
+++ b/en/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.line ​
Description: 本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
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.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: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 另一条直线
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
def cal_distance(self, other: Line3 | Point3) -> float ​
Description: 计算直线和直线或点之间的距离。
Arguments:
  • other: 平行直线或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 另一条直线
Return: 交点
Raises:
  • ValueError 直线平行
  • ValueError 直线不共面
Source code
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • point: 指定点
Return: 垂线
Source code
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
Return: 点
Source code
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
Source code
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
Description: 判断两条直线是否近似平行。
Arguments:
  • other: 另一条直线
  • epsilon: 误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • other: 另一条直线
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • other: 另一条直线
Return: 是否共线
Source code
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • point: 点
Return: 是否在直线上
Source code
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
Return: 是否共面
Source code
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return: 直线
Source code
python
@classmethod
+        self.point.z = 0
@classmethod
def from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • p1: 点1
  • p2: 点2
Return: 直线
Source code
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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: 另一条直线
Return: 交点
Source code
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
Source code
python
def __eq__(self, other) -> bool:
+        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:
Source code
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html
index 0fe9850..d794901 100644
--- a/en/api/mp_math/mp_math_typing.html
+++ b/en/api/mp_math/mp_math_typing.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
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.mp_math_typing ​
Description: 本模块用于内部类型提示
var RealNumber = int | float ​
  • Type: TypeAlias
  • Description: 实数
var Number = RealNumber | complex ​
  • Type: TypeAlias
  • Description: 数
var SingleVar = TypeVar('SingleVar', bound=Number) ​
  • Description: 单变量
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
  • Description: 数组变量
var Var = SingleVar | ArrayVar ​
  • Type: TypeAlias
  • Description: 变量
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • Type: TypeAlias
  • Description: 一元单变量函数
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • Type: TypeAlias
  • Description: 一元数组函数
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • Type: TypeAlias
  • Description: 一元函数
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • Type: TypeAlias
  • Description: 二元单变量函数
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • Type: TypeAlias
  • Description: 二元数组函数
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • Type: TypeAlias
  • Description: 二元函数
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • Type: TypeAlias
  • Description: 三元单变量函数
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • Type: TypeAlias
  • Description: 三元数组函数
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • Type: TypeAlias
  • Description: 三元函数
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • Type: TypeAlias
  • Description: 多元单变量函数
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • Type: TypeAlias
  • Description: 多元数组函数
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • Type: TypeAlias
  • Description: 多元函数
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html
index d4eff0d..30fadac 100644
--- a/en/api/mp_math/plane.html
+++ b/en/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.plane ​
Description: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
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.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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return: 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
def approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 另一个平面
Return: 是否近似相等
Source code
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • other: 另一个平面
Return: 夹角弧度
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • other: 另一个平面或点
Return: 距离
Raises:
  • TypeError 不支持的类型
Source code
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 另一个平面
Return: 两平面的交线
Source code
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • other: 不与平面平行或在平面上的直线
Return: 交点
Raises:
  • ValueError 平面与直线平行或重合
Source code
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
Return: 所求平面
Source code
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 另一个平面
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
Description: 平面的法向量。
Return: 法向量
Source code
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
Description: 工厂函数 由点和法向量构造平面(点法式构造)。
Arguments:
  • point: 平面上的一点
  • normal: 法向量
Return: 平面
Source code
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
Return: 平面
Source code
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
Return: 平面
Source code
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
Return: 平面
Source code
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
Return: 平面
Source code
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • other:
Return: 不平行平面的交线，平面平行返回None
Source code
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
Source code
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
Source code
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html
index be89964..e2003ec 100644
--- a/en/api/mp_math/point.html
+++ b/en/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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.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: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
Source code
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
def self + other ​
Description: P + V -> P P + P -> P
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
def __eq__(self, other) ​
Description: 判断两个点是否相等。
Arguments:
  • other:
Source code
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
Description: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
Arguments:
  • other:
Source code
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/segment.html b/en/api/mp_math/segment.html
index 4ee1140..7bc4bf5 100644
--- a/en/api/mp_math/segment.html
+++ b/en/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.segment ​
Description: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
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.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。 :param p1: :param p2:
Source code
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/utils.html b/en/api/mp_math/utils.html
index 3f06c18..96bbc04 100644
--- a/en/api/mp_math/utils.html
+++ b/en/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return: 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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.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: 待限定的值
  • min_: 最小值
  • max_: 最大值
Return: 限制后的值
Source code
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,8 +28,8 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
Source code
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
Source code
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
Source code
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -39,9 +39,9 @@
         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)
method raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
Source code
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
Source code
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
Source code
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: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -51,7 +51,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -64,7 +64,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 数
  • only_neg: 是否只返回负数的符号
Return: 符号 + - ""
Source code
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -81,7 +81,7 @@
         return f'-{abs(x)}'
     else:
         return ''
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/vector.html b/en/api/mp_math/vector.html
index cbece0e..98a57ff 100644
--- a/en/api/mp_math/vector.html
+++ b/en/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
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 ​
method __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
+    
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: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • other:
  • epsilon:
Return: 是否近似相等
Source code
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • other: 另一个向量
Return: 夹角
Source code
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
Return: 行列式的结果
Source code
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似平行。
Arguments:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
Return: 是否近似平行
Source code
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • other: 另一个向量
Return: 是否平行
Source code
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Source code
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def unit(self) -> Vector3 ​
Description: 获取该向量的单位向量。
Return: 单位向量
Source code
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
def __abs__(self) ​
Source code
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
+    ...
def self + other ​
Description: V + P -> P
V + V -> V
Arguments:
  • other:
Source code
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • other:
Return: 是否相等
Source code
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • other:
Return: 是否相等
Source code
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :param other: :return:
Source code
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
Source code
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
Source code
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
Source code
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
+    ...
def self - other ​
Description: V - P -> P
V - V -> V
Arguments:
  • other:
Source code
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
Description: P - V -> P
Arguments:
  • other:
Source code
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
Source code
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> '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:
  • other:
Source code
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
Source code
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
Source code
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
Source code
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
Source code
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • Type: Vector3
  • Description: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • Type: Vector3
  • Description: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • Type: Vector3
  • Description: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • Type: Vector3
  • Description: z轴单位向量
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/particle/index.html b/en/api/particle/index.html
index 8397aeb..3287e44 100644
--- a/en/api/particle/index.html
+++ b/en/api/particle/index.html
@@ -18,7 +18,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/presets/index.html b/en/api/presets/index.html
index bf38084..8612f65 100644
--- a/en/api/presets/index.html
+++ b/en/api/presets/index.html
@@ -18,7 +18,7 @@
   
   
     
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
Appearance
mbcp.presets ​
Description: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/presets/model/index.html b/en/api/presets/model/index.html
index 712fabb..86e63a0 100644
--- a/en/api/presets/model/index.html
+++ b/en/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
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
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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/guide/index.html b/en/guide/index.html
index 1d6b4c9..9303b4e 100644
--- a/en/guide/index.html
+++ b/en/guide/index.html
@@ -18,7 +18,7 @@
   
   
     
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
Appearance
开始不了一点 ​
∫12x111
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/index.html b/en/index.html
index 5f91acb..06c73ec 100644
--- a/en/index.html
+++ b/en/index.html
@@ -18,7 +18,7 @@
   
   
     
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
Appearance
MBCP docs
More basic change particle
A Library for Python to create particle effects and geometric figures
Get Started
API Reference
Easy to use
Through a simple interface, most of the geometric operations and particle production requirements have been achieved
Integrated
Encapsulated and integratednumpy, scipy and sympy, making script writing as simple as using Geogebra
Rich presets
Rich presets and examples, you can use it directly, and you can also customize the parameters to create your own effects
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/guide/index.html b/guide/index.html
index 4b1214a..bef4a29 100644
--- a/guide/index.html
+++ b/guide/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
开始不了一点 ​
∫12x111
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

-    
+    
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
开始不了一点 ​
∫12x111
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

+    
     
   
 
\ No newline at end of file
diff --git a/hashmap.json b/hashmap.json
index 5c5309b..58658c2 100644
--- a/hashmap.json
+++ b/hashmap.json
@@ -1 +1 @@
-{"api_index.md":"C_wESrrY","api_mp_math_angle.md":"iDErkOWa","api_mp_math_const.md":"BAf8mK4W","api_mp_math_equation.md":"Di7kIkyq","api_mp_math_function.md":"roDde0nH","api_mp_math_index.md":"BNf7bQqL","api_mp_math_line.md":"DbfheWE4","api_mp_math_mp_math_typing.md":"DlnJmkos","api_mp_math_plane.md":"DLuC3Mxh","api_mp_math_point.md":"DAQFtNol","api_mp_math_segment.md":"CQz_FDoI","api_mp_math_utils.md":"C2moaW8N","api_mp_math_vector.md":"BiNus8y5","api_particle_index.md":"Cm3Vk-es","api_presets_index.md":"CD62I2gv","api_presets_model_index.md":"CJMO-ffZ","demo_index.md":"D-H9zRUE","en_api_index.md":"Dj_5nFTt","en_api_mp_math_angle.md":"DI0aMl64","en_api_mp_math_const.md":"gGpXUShq","en_api_mp_math_equation.md":"CFa2gNNX","en_api_mp_math_function.md":"D5HNykIX","en_api_mp_math_index.md":"BEjLBMpH","en_api_mp_math_line.md":"BI7jrk5A","en_api_mp_math_mp_math_typing.md":"Dnl2aJQ4","en_api_mp_math_plane.md":"C6JEigTz","en_api_mp_math_point.md":"DgKVopYL","en_api_mp_math_segment.md":"GweOoNT9","en_api_mp_math_utils.md":"VHDSe3i2","en_api_mp_math_vector.md":"BlzUS0V3","en_api_particle_index.md":"BfyNQiRg","en_api_presets_index.md":"BWb2fpTg","en_api_presets_model_index.md":"BOZde1R5","en_guide_index.md":"DrDHTYCZ","en_index.md":"MCm69eyE","guide_index.md":"Cfmzk2IH","index.md":"BjJ9-kbE","ja_api_index.md":"CnUeuifx","ja_api_mp_math_angle.md":"mNl1_TuR","ja_api_mp_math_const.md":"DGXAgDfn","ja_api_mp_math_equation.md":"Bx4R1cWT","ja_api_mp_math_function.md":"D1A2lXjy","ja_api_mp_math_index.md":"CTZZ-p9Z","ja_api_mp_math_line.md":"CUb8HcBw","ja_api_mp_math_mp_math_typing.md":"BNymgrCT","ja_api_mp_math_plane.md":"CzPHp-i-","ja_api_mp_math_point.md":"1OBHSorb","ja_api_mp_math_segment.md":"Elu4YWS-","ja_api_mp_math_utils.md":"DdUJsEiD","ja_api_mp_math_vector.md":"BIkkuu3D","ja_api_particle_index.md":"Jr41Y3TS","ja_api_presets_index.md":"CQqdQbIZ","ja_api_presets_model_index.md":"DGIEt4ke","ja_guide_index.md":"BxGnZYwR","ja_index.md":"CtozMsIU","zht_api_index.md":"CgZH6aHQ","zht_api_mp_math_angle.md":"BHWp5-Wz","zht_api_mp_math_const.md":"xwQvuYck","zht_api_mp_math_equation.md":"Da-XfzS0","zht_api_mp_math_function.md":"CFVTTeOW","zht_api_mp_math_index.md":"mmeMMriu","zht_api_mp_math_line.md":"CERQpbvD","zht_api_mp_math_mp_math_typing.md":"CNiSnuMw","zht_api_mp_math_plane.md":"8lFm9uJ1","zht_api_mp_math_point.md":"CH6HpvMW","zht_api_mp_math_segment.md":"BZQVMFnu","zht_api_mp_math_utils.md":"CAphuB0R","zht_api_mp_math_vector.md":"B57rC4-I","zht_api_particle_index.md":"8GaGB1ul","zht_api_presets_index.md":"DvOViSox","zht_api_presets_model_index.md":"D2Dc7np7","zht_guide_index.md":"CsuFVFxu","zht_index.md":"V9U3SwDR"}
+{"api_index.md":"C_wESrrY","api_mp_math_angle.md":"vKQLLqTS","api_mp_math_const.md":"BAf8mK4W","api_mp_math_equation.md":"DpRfW_6Z","api_mp_math_function.md":"Cj4FyaYl","api_mp_math_index.md":"BNf7bQqL","api_mp_math_line.md":"DPWL9O-M","api_mp_math_mp_math_typing.md":"DlnJmkos","api_mp_math_plane.md":"DTAJAb0P","api_mp_math_point.md":"vtgIded6","api_mp_math_segment.md":"D-8aRB8W","api_mp_math_utils.md":"DaaoR634","api_mp_math_vector.md":"BTnPeAKR","api_particle_index.md":"Cm3Vk-es","api_presets_index.md":"CD62I2gv","api_presets_model_index.md":"gO0Notp6","demo_index.md":"D-H9zRUE","en_api_index.md":"Dj_5nFTt","en_api_mp_math_angle.md":"Bu07wjnV","en_api_mp_math_const.md":"gGpXUShq","en_api_mp_math_equation.md":"DqlD6s-6","en_api_mp_math_function.md":"Bgn-YygZ","en_api_mp_math_index.md":"BEjLBMpH","en_api_mp_math_line.md":"BGq09mco","en_api_mp_math_mp_math_typing.md":"Dnl2aJQ4","en_api_mp_math_plane.md":"C3KPGKE4","en_api_mp_math_point.md":"D7ZdR7VM","en_api_mp_math_segment.md":"DMW-YUfw","en_api_mp_math_utils.md":"B3i5gz_2","en_api_mp_math_vector.md":"CgtIoM4A","en_api_particle_index.md":"BfyNQiRg","en_api_presets_index.md":"BWb2fpTg","en_api_presets_model_index.md":"pbEu-669","en_guide_index.md":"DrDHTYCZ","en_index.md":"MCm69eyE","guide_index.md":"Cfmzk2IH","index.md":"BjJ9-kbE","ja_api_index.md":"CnUeuifx","ja_api_mp_math_angle.md":"DTK1PNuJ","ja_api_mp_math_const.md":"DGXAgDfn","ja_api_mp_math_equation.md":"Bt8bfjRZ","ja_api_mp_math_function.md":"Bx9H66-W","ja_api_mp_math_index.md":"CTZZ-p9Z","ja_api_mp_math_line.md":"DYJV4KNE","ja_api_mp_math_mp_math_typing.md":"BNymgrCT","ja_api_mp_math_plane.md":"D-yHaxP-","ja_api_mp_math_point.md":"DjHRkHI5","ja_api_mp_math_segment.md":"37V8kAc1","ja_api_mp_math_utils.md":"BbdhM1tp","ja_api_mp_math_vector.md":"BBVnCwJa","ja_api_particle_index.md":"Jr41Y3TS","ja_api_presets_index.md":"CQqdQbIZ","ja_api_presets_model_index.md":"C-Ypf-qh","ja_guide_index.md":"BxGnZYwR","ja_index.md":"CtozMsIU","zht_api_index.md":"CgZH6aHQ","zht_api_mp_math_angle.md":"lzcXwnW6","zht_api_mp_math_const.md":"xwQvuYck","zht_api_mp_math_equation.md":"Bn6MiQ1c","zht_api_mp_math_function.md":"C6pPUbwO","zht_api_mp_math_index.md":"mmeMMriu","zht_api_mp_math_line.md":"DX62bgjZ","zht_api_mp_math_mp_math_typing.md":"CNiSnuMw","zht_api_mp_math_plane.md":"DJ_9NQFz","zht_api_mp_math_point.md":"D1nAiRP0","zht_api_mp_math_segment.md":"CMRey-MG","zht_api_mp_math_utils.md":"BDpW2Fd4","zht_api_mp_math_vector.md":"DGVOQo3Y","zht_api_particle_index.md":"8GaGB1ul","zht_api_presets_index.md":"DvOViSox","zht_api_presets_model_index.md":"BJWX_k6K","zht_guide_index.md":"CsuFVFxu","zht_index.md":"V9U3SwDR"}
diff --git a/index.html b/index.html
index 6ca285f..f9fb065 100644
--- a/index.html
+++ b/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
MBCP docs
More basic change particle
用于几何运算和粒子制作的库
快速开始
API文档
高可用性
通过简单的接口，实现了大部分几何运算和粒子制作的需求
高集成度
对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单
内置预设
提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作
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/ja/api/index.html b/ja/api/index.html
index fcd9569..7bef607 100644
--- a/ja/api/index.html
+++ b/ja/api/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp ​
説明: 本模块塞了一些预设的粒子生成器
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp ​
説明: 本模块塞了一些预设的粒子生成器
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/angle.html b/ja/api/mp_math/angle.html
index c58f388..a7b8eab 100644
--- a/ja/api/mp_math/angle.html
+++ b/ja/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード
python
@property
+        self.radian = value * PI / 180
@property
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
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード
python
@property
+    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
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード
python
@property
+    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
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード
python
@property
+    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
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード
python
@property
+    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
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード
python
@property
+    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
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード
python
@property
+    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
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード
python
@property
+    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
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
ソースコード
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
ソースコード
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
ソースコード
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
ソースコード
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
ソースコード
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
ソースコード
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
def self / other ​
ソースコード
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html
index 4f112d0..f82d18d 100644
--- a/ja/api/mp_math/const.html
+++ b/ja/api/mp_math/const.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI = math.pi ​
  • 説明: 常量 π
var E = math.e ​
  • 説明: 自然对数的底 exp(1)
var GOLDEN_RATIO = (1 + math.sqrt(5)) / 2 ​
  • 説明: 黄金分割比
var GAMMA = 0.5772156649015329 ​
  • 説明: 欧拉常数
var EPSILON = 0.0001 ​
  • 説明: 精度误差
var APPROX = 0.001 ​
  • 説明: 约等于判定误差
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI = math.pi ​
  • 説明: 常量 π
var E = math.e ​
  • 説明: 自然对数的底 exp(1)
var GOLDEN_RATIO = (1 + math.sqrt(5)) / 2 ​
  • 説明: 黄金分割比
var GAMMA = 0.5772156649015329 ​
  • 説明: 欧拉常数
var EPSILON = 0.0001 ​
  • 説明: 精度误差
var APPROX = 0.001 ​
  • 説明: 约等于判定误差
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html
index 9886498..1c8f91e 100644
--- a/ja/api/mp_math/equation.html
+++ b/ja/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -39,7 +39,7 @@
     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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
戻り値: 偏导函数
例外:
  • ValueError 无效变量类型
ソースコード
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -81,7 +81,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
戻り値: 柯里化后的函数
ソースコード
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
戻り値: 柯里化后的函数
ソースコード
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -97,7 +97,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html
index deddb73..7b308fe 100644
--- a/ja/api/mp_math/function.html
+++ b/ja/api/mp_math/function.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
戻り値: 梯度
ソースコード
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
戻り値: 梯度
ソースコード
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 @@
     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)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html
index b95ec3b..dca66e0 100644
--- a/ja/api/mp_math/index.html
+++ b/ja/api/mp_math/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math ​
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math ​
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/line.html b/ja/api/mp_math/line.html
index 72ece41..565050c 100644
--- a/ja/api/mp_math/line.html
+++ b/ja/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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: 直线上的一点
  • direction: 直线的方向向量
ソースコード
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
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: 另一条直线
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 另一条直线
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
引数:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
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:
  • other: 平行直线或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 另一条直线
戻り値: 交点
例外:
  • ValueError 直线平行
  • ValueError 直线不共面
ソースコード
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • point: 指定点
戻り値: 垂线
ソースコード
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
戻り値: 点
ソースコード
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
ソースコード
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
引数:
  • other: 另一条直线
  • epsilon: 误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • other: 另一条直线
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • other: 另一条直线
戻り値: 是否共线
ソースコード
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • point: 点
戻り値: 是否在直线上
ソースコード
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
戻り値: 是否共面
ソースコード
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
  • p1: 点1
  • p2: 点2
戻り値: 直线
ソースコード
python
@classmethod
+        self.point.z = 0
@classmethod
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:
  • p1: 点1
  • p2: 点2
戻り値: 直线
ソースコード
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    return cls(p1, direction)
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: 另一条直线
戻り値: 交点
ソースコード
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
ソースコード
python
def __eq__(self, other) -> bool:
+        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:
ソースコード
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html
index adec204..33c907e 100644
--- a/ja/api/mp_math/mp_math_typing.html
+++ b/ja/api/mp_math/mp_math_typing.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber = int | float ​
  • タイプ: TypeAlias
  • 説明: 实数
var Number = RealNumber | complex ​
  • タイプ: TypeAlias
  • 説明: 数
var SingleVar = TypeVar('SingleVar', bound=Number) ​
  • 説明: 单变量
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
  • 説明: 数组变量
var Var = SingleVar | ArrayVar ​
  • タイプ: TypeAlias
  • 説明: 变量
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 一元单变量函数
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 一元数组函数
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • タイプ: TypeAlias
  • 説明: 一元函数
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 二元单变量函数
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 二元数组函数
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • タイプ: TypeAlias
  • 説明: 二元函数
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 三元单变量函数
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 三元数组函数
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • タイプ: TypeAlias
  • 説明: 三元函数
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 多元单变量函数
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 多元数组函数
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • タイプ: TypeAlias
  • 説明: 多元函数
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber = int | float ​
  • タイプ: TypeAlias
  • 説明: 实数
var Number = RealNumber | complex ​
  • タイプ: TypeAlias
  • 説明: 数
var SingleVar = TypeVar('SingleVar', bound=Number) ​
  • 説明: 单变量
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
  • 説明: 数组变量
var Var = SingleVar | ArrayVar ​
  • タイプ: TypeAlias
  • 説明: 变量
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 一元单变量函数
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 一元数组函数
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • タイプ: TypeAlias
  • 説明: 一元函数
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 二元单变量函数
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 二元数组函数
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • タイプ: TypeAlias
  • 説明: 二元函数
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 三元单变量函数
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 三元数组函数
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • タイプ: TypeAlias
  • 説明: 三元函数
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • タイプ: TypeAlias
  • 説明: 多元单变量函数
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • タイプ: TypeAlias
  • 説明: 多元数组函数
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • タイプ: TypeAlias
  • 説明: 多元函数
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html
index 5e2bcc5..eacc4e4 100644
--- a/ja/api/mp_math/plane.html
+++ b/ja/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
def approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 另一个平面
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • other: 另一个平面
戻り値: 夹角弧度
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
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:
  • other: 另一个平面或点
戻り値: 距离
例外:
  • TypeError 不支持的类型
ソースコード
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 另一个平面
戻り値: 两平面的交线
ソースコード
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • other: 不与平面平行或在平面上的直线
戻り値: 交点
例外:
  • ValueError 平面与直线平行或重合
ソースコード
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
戻り値: 所求平面
ソースコード
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 另一个平面
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 法向量
ソースコード
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
説明: 工厂函数 由点和法向量构造平面(点法式构造)。
引数:
  • point: 平面上的一点
  • normal: 法向量
戻り値: 平面
ソースコード
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
戻り値: 平面
ソースコード
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
戻り値: 平面
ソースコード
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
戻り値: 平面
ソースコード
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • other:
戻り値: 不平行平面的交线，平面平行返回None
ソースコード
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
ソースコード
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
ソースコード
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html
index c7a9e47..b611b91 100644
--- a/ja/api/mp_math/point.html
+++ b/ja/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
ソースコード
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
def self + other ​
説明: P + V -> P P + P -> P
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
引数:
  • other:
ソースコード
python
def __eq__(self, other):
+    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:
  • other:
ソースコード
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
引数:
  • other:
ソースコード
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html
index b6a0953..844c070 100644
--- a/ja/api/mp_math/segment.html
+++ b/ja/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html
index 7c25d8d..752c0f7 100644
--- a/ja/api/mp_math/utils.html
+++ b/ja/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.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: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,8 +28,8 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
ソースコード
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
ソースコード
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -39,9 +39,9 @@
         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)
method raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
ソースコード
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
ソースコード
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
ソースコード
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: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -51,7 +51,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -64,7 +64,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
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: 数
  • only_neg: 是否只返回负数的符号
戻り値: 符号 + - ""
ソースコード
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -81,7 +81,7 @@
         return f'-{abs(x)}'
     else:
         return ''
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/mp_math/vector.html b/ja/api/mp_math/vector.html
index 634030d..b88c083 100644
--- a/ja/api/mp_math/vector.html
+++ b/ja/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
戻り値: 是否近似相等
ソースコード
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • other: 另一个向量
戻り値: 夹角
ソースコード
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
戻り値: 行列式的结果
ソースコード
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
引数:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
戻り値: 是否近似平行
ソースコード
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • other: 另一个向量
戻り値: 是否平行
ソースコード
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
python
def normalize(self):
+    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
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
ソースコード
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
ソースコード
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
説明: 向量的模。
戻り値: 模
ソースコード
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
戻り値: 单位向量
ソースコード
python
@property
+    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: 单位向量
ソースコード
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
ソースコード
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return self / self.length
def __abs__(self) ​
ソースコード
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
+    ...
def self + other ​
説明: V + P -> P
V + V -> V
引数:
  • other:
ソースコード
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • other:
戻り値: 是否相等
ソースコード
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • other:
戻り値: 是否相等
ソースコード
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    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。 :param other: :return:
ソースコード
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
ソースコード
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
+    ...
def self - other ​
説明: V - P -> P
V - V -> V
引数:
  • other:
ソースコード
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
説明: P - V -> P
引数:
  • other:
ソースコード
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
+    ...
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:
  • other:
ソースコード
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
ソースコード
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
ソースコード
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
ソースコード
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
ソースコード
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • タイプ: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • タイプ: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • タイプ: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • タイプ: Vector3
  • 説明: z轴单位向量
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html
index 50979c4..90da9ab 100644
--- a/ja/api/particle/index.html
+++ b/ja/api/particle/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.particle ​
説明: 本模块定义了粒子生成相关的工具
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.particle ​
説明: 本模块定义了粒子生成相关的工具
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html
index 8b5ea3e..e154c81 100644
--- a/ja/api/presets/index.html
+++ b/ja/api/presets/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.presets ​
説明: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.presets ​
説明: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/api/presets/model/index.html b/ja/api/presets/model/index.html
index 3b933c3..a2504ba 100644
--- a/ja/api/presets/model/index.html
+++ b/ja/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
python
@staticmethod
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/ja/guide/index.html b/ja/guide/index.html
index 17b2f07..6e22213 100644
--- a/ja/guide/index.html
+++ b/ja/guide/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
开始不了一点 ​
∫12x111
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
开始不了一点 ​
∫12x111
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/ja/index.html b/ja/index.html
index f9213c8..272acdd 100644
--- a/ja/index.html
+++ b/ja/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
MBCP docs
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
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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/index.html b/zht/api/index.html
index a08b205..5f70636 100644
--- a/zht/api/index.html
+++ b/zht/api/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp ​
説明: 本模块塞了一些预设的粒子生成器
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp ​
説明: 本模块塞了一些预设的粒子生成器
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/angle.html b/zht/api/mp_math/angle.html
index 3bdddc5..7409d62 100644
--- a/zht/api/mp_math/angle.html
+++ b/zht/api/mp_math/angle.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
method __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
變數説明:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
源碼
python
def __init__(self, value: float, is_radian: bool=False):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -27,96 +27,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property ​
method complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
返回: 余角
源碼
python
@property
+        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
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property ​
method supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
返回: 补角
源碼
python
@property
+    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
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property ​
method degree(self) -> float ​
説明: 角度。
返回: 弧度
源碼
python
@property
+    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
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property ​
method minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
返回: 最小正角度
源碼
python
@property
+    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
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property ​
method maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
返回: 最大负角度
源碼
python
@property
+    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
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property ​
method sin(self) -> float ​
説明: 正弦值。
返回: 正弦值
源碼
python
@property
+    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
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property ​
method cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
説明: 余弦值。
返回: 余弦值
源碼
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property ​
method tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
説明: 正切值。
返回: 正切值
源碼
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property ​
method cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
説明: 余切值。
返回: 余切值
源碼
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property ​
method sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
説明: 正割值。
返回: 正割值
源碼
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property ​
method csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
説明: 余割值。
返回: 余割值
源碼
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
method self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian + other.radian, is_radian=True)
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
-    return approx(self.radian, other.radian)
method self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
-    return AnyAngle(self.radian - other.radian, is_radian=True)
method self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
-    return AnyAngle(self.radian * other, is_radian=True)
@overload ​
method self / other: float => AnyAngle ​
源碼
python
@overload
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源碼
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
源碼
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
源碼
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
源碼
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload ​
method self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
源碼
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
method self / other ​
源碼
python
def __truediv__(self, other):
+    ...
def self / other ​
源碼
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/const.html b/zht/api/mp_math/const.html
index 571196d..76484cc 100644
--- a/zht/api/mp_math/const.html
+++ b/zht/api/mp_math/const.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI = math.pi ​
  • 説明: 常量 π
var E = math.e ​
  • 説明: 自然对数的底 exp(1)
var GOLDEN_RATIO = (1 + math.sqrt(5)) / 2 ​
  • 説明: 黄金分割比
var GAMMA = 0.5772156649015329 ​
  • 説明: 欧拉常数
var EPSILON = 0.0001 ​
  • 説明: 精度误差
var APPROX = 0.001 ​
  • 説明: 约等于判定误差
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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

+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/equation.html b/zht/api/mp_math/equation.html
index b86fd12..30b6bbf 100644
--- a/zht/api/mp_math/equation.html
+++ b/zht/api/mp_math/equation.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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 ​
method __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
method __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
+    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
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -39,7 +39,7 @@
     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))])
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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
+        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: 函数
  • var: 变量位置，可为整数(一阶偏导)或整数元组(高阶偏导)
  • epsilon: 偏移量
返回: 偏导函数
抛出:
  • ValueError 无效变量类型
源碼
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -81,7 +81,7 @@
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源碼
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+        raise ValueError('Invalid var type')
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:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
源碼
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -97,7 +97,7 @@
         """@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

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/function.html b/zht/api/mp_math/function.html
index 11d5766..24c6474 100644
--- a/zht/api/mp_math/function.html
+++ b/zht/api/mp_math/function.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源碼
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源碼
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 @@
     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)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/index.html b/zht/api/mp_math/index.html
index 9bae1c4..727e610 100644
--- a/zht/api/mp_math/index.html
+++ b/zht/api/mp_math/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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：
  • AnyAngle：任意角
  • CurveEquation：曲线方程
  • Line3：三维直线
  • Plane3：三维平面
  • Point3：三维点
  • Segment3：三维线段
  • Vector3：三维向量
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html
index 3dae8a5..2429d44 100644
--- a/zht/api/mp_math/line.html
+++ b/zht/api/mp_math/line.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
method __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.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: 直线上的一点
  • direction: 直线的方向向量
源碼
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -25,7 +25,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
method approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
+    self.direction = direction
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: 另一条直线
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -34,7 +34,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
method cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
+    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
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: 另一条直线
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -44,7 +44,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    return self.direction.cal_angle(other.direction)
method cal_distance(self, other: Line3 | Point3) -> float ​
説明: 计算直线和直线或点之间的距离。
變數説明:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
+    return self.direction.cal_angle(other.direction)
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:
  • other: 平行直线或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -67,7 +67,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
method cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
+        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 另一条直线
返回: 交点
抛出:
  • ValueError 直线平行
  • ValueError 直线不共面
源碼
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -82,7 +82,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
method cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
+    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
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:
  • point: 指定点
返回: 垂线
源碼
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -90,7 +90,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
method get_point(self, t: RealNumber) -> Point3 ​
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:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
+    return Line3(point, self.direction.cross(point - self.point))
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:
  • t: 参数t
返回: 点
源碼
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -98,13 +98,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
method get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
+    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: x(t), y(t), z(t)
源碼
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             x(t), y(t), z(t)
         """
-    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
method is_approx_parallel(self, other: Line3, epsilon: float = 1e-06) -> bool ​
説明: 判断两条直线是否近似平行。
變數説明:
  • other: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
+    return (lambda t: self.point.x + self.direction.x * t, lambda t: self.point.y + self.direction.y * t, lambda t: self.point.z + self.direction.z * t)
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: 另一条直线
  • epsilon: 误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -113,7 +113,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
method is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
+    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • other: 另一条直线
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -121,7 +121,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
method is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
+    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • other: 另一条直线
返回: 是否共线
源碼
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -129,7 +129,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
method is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
+    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • point: 点
返回: 是否在直线上
源碼
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -137,7 +137,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
method is_coplanar(self, other: Line3) -> bool ​
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:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
+    return (point - self.point).is_parallel(self.direction)
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:
  • other: 另一条直线
返回: 是否共面
源碼
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -146,7 +146,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
method simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼
python
def simplify(self):
+    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
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -159,7 +159,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod ​
method from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
  • p1: 点1
  • p2: 点2
返回: 直线
源碼
python
@classmethod
+        self.point.z = 0
@classmethod
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:
  • p1: 点1
  • p2: 点2
返回: 直线
源碼
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -170,7 +170,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
method __and__(self, other: Line3) -> Line3 | Point3 | None ​
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: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
+    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: 另一条直线
返回: 交点
源碼
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -183,7 +183,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
method __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
源碼
python
def __eq__(self, other) -> bool:
+        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:
源碼
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -195,7 +195,7 @@
 
         """
     return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/mp_math_typing.html b/zht/api/mp_math/mp_math_typing.html
index aa369d1..b6349c9 100644
--- a/zht/api/mp_math/mp_math_typing.html
+++ b/zht/api/mp_math/mp_math_typing.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber = int | float ​
  • 類型: TypeAlias
  • 説明: 实数
var Number = RealNumber | complex ​
  • 類型: TypeAlias
  • 説明: 数
var SingleVar = TypeVar('SingleVar', bound=Number) ​
  • 説明: 单变量
var ArrayVar = TypeVar('ArrayVar', bound=Iterable[Number]) ​
  • 説明: 数组变量
var Var = SingleVar | ArrayVar ​
  • 類型: TypeAlias
  • 説明: 变量
var OneSingleVarFunc = Callable[[SingleVar], SingleVar] ​
  • 類型: TypeAlias
  • 説明: 一元单变量函数
var OneArrayFunc = Callable[[ArrayVar], ArrayVar] ​
  • 類型: TypeAlias
  • 説明: 一元数组函数
var OneVarFunc = OneSingleVarFunc | OneArrayFunc ​
  • 類型: TypeAlias
  • 説明: 一元函数
var TwoSingleVarsFunc = Callable[[SingleVar, SingleVar], SingleVar] ​
  • 類型: TypeAlias
  • 説明: 二元单变量函数
var TwoArraysFunc = Callable[[ArrayVar, ArrayVar], ArrayVar] ​
  • 類型: TypeAlias
  • 説明: 二元数组函数
var TwoVarsFunc = TwoSingleVarsFunc | TwoArraysFunc ​
  • 類型: TypeAlias
  • 説明: 二元函数
var ThreeSingleVarsFunc = Callable[[SingleVar, SingleVar, SingleVar], SingleVar] ​
  • 類型: TypeAlias
  • 説明: 三元单变量函数
var ThreeArraysFunc = Callable[[ArrayVar, ArrayVar, ArrayVar], ArrayVar] ​
  • 類型: TypeAlias
  • 説明: 三元数组函数
var ThreeVarsFunc = ThreeSingleVarsFunc | ThreeArraysFunc ​
  • 類型: TypeAlias
  • 説明: 三元函数
var MultiSingleVarsFunc = Callable[..., SingleVar] ​
  • 類型: TypeAlias
  • 説明: 多元单变量函数
var MultiArraysFunc = Callable[..., ArrayVar] ​
  • 類型: TypeAlias
  • 説明: 多元数组函数
var MultiVarsFunc = MultiSingleVarsFunc | MultiArraysFunc ​
  • 類型: TypeAlias
  • 説明: 多元函数
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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

+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/plane.html b/zht/api/mp_math/plane.html
index a4aa312..6a51964 100644
--- a/zht/api/mp_math/plane.html
+++ b/zht/api/mp_math/plane.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
method __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.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: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -29,7 +29,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
method approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other: 另一个平面
返回: 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
+    self.d = d
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: 另一个平面
返回: 是否近似相等
源碼
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -47,7 +47,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
method cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
變數説明:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
+        return False
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:
  • other: 另一个平面
返回: 夹角弧度
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -62,7 +62,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
變數説明:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
+        raise TypeError(f'Unsupported type: {type(other)}')
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:
  • other: 另一个平面或点
返回: 距离
抛出:
  • TypeError 不支持的类型
源碼
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -77,7 +77,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
method cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
+        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
變數説明:
  • other: 另一个平面
返回: 两平面的交线
源碼
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -102,7 +102,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
method cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
+    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • other: 不与平面平行或在平面上的直线
返回: 交点
抛出:
  • ValueError 平面与直线平行或重合
源碼
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -116,7 +116,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
method cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
+    return Point3(x(t), y(t), z(t))
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:
  • point: 指定点
返回: 所求平面
源碼
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -124,7 +124,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
method is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
+    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 另一个平面
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -132,14 +132,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property ​
method normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
+    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 法向量
源碼
python
@property
 def normal(self) -> 'Vector3':
     """
         平面的法向量。
         Returns:
             法向量
         """
-    return Vector3(self.a, self.b, self.c)
@classmethod ​
method from_point_and_normal(cls, point: Point3, normal: Vector3) -> Plane3 ​
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:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源碼
python
@classmethod
+    return Vector3(self.a, self.b, self.c)
@classmethod
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:
  • point: 平面上的一点
  • normal: 法向量
返回: 平面
源碼
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -151,7 +151,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod ​
method from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
+    return cls(a, b, c, d)
@classmethod
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: 点1
  • p2: 点2
  • p3: 点3
返回: 平面
源碼
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -165,7 +165,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod ​
method from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(p1, normal)
@classmethod
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: 直线1
  • l2: 直线2
返回: 平面
源碼
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -179,7 +179,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod ​
method from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
+    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
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:
  • point: 面上一点
  • line: 面上直线，不包含点
返回: 平面
源碼
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -189,11 +189,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload ​
method __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
+    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload ​
method __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
method __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
+    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • other:
返回: 不平行平面的交线，平面平行返回None
源碼
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -210,10 +210,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
method __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
-    return self.approx(other)
method __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源碼
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源碼
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html
index 2d19188..0f079ff 100644
--- a/zht/api/mp_math/point.html
+++ b/zht/api/mp_math/point.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -37,11 +37,11 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload ​
method self + other: Vector3 => Point3 ​
源碼
python
@overload
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
@overload
def self + other: Vector3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
def self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -49,14 +49,14 @@
             other:
         Returns:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
method __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
def __eq__(self, other) ​
説明: 判断两个点是否相等。
變數説明:
  • other:
源碼
python
def __eq__(self, other):
     """
         判断两个点是否相等。
         Args:
             other:
         Returns:
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self - other: Point3 => Vector3 ​
説明: P - P -> V
P - V -> P 已在 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
+    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 :class:Vector3 中实现
變數説明:
  • other:
源碼
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -68,7 +68,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html
index 356df51..0d4a657 100644
--- a/zht/api/mp_math/segment.html
+++ b/zht/api/mp_math/segment.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
method __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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。 :param p1: :param p2:
源碼
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -31,7 +31,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html
index 08e7e58..e64c2dc 100644
--- a/zht/api/mp_math/utils.html
+++ b/zht/api/mp_math/utils.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.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: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -28,8 +28,8 @@
     Returns:
         限制后的值
     """
-    return max(min(x, max_), min_)
class Approx ​
method __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
-    self.value = value
method __eq__(self, other) ​
源碼
python
def __eq__(self, other):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源碼
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源碼
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -39,9 +39,9 @@
         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)
method raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
-    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
method __ne__(self, other) ​
源碼
python
def __ne__(self, other):
-    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源碼
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源碼
python
def __ne__(self, other):
+    return not self.__eq__(other)
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: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源碼
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     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:
@@ -51,7 +51,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
func sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
+    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -64,7 +64,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
func sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
+        return ''
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: 数
  • only_neg: 是否只返回负数的符号
返回: 符号 + - ""
源碼
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -81,7 +81,7 @@
         return f'-{abs(x)}'
     else:
         return ''
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html
index ad63774..b669081 100644
--- a/zht/api/mp_math/vector.html
+++ b/zht/api/mp_math/vector.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
method __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -27,7 +27,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
method approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    self.z = z
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:
  • other:
  • epsilon:
返回: 是否近似相等
源碼
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -37,7 +37,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
method cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
+    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • other: 另一个向量
返回: 夹角
源碼
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
method cross(self, other: Vector3) -> Vector3 ​
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:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
+    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
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:
  • other:
返回: 行列式的结果
源碼
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -65,7 +65,7 @@
         Returns:
             行列式的结果
         """
-    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
method is_approx_parallel(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似平行。
變數説明:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
+    return Vector3(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
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:
  • other: 另一个向量
  • epsilon: 允许的误差
返回: 是否近似平行
源碼
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -74,7 +74,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
method is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
+    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • other: 另一个向量
返回: 是否平行
源碼
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -82,7 +82,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
method normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
+    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
python
def normalize(self):
     """
         将向量归一化。
 
@@ -91,32 +91,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property ​
method np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源碼
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    return np.array([self.x, self.y, self.z])
@property ​
method length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
説明: 向量的模。
返回: 模
源碼
python
@property
 def length(self) -> float:
     """
         向量的模。
         Returns:
             模
         """
-    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property ​
method unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
+    return math.sqrt(self.x ** 2 + self.y ** 2 + self.z ** 2)
@property
def unit(self) -> Vector3 ​
説明: 获取该向量的单位向量。
返回: 单位向量
源碼
python
@property
 def unit(self) -> 'Vector3':
     """
         获取该向量的单位向量。
         Returns:
             单位向量
         """
-    return self / self.length
method __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload ​
method self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
def __abs__(self) ​
源碼
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
method self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
+    ...
def self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • other:
源碼
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -131,7 +131,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
method __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • other:
返回: 是否相等
源碼
python
def __eq__(self, other):
+        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • other:
返回: 是否相等
源碼
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -139,7 +139,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
method self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
+    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。 :param other: :return:
源碼
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -147,11 +147,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload ​
method self - other: Vector3 => Vector3 ​
源碼
python
@overload
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
源碼
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源碼
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
method self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
+    ...
def self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • other:
源碼
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -165,7 +165,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
method self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
+        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
説明: P - V -> P
變數説明:
  • other:
源碼
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -176,11 +176,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload ​
method self * other: Vector3 => Vector3 ​
源碼
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload ​
method self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
method self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> '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:
  • other:
源碼
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -193,18 +193,18 @@
     elif isinstance(other, (float, int)):
         return Vector3(self.x * other, self.y * other, self.z * other)
     else:
-        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
method self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
-    return self.__mul__(other)
method self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源碼
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
python
def __matmul__(self, other: 'Vector3') -> 'RealNumber':
     """
         点乘。
         Args:
             other:
         Returns:
         """
-    return self.x * other.x + self.y * other.y + self.z * other.z
method self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
-    return Vector3(self.x / other, self.y / other, self.z / other)
method - self ​
源碼
python
def __neg__(self):
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源碼
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源碼
python
def __neg__(self):
     return Vector3(-self.x, -self.y, -self.z)
var zero_vector3 = Vector3(0, 0, 0) ​
  • 類型: Vector3
  • 説明: 零向量
var x_axis = Vector3(1, 0, 0) ​
  • 類型: Vector3
  • 説明: x轴单位向量
var y_axis = Vector3(0, 1, 0) ​
  • 類型: Vector3
  • 説明: y轴单位向量
var z_axis = Vector3(0, 0, 1) ​
  • 類型: Vector3
  • 説明: z轴单位向量
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html
index 5657670..11a51e0 100644
--- a/zht/api/particle/index.html
+++ b/zht/api/particle/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
-    
+    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/presets/index.html b/zht/api/presets/index.html
index 7f7face..209a505 100644
--- a/zht/api/presets/index.html
+++ b/zht/api/presets/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.presets ​
説明: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.presets ​
説明: Copyright (C) 2020-2024 LiteyukiStudio. All Rights Reserved
@Time : 2024/8/12 下午9:12 @Author : snowykami @Email : snowykami@outlook.com @File : init.py @Software: PyCharm
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html
index a47c2e1..698ab1d 100644
--- a/zht/api/presets/model/index.html
+++ b/zht/api/presets/model/index.html
@@ -12,12 +12,12 @@
     
     
     
-    
+    
     
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod ​
method sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
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
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -35,7 +35,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/zht/guide/index.html b/zht/guide/index.html
index 991587c..bf837fe 100644
--- a/zht/guide/index.html
+++ b/zht/guide/index.html
@@ -17,8 +17,8 @@
     
   
   
-    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
开始不了一点 ​
∫12x111
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
开始不了一点 ​
∫12x111
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

+    
     
   
 
\ No newline at end of file
diff --git a/zht/index.html b/zht/index.html
index 124b40e..8fb156d 100644
--- a/zht/index.html
+++ b/zht/index.html
@@ -18,7 +18,7 @@
   
   
     
MBCP docs
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
日本語
Appearance
MBCP docs
More basic change particle
用於幾何運算和粒子製作的軟體庫
跟隨引導
API文檔
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

-    
+    
     
   
 
\ No newline at end of file