diff --git a/404.html b/404.html index 111ccae..30e4a82 100644 --- a/404.html +++ b/404.html @@ -6,7 +6,7 @@ 404 | MBCP 文档 - + @@ -16,7 +16,7 @@
- + \ No newline at end of file diff --git a/api/api.html b/api/api.html index 05dbda4..305a073 100644 --- a/api/api.html +++ b/api/api.html @@ -6,7 +6,7 @@ mbcp | MBCP 文档 - + @@ -19,7 +19,7 @@
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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/index.html b/api/index.html index 842874c..e821e53 100644 --- a/api/index.html +++ b/api/index.html @@ -6,7 +6,7 @@ mbcp | MBCP 文档 - + @@ -19,7 +19,7 @@
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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 9307fc0..b2a9291 100644 --- a/api/mp_math/angle.html +++ b/api/mp_math/angle.html @@ -6,19 +6,19 @@ mbcp.mp_math.angle | MBCP 文档 - + - + -
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mbcp.mp_math.angle ​

说明: 本模块定义了角度相关的类

class Angle ​

class AnyAngle(Angle) ​

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

说明: 任意角度。

参数:

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

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diff --git a/api/mp_math/const.html b/api/mp_math/const.html
index 697b377..eb4ddcc 100644
--- a/api/mp_math/const.html
+++ b/api/mp_math/const.html
@@ -6,7 +6,7 @@
     mbcp.mp_math.const | MBCP 文档
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
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mbcp.mp_math.const ​
说明: 本模块定义了一些常用的常量
var PI = 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

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diff --git a/api/mp_math/equation.html b/api/mp_math/equation.html
index 1bf23a2..dcbd5a7 100644
--- a/api/mp_math/equation.html
+++ b/api/mp_math/equation.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.equation | MBCP 文档
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
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mbcp.mp_math.equation ​
说明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • 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):
+    
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mbcp.mp_math.equation ​
说明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码
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
在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
参数:
  • func: 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
在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/function.html b/api/mp_math/function.html
index 63bfe46..537e647 100644
--- a/api/mp_math/function.html
+++ b/api/mp_math/function.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.function | MBCP 文档
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
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mbcp.mp_math.function ​
说明: AAA
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:
+    
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mbcp.mp_math.function ​
说明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
参数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源代码
在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -37,7 +37,7 @@
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
说明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
参数:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
示例:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
源代码
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
源代码
在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/index.html b/api/mp_math/index.html
index 58d46e9..a05c9d6 100644
--- a/api/mp_math/index.html
+++ b/api/mp_math/index.html
@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP 文档
     
     
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MBCP 文档
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mbcp.mp_math ​
说明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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

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diff --git a/api/mp_math/line.html b/api/mp_math/line.html
index 8e7ad23..6d79520 100644
--- a/api/mp_math/line.html
+++ b/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP 文档
     
     
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mbcp.mp_math.line ​
说明: 本模块定义了三维空间中的直线类
class Line3 ​
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'):
+    
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mbcp.mp_math.line ​
说明: 本模块定义了三维空间中的直线类
class Line3 ​
def __init__(self, point: Point3, direction: Vector3) ​
说明: 三维空间中的直线。由一个点和一个方向向量确定。
参数:
  • point: 直线上的一点
  • direction: 直线的方向向量
源代码
在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
说明: 计算直线和直线之间的夹角。
参数:
  • other: 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
在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    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:
+    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
在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -68,7 +68,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
说明: 计算两条直线的交点。
参数:
  • other: 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
在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -83,7 +83,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
说明: 计算直线经过指定点p的垂线。
参数:
  • 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
在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -91,7 +91,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
def get_point(self, t: RealNumber) -> Point3 ​
说明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
参数:
  • 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
在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -99,13 +99,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
说明: 获取直线的参数方程。
返回: 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
在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -114,7 +114,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
说明: 判断两条直线是否平行。
参数:
  • 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
在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -122,7 +122,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
说明: 判断两条直线是否共线。
参数:
  • 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
在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -130,7 +130,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
说明: 判断点是否在直线上。
参数:
  • 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
在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -138,7 +138,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
def is_coplanar(self, other: Line3) -> bool ​
说明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
参数:
  • 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
在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -147,7 +147,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
def simplify(self) ​
说明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源代码
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
在GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -160,7 +160,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
def from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
说明: 工厂函数 由两点构造直线。
参数:
  • 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
在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -171,7 +171,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
def __and__(self, other: Line3) -> Line3 | Point3 | None ​
说明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
参数:
  • other: 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
在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -184,7 +184,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
def __eq__(self, other) -> bool ​
说明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
参数:
  • other:
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
在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -196,7 +196,7 @@
 
         """
     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

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diff --git a/api/mp_math/mp_math.html b/api/mp_math/mp_math.html
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--- a/api/mp_math/mp_math.html
+++ b/api/mp_math/mp_math.html
@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP 文档
     
     
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mbcp.mp_math ​
说明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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

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diff --git a/api/mp_math/mp_math_typing.html b/api/mp_math/mp_math_typing.html
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--- a/api/mp_math/mp_math_typing.html
+++ b/api/mp_math/mp_math_typing.html
@@ -6,7 +6,7 @@
     mbcp.mp_math.mp_math_typing | MBCP 文档
     
     
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mbcp.mp_math.mp_math_typing ​
说明: 本模块用于内部类型提示
var RealNumber = 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

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diff --git a/api/mp_math/plane.html b/api/mp_math/plane.html
index f958de4..c8101b0 100644
--- a/api/mp_math/plane.html
+++ b/api/mp_math/plane.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.plane | MBCP 文档
     
     
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mbcp.mp_math.plane ​
说明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: 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):
+    
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mbcp.mp_math.plane ​
说明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
说明: 计算平面与平面之间的夹角。
参数:
  • 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
在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_distance(self, other: Plane3 | Point3) -> float ​
说明: 计算平面与平面或点之间的距离。
参数:
  • 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
在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
说明: 计算两平面的交线。
参数:
  • other: 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
在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -103,7 +103,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
说明: 计算平面与直线的交点。
参数:
  • 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
在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -117,7 +117,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
def cal_parallel_plane3(self, point: Point3) -> Plane3 ​
说明: 计算平行于该平面且过指定点的平面。
参数:
  • 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
在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -125,7 +125,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
说明: 判断两个平面是否平行。
参数:
  • other: 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
在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -133,14 +133,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
说明: 平面的法向量。
返回: 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
在GitHub上查看
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
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
+    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
在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -152,7 +152,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod
def from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
说明: 工厂函数 由三点构造平面。
参数:
  • p1: 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
在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -166,7 +166,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
说明: 工厂函数 由两直线构造平面。
参数:
  • l1: 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
在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -180,7 +180,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
def from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
说明: 工厂函数 由点和直线构造平面。
参数:
  • 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
在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -190,11 +190,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __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
在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源代码
在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • 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
在GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -211,10 +211,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
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':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源代码
在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源代码
在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/point.html b/api/mp_math/point.html
index 3823cd7..86247ce 100644
--- a/api/mp_math/point.html
+++ b/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP 文档
     
     
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mbcp.mp_math.point ​
说明: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
说明: 笛卡尔坐标系中的点。
参数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源代码
python
def __init__(self, x: float, y: float, z: float):
+    
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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
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • 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
在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -38,11 +38,11 @@
         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
def 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
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
说明: P + V -> P P + P -> P
参数:
  • 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
在GitHub上查看
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,14 +50,14 @@
             other:
         Returns:
         """
-    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):
+    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
在GitHub上查看
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)
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':
+    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
在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,7 +69,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/segment.html b/api/mp_math/segment.html
index fbfdab6..75fd5b6 100644
--- a/api/mp_math/segment.html
+++ b/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP 文档
     
     
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mbcp.mp_math.segment ​
说明: 本模块定义了三维空间中的线段类
class Segment3 ​
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'):
+    
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mbcp.mp_math.segment ​
说明: 本模块定义了三维空间中的线段类
class Segment3 ​
def __init__(self, p1: Point3, p2: Point3) ​
说明: 三维空间中的线段。 :param p1: :param p2:
源代码
在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -32,7 +32,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/api/mp_math/utils.html b/api/mp_math/utils.html
index de95a48..63cba0b 100644
--- a/api/mp_math/utils.html
+++ b/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP 文档
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
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mbcp.mp_math.utils ​
说明: 本模块定义了一些常用的工具函数
def clamp(x: float, min_: float, max_: float) -> float ​
说明: 区间限定函数
参数:
  • x: 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 文档
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mbcp.mp_math.utils ​
说明: 本模块定义了一些常用的工具函数
def clamp(x: float, min_: float, max_: float) -> float ​
说明: 区间限定函数
参数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源代码
在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,8 +29,8 @@
     Returns:
         限制后的值
     """
-    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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源代码
在GitHub上查看
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源代码
在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -40,9 +40,9 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
def raise_type_error(self, other) ​
源代码
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源代码
在GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源代码
在GitHub上查看
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -52,7 +52,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
说明: 获取数的符号。
参数:
  • x: 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
在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -65,7 +65,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
说明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
参数:
  • x: 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
在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -82,7 +82,7 @@
         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 c941895..460f386 100644
--- a/api/mp_math/vector.html
+++ b/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP 文档
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP 文档
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mbcp.mp_math.vector ​
说明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: 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):
+    
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mbcp.mp_math.vector ​
说明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
  • 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
在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
说明: 计算两个向量之间的夹角。
参数:
  • 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
在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • 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
在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • 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
在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
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
在GitHub上查看
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,32 +92,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源代码
在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    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
在GitHub上查看
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
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
+    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
在GitHub上查看
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
def __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
def __abs__(self) ​
源代码
在GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
说明: V + P -> P
V + V -> V
参数:
  • 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
在GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -132,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
说明: 判断两个向量是否相等。
参数:
  • 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
在GitHub上查看
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -140,7 +140,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def self + other: Point3 => Point3 ​
说明: P + V -> P
别去点那边实现了。 :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
在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -148,11 +148,11 @@
         :param other:
         :return:
         """
-    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
+    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def self - other: Vector3 => Vector3 ​
源代码
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源代码
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def self - other ​
说明: V - P -> P
V - V -> V
参数:
  • 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
在GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -166,7 +166,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
说明: P - V -> P
参数:
  • 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
在GitHub上查看
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -177,11 +177,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源代码
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源代码
在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码
在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • 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
在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -194,18 +194,18 @@
     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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源代码
在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
在GitHub上查看
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
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 self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源代码
在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源代码
在GitHub上查看
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 8685e8a..8c87a92 100644
--- a/api/particle/index.html
+++ b/api/particle/index.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP 文档
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/particle/particle.html b/api/particle/particle.html
index 35a6b58..220e8ce 100644
--- a/api/particle/particle.html
+++ b/api/particle/particle.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP 文档
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/index.html b/api/presets/index.html
index cd30ab2..51d348e 100644
--- a/api/presets/index.html
+++ b/api/presets/index.html
@@ -6,7 +6,7 @@
     mbcp.presets | MBCP 文档
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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 4cfafb3..b97727a 100644
--- a/api/presets/model/index.html
+++ b/api/presets/model/index.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP 文档
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
+    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/model/model.html b/api/presets/model/model.html
index 8d7191e..45bb898 100644
--- a/api/presets/model/model.html
+++ b/api/presets/model/model.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP 文档
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
说明: 生成球体上的点集。
参数:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源代码
python
@staticmethod
+    
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/api/presets/presets.html b/api/presets/presets.html
index af37783..560e419 100644
--- a/api/presets/presets.html
+++ b/api/presets/presets.html
@@ -6,7 +6,7 @@
     mbcp.presets | MBCP 文档
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
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/assets/api_mp_math_angle.md.vKQLLqTS.js b/assets/api_mp_math_angle.md.bQbgL5rc.js
similarity index 75%
rename from assets/api_mp_math_angle.md.vKQLLqTS.js
rename to assets/api_mp_math_angle.md.bQbgL5rc.js
index 31fd76e..7f11e61 100644
--- a/assets/api_mp_math_angle.md.vKQLLqTS.js
+++ b/assets/api_mp_math_angle.md.bQbgL5rc.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) ​
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):
+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":"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
在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as 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
def 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
在GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
说明: 补角：两角的和为180°。
返回: 补角
源代码
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
在GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
说明: 角度。
返回: 弧度
源代码
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
在GitHub上查看
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
说明: 最小正角。
返回: 最小正角度
源代码
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
在GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> AnyAngle ​
说明: 最大负角。
返回: 最大负角度
源代码
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
在GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
说明: 正弦值。
返回: 正弦值
源代码
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
在GitHub上查看
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def cos(self) -> float ​
说明: 余弦值。
返回: 余弦值
源代码
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
在GitHub上查看
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def tan(self) -> float ​
说明: 正切值。
返回: 正切值
源代码
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
在GitHub上查看
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def cot(self) -> float ​
说明: 余切值。
返回: 余切值
源代码
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
在GitHub上查看
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
说明: 正割值。
返回: 正割值
源代码
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
在GitHub上查看
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
说明: 余割值。
返回: 余割值
源代码
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
在GitHub上查看
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源代码
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
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源代码
在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
源代码
在GitHub上查看
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
源代码
在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
源代码
在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
源代码
在GitHub上查看
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
源代码
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
源代码
在GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
源代码
python
def __truediv__(self, other):
+    ...
def self / other ​
源代码
在GitHub上查看
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/api_mp_math_angle.md.vKQLLqTS.lean.js b/assets/api_mp_math_angle.md.bQbgL5rc.lean.js
similarity index 72%
rename from assets/api_mp_math_angle.md.vKQLLqTS.lean.js
rename to assets/api_mp_math_angle.md.bQbgL5rc.lean.js
index 9e9de3c..ffcb2ce 100644
--- a/assets/api_mp_math_angle.md.vKQLLqTS.lean.js
+++ b/assets/api_mp_math_angle.md.bQbgL5rc.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 E=s(t,[["render",h]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=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 F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/api_mp_math_equation.md.B2FeM0MH.lean.js b/assets/api_mp_math_equation.md.B2FeM0MH.lean.js
deleted file mode 100644
index 57f0afc..0000000
--- a/assets/api_mp_math_equation.md.B2FeM0MH.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.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("",23),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const u=s(l,[["render",h]]);export{F as __pageData,u as default};
diff --git a/assets/api_mp_math_equation.md.B2FeM0MH.js b/assets/api_mp_math_equation.md.hWRUu0yD.js
similarity index 83%
rename from assets/api_mp_math_equation.md.B2FeM0MH.js
rename to assets/api_mp_math_equation.md.hWRUu0yD.js
index be7c233..dabb675 100644
--- a/assets/api_mp_math_equation.md.B2FeM0MH.js
+++ b/assets/api_mp_math_equation.md.hWRUu0yD.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.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):
+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"}'),t={name:"api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
说明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
说明: 曲线方程。
参数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源代码
在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
说明: 计算曲线上的点。
参数:
  • *t:
  • 参数:
返回: 目标点
源代码
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
在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
说明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
参数:
  • func: 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
在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const u=s(l,[["render",h]]);export{F as __pageData,u as default};
+        raise ValueError('Invalid var type')
`,23),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};
diff --git a/assets/api_mp_math_equation.md.hWRUu0yD.lean.js b/assets/api_mp_math_equation.md.hWRUu0yD.lean.js
new file mode 100644
index 0000000..0b18e29
--- /dev/null
+++ b/assets/api_mp_math_equation.md.hWRUu0yD.lean.js
@@ -0,0 +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":"api/mp_math/equation.md","filePath":"zh/api/mp_math/equation.md"}'),t={name:"api/mp_math/equation.md"},l=n("",23),p=[l];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/api_mp_math_function.md.BnSMoIoo.js b/assets/api_mp_math_function.md.C9eBzKgT.js
similarity index 96%
rename from assets/api_mp_math_function.md.BnSMoIoo.js
rename to assets/api_mp_math_function.md.C9eBzKgT.js
index 7201cde..7c91927 100644
--- a/assets/api_mp_math_function.md.BnSMoIoo.js
+++ b/assets/api_mp_math_function.md.C9eBzKgT.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
说明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
参数:
  • 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:
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
说明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
说明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
参数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源代码
在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -17,7 +17,7 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
说明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
参数:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
示例:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
源代码
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
源代码
在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -39,4 +39,4 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+    return curried_func
`,13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/api_mp_math_function.md.BnSMoIoo.lean.js b/assets/api_mp_math_function.md.C9eBzKgT.lean.js
similarity index 98%
rename from assets/api_mp_math_function.md.BnSMoIoo.lean.js
rename to assets/api_mp_math_function.md.C9eBzKgT.lean.js
index 9270086..0b7d0ef 100644
--- a/assets/api_mp_math_function.md.BnSMoIoo.lean.js
+++ b/assets/api_mp_math_function.md.C9eBzKgT.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/api_mp_math_line.md.DPWL9O-M.js b/assets/api_mp_math_line.md.DDkzT0e0.js
similarity index 76%
rename from assets/api_mp_math_line.md.DPWL9O-M.js
rename to assets/api_mp_math_line.md.DDkzT0e0.js
index c39f908..c26762d 100644
--- a/assets/api_mp_math_line.md.DPWL9O-M.js
+++ b/assets/api_mp_math_line.md.DDkzT0e0.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"}'),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'):
+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 ​
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
在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
说明: 判断两条直线是否近似相等。
参数:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,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)
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':
+    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
在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -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)
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:
+    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
在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -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.')
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':
+        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
在GitHub上查看
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
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':
+    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
在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -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))
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':
+    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
在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -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
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]:
+    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
在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -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)
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:
+    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
在GitHub上查看
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)
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:
+    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
在GitHub上查看
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)
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:
+    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
在GitHub上查看
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)
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:
+    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
在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -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
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):
+    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
在GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -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
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
+        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
在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -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)
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':
+    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
在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -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)
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:
+        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
在GitHub上查看
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),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};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_line.md.DPWL9O-M.lean.js b/assets/api_mp_math_line.md.DDkzT0e0.lean.js
similarity index 57%
rename from assets/api_mp_math_line.md.DPWL9O-M.lean.js
rename to assets/api_mp_math_line.md.DDkzT0e0.lean.js
index 29f45da..90e72a2 100644
--- a/assets/api_mp_math_line.md.DPWL9O-M.lean.js
+++ b/assets/api_mp_math_line.md.DDkzT0e0.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"}'),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};
+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),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/api_mp_math_plane.md.DTAJAb0P.js b/assets/api_mp_math_plane.md.DCL3lFbz.js
similarity index 83%
rename from assets/api_mp_math_plane.md.DTAJAb0P.js
rename to assets/api_mp_math_plane.md.DCL3lFbz.js
index a3869df..6c2294a 100644
--- a/assets/api_mp_math_plane.md.DTAJAb0P.js
+++ b/assets/api_mp_math_plane.md.DCL3lFbz.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 ​
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):
+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.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"},t=n(`
mbcp.mp_math.plane ​
说明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
说明: 平面方程：ax + by + cz + d = 0
参数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源代码
在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
说明: 判断两个平面是否近似相等。
参数:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,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
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':
+        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
在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,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)}')
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:
+        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
在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,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)}')
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':
+        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
在GitHub上查看
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)
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':
+    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
在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -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))
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':
+    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
在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -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)
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:
+    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
在GitHub上查看
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
def 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
在GitHub上查看
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
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
+    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
在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -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
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
+    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
在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -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
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
+    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
在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -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
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
+    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
在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -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
def __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
在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源代码
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源代码
在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
说明: 取两平面的交集（人话：交线）
参数:
  • 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
在GitHub上查看
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)}'")
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};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源代码
在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源代码
在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_plane.md.DTAJAb0P.lean.js b/assets/api_mp_math_plane.md.DCL3lFbz.lean.js
similarity index 58%
rename from assets/api_mp_math_plane.md.DTAJAb0P.lean.js
rename to assets/api_mp_math_plane.md.DCL3lFbz.lean.js
index a41a37c..1398a50 100644
--- a/assets/api_mp_math_plane.md.DTAJAb0P.lean.js
+++ b/assets/api_mp_math_plane.md.DCL3lFbz.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":"api/mp_math/plane.md","filePath":"zh/api/mp_math/plane.md"}'),l={name:"api/mp_math/plane.md"},h=n("",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};
+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.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"},t=n("",105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/api_mp_math_point.md.vtgIded6.js b/assets/api_mp_math_point.md.Y0Sc19zU.js
similarity index 73%
rename from assets/api_mp_math_point.md.vtgIded6.js
rename to assets/api_mp_math_point.md.Y0Sc19zU.js
index 0929386..24efa5d 100644
--- a/assets/api_mp_math_point.md.vtgIded6.js
+++ b/assets/api_mp_math_point.md.Y0Sc19zU.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"},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):
+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
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
说明: 判断两个点是否近似相等。
参数:
  • 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
在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -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
def 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
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
说明: P + V -> P P + P -> P
参数:
  • 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
在GitHub上查看
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)
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):
+    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
在GitHub上查看
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)
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':
+    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
在GitHub上查看
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,r,o,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,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/api_mp_math_point.md.vtgIded6.lean.js b/assets/api_mp_math_point.md.Y0Sc19zU.lean.js
similarity index 72%
rename from assets/api_mp_math_point.md.vtgIded6.lean.js
rename to assets/api_mp_math_point.md.Y0Sc19zU.lean.js
index f1c7b94..223eb91 100644
--- a/assets/api_mp_math_point.md.vtgIded6.lean.js
+++ b/assets/api_mp_math_point.md.Y0Sc19zU.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"},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};
+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,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/api_mp_math_segment.md.D-8aRB8W.js b/assets/api_mp_math_segment.md.B-ptCnQ0.js
similarity index 83%
rename from assets/api_mp_math_segment.md.D-8aRB8W.js
rename to assets/api_mp_math_segment.md.B-ptCnQ0.js
index 858fe2f..15327af 100644
--- a/assets/api_mp_math_segment.md.D-8aRB8W.js
+++ b/assets/api_mp_math_segment.md.B-ptCnQ0.js
@@ -1,4 +1,4 @@
-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'):
+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"},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
在GitHub上查看
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 o
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,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};
+    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/api_mp_math_segment.md.D-8aRB8W.lean.js b/assets/api_mp_math_segment.md.B-ptCnQ0.lean.js
similarity index 58%
rename from assets/api_mp_math_segment.md.D-8aRB8W.lean.js
rename to assets/api_mp_math_segment.md.B-ptCnQ0.lean.js
index 411b9f3..eca218f 100644
--- a/assets/api_mp_math_segment.md.D-8aRB8W.lean.js
+++ b/assets/api_mp_math_segment.md.B-ptCnQ0.lean.js
@@ -1 +1 @@
-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};
+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"},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/api_mp_math_utils.md.DaaoR634.lean.js b/assets/api_mp_math_utils.md.DaaoR634.lean.js
deleted file mode 100644
index aa06c91..0000000
--- a/assets/api_mp_math_utils.md.DaaoR634.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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/api_mp_math_utils.md.DaaoR634.js b/assets/api_mp_math_utils.md.mUQ56HGQ.js
similarity index 71%
rename from assets/api_mp_math_utils.md.DaaoR634.js
rename to assets/api_mp_math_utils.md.mUQ56HGQ.js
index 515a6f5..cdceb27 100644
--- a/assets/api_mp_math_utils.md.DaaoR634.js
+++ b/assets/api_mp_math_utils.md.mUQ56HGQ.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
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:
+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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),t={name:"api/mp_math/utils.md"},l=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
在GitHub上查看
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 ​
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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源代码
在GitHub上查看
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源代码
在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -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)
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源代码
在GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源代码
在GitHub上查看
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
说明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
参数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
返回: 是否近似相等
源代码
在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -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
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:
+    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
在GitHub上查看
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 ''
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:
+        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
在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_utils.md.mUQ56HGQ.lean.js b/assets/api_mp_math_utils.md.mUQ56HGQ.lean.js
new file mode 100644
index 0000000..cfe527c
--- /dev/null
+++ b/assets/api_mp_math_utils.md.mUQ56HGQ.lean.js
@@ -0,0 +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.utils","description":"","frontmatter":{"title":"mbcp.mp_math.utils","editLink":false},"headers":[],"relativePath":"api/mp_math/utils.md","filePath":"zh/api/mp_math/utils.md"}'),t={name:"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 E=s(t,[["render",p]]);export{F as __pageData,E as default};
diff --git a/assets/api_mp_math_vector.md.BTnPeAKR.lean.js b/assets/api_mp_math_vector.md.BTnPeAKR.lean.js
deleted file mode 100644
index 43fec61..0000000
--- a/assets/api_mp_math_vector.md.BTnPeAKR.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.BTnPeAKR.js b/assets/api_mp_math_vector.md.BeAN7TkI.js
similarity index 77%
rename from assets/api_mp_math_vector.md.BTnPeAKR.js
rename to assets/api_mp_math_vector.md.BeAN7TkI.js
index a376927..18b47a2 100644
--- a/assets/api_mp_math_vector.md.BTnPeAKR.js
+++ b/assets/api_mp_math_vector.md.BeAN7TkI.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.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):
+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"},e=t(`
mbcp.mp_math.vector ​
说明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
说明: 3维向量
参数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源代码
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
说明: 判断两个向量是否近似相等。
参数:
  • 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
在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as n}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])
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':
+    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
在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
说明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
参数:
  • 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
在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as n}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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
说明: 判断两个向量是否平行。
参数:
  • 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
在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
说明: 将向量归一化。
自体归一化，不返回值。
源代码
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
在GitHub上查看
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 n}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源代码
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源代码
在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    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
在GitHub上查看
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
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
+    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
在GitHub上查看
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
def __abs__(self) ​
源代码
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码
python
@overload
+    return self / self.length
def __abs__(self) ​
源代码
在GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源代码
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源代码
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
说明: V + P -> P
V + V -> V
参数:
  • 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
在GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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):
+        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
在GitHub上查看
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 n}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)
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':
+    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
在GitHub上查看
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 n}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
def 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
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源代码
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源代码
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def self - other ​
说明: V - P -> P
V - V -> V
参数:
  • 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
在GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}"')
def 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
在GitHub上查看
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 n}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
def 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
在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源代码
在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
说明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
参数:
  • 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
在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源代码
在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
说明: 点乘。
参数:
  • other:
源代码
在GitHub上查看
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
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};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源代码
在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源代码
在GitHub上查看
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=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
diff --git a/assets/api_mp_math_vector.md.BeAN7TkI.lean.js b/assets/api_mp_math_vector.md.BeAN7TkI.lean.js
new file mode 100644
index 0000000..898e5c6
--- /dev/null
+++ b/assets/api_mp_math_vector.md.BeAN7TkI.lean.js
@@ -0,0 +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.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"},e=t("",127),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_model_index.md.gO0Notp6.js b/assets/api_presets_model_index.md.BGeoOSCd.js
similarity index 92%
rename from assets/api_presets_model_index.md.gO0Notp6.js
rename to assets/api_presets_model_index.md.BGeoOSCd.js
index 6293b88..e1d9744 100644
--- a/assets/api_presets_model_index.md.gO0Notp6.js
+++ b/assets/api_presets_model_index.md.BGeoOSCd.js
@@ -1,4 +1,4 @@
-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
+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
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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,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};
+    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/api_presets_model_index.md.gO0Notp6.lean.js b/assets/api_presets_model_index.md.BGeoOSCd.lean.js
similarity index 64%
rename from assets/api_presets_model_index.md.gO0Notp6.lean.js
rename to assets/api_presets_model_index.md.BGeoOSCd.lean.js
index fdc554c..f7f315d 100644
--- a/assets/api_presets_model_index.md.gO0Notp6.lean.js
+++ b/assets/api_presets_model_index.md.BGeoOSCd.lean.js
@@ -1 +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":"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};
+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,g){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_model_model.md.s8f68j_n.js b/assets/api_presets_model_model.md.D34eFRNH.js
similarity index 92%
rename from assets/api_presets_model_model.md.s8f68j_n.js
rename to assets/api_presets_model_model.md.D34eFRNH.js
index 549692f..42d6e85 100644
--- a/assets/api_presets_model_model.md.s8f68j_n.js
+++ b/assets/api_presets_model_model.md.D34eFRNH.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/model.md","filePath":"zh/api/presets/model/model.md"}'),t={name:"api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
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
+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/model.md","filePath":"zh/api/presets/model/model.md"}'),t={name:"api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
说明: 几何模型点集
class GeometricModels ​
@staticmethod
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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,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,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{y as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/api_presets_model_model.md.s8f68j_n.lean.js b/assets/api_presets_model_model.md.D34eFRNH.lean.js
similarity index 77%
rename from assets/api_presets_model_model.md.s8f68j_n.lean.js
rename to assets/api_presets_model_model.md.D34eFRNH.lean.js
index d72c0d9..7aba8e4 100644
--- a/assets/api_presets_model_model.md.s8f68j_n.lean.js
+++ b/assets/api_presets_model_model.md.D34eFRNH.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/model.md","filePath":"zh/api/presets/model/model.md"}'),t={name:"api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{y as __pageData,F 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":"api/presets/model/model.md","filePath":"zh/api/presets/model/model.md"}'),t={name:"api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_mp_math_angle.md.Bu07wjnV.js b/assets/en_api_mp_math_angle.md.Cj4ayIet.js
similarity index 74%
rename from assets/en_api_mp_math_angle.md.Bu07wjnV.js
rename to assets/en_api_mp_math_angle.md.Cj4ayIet.js
index 3965a1b..72307f9 100644
--- a/assets/en_api_mp_math_angle.md.Bu07wjnV.js
+++ b/assets/en_api_mp_math_angle.md.Cj4ayIet.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"}'),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):
+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
View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
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
View on GitHub
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
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
View on GitHub
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
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
View on GitHub
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
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
View on GitHub
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
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
View on GitHub
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
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
View on GitHub
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
View on GitHub
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
View on GitHub
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
View on GitHub
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
View on GitHub
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
View on GitHub
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
Source code
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
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
Source code
View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
Source code
View on GitHub
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
Source code
View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
Source code
View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
Source code
View on GitHub
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
Source code
View on GitHub
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
Source code
python
def __truediv__(self, other):
+    ...
def self / other ​
Source code
View on GitHub
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[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.Bu07wjnV.lean.js b/assets/en_api_mp_math_angle.md.Cj4ayIet.lean.js
similarity index 100%
rename from assets/en_api_mp_math_angle.md.Bu07wjnV.lean.js
rename to assets/en_api_mp_math_angle.md.Cj4ayIet.lean.js
diff --git a/assets/en_api_mp_math_equation.md.vEMIOITc.js b/assets/en_api_mp_math_equation.md.BihILJCI.js
similarity index 83%
rename from assets/en_api_mp_math_equation.md.vEMIOITc.js
rename to assets/en_api_mp_math_equation.md.BihILJCI.js
index ed2589f..8e387dc 100644
--- a/assets/en_api_mp_math_equation.md.vEMIOITc.js
+++ b/assets/en_api_mp_math_equation.md.BihILJCI.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"}'),l={name:"en/api/mp_math/equation.md"},t=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):
+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
View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,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
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, ...]:
+    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
View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,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))])
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:
+        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
View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,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')
`,23),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};
+        raise ValueError('Invalid var type')
`,23),p=[l];function h(e,k,r,E,d,g){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/en_api_mp_math_equation.md.vEMIOITc.lean.js b/assets/en_api_mp_math_equation.md.BihILJCI.lean.js
similarity index 60%
rename from assets/en_api_mp_math_equation.md.vEMIOITc.lean.js
rename to assets/en_api_mp_math_equation.md.BihILJCI.lean.js
index 82ba99e..8ef4e88 100644
--- a/assets/en_api_mp_math_equation.md.vEMIOITc.lean.js
+++ b/assets/en_api_mp_math_equation.md.BihILJCI.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":"en/api/mp_math/equation.md","filePath":"en/api/mp_math/equation.md"}'),l={name:"en/api/mp_math/equation.md"},t=n("",23),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};
+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("",23),p=[l];function h(e,k,r,E,d,g){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/en_api_mp_math_function.md.BWhqj_9Y.js b/assets/en_api_mp_math_function.md.BR29hv60.js
similarity index 95%
rename from assets/en_api_mp_math_function.md.BWhqj_9Y.js
rename to assets/en_api_mp_math_function.md.BR29hv60.js
index 0f9eb80..05b2227 100644
--- a/assets/en_api_mp_math_function.md.BWhqj_9Y.js
+++ b/assets/en_api_mp_math_function.md.BR29hv60.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"en/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
Description: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
Arguments:
  • 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:
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"en/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
Description: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
Arguments:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
Return: 梯度
Source code
View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -17,7 +17,7 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
Description: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
Arguments:
  • func: 函数
  • *args: 参数
Return: 柯里化后的函数
Examples:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
Source code
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
Source code
View on GitHub
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -39,4 +39,4 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+    return curried_func
`,13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/en_api_mp_math_function.md.BWhqj_9Y.lean.js b/assets/en_api_mp_math_function.md.BR29hv60.lean.js
similarity index 95%
rename from assets/en_api_mp_math_function.md.BWhqj_9Y.lean.js
rename to assets/en_api_mp_math_function.md.BR29hv60.lean.js
index fe66848..d78993f 100644
--- a/assets/en_api_mp_math_function.md.BWhqj_9Y.lean.js
+++ b/assets/en_api_mp_math_function.md.BR29hv60.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"en/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"en/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),o=[d],k=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,o)),k]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/en_api_mp_math_line.md.BGq09mco.js b/assets/en_api_mp_math_line.md.CIOnk8LF.js
similarity index 78%
rename from assets/en_api_mp_math_line.md.BGq09mco.js
rename to assets/en_api_mp_math_line.md.CIOnk8LF.js
index c6d7568..bec7cdc 100644
--- a/assets/en_api_mp_math_line.md.BGq09mco.js
+++ b/assets/en_api_mp_math_line.md.CIOnk8LF.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"}'),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'):
+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 ​
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
View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 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
View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,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)
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':
+    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
View on GitHub
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)
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:
+    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
View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -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.')
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':
+        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
View on GitHub
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
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':
+    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
View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -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))
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':
+    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
View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -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
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]:
+    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
View on GitHub
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)
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:
+    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
View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -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)
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:
+    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
View on GitHub
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)
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:
+    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
View on GitHub
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)
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:
+    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
View on GitHub
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)
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:
+    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
View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -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
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):
+    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
View on GitHub
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -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
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
+        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
View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -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)
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':
+    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
View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -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)
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:
+        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
View on GitHub
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=[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};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",p]]);export{E as __pageData,c as default};
diff --git a/assets/en_api_mp_math_line.md.BGq09mco.lean.js b/assets/en_api_mp_math_line.md.CIOnk8LF.lean.js
similarity index 58%
rename from assets/en_api_mp_math_line.md.BGq09mco.lean.js
rename to assets/en_api_mp_math_line.md.CIOnk8LF.lean.js
index 9841c6a..1ac2e38 100644
--- a/assets/en_api_mp_math_line.md.BGq09mco.lean.js
+++ b/assets/en_api_mp_math_line.md.CIOnk8LF.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"}'),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};
+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 p(h,k,r,o,d,g){return a(),i("div",null,e)}const c=s(t,[["render",p]]);export{E as __pageData,c as default};
diff --git a/assets/en_api_mp_math_plane.md.C3KPGKE4.js b/assets/en_api_mp_math_plane.md.Cbmy4F0P.js
similarity index 83%
rename from assets/en_api_mp_math_plane.md.C3KPGKE4.js
rename to assets/en_api_mp_math_plane.md.Cbmy4F0P.js
index 5a2f8ed..1b061b3 100644
--- a/assets/en_api_mp_math_plane.md.C3KPGKE4.js
+++ b/assets/en_api_mp_math_plane.md.Cbmy4F0P.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 ​
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):
+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.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
View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 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
View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,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
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':
+        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
View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,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)}')
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:
+        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
View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,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)}')
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':
+        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
View on GitHub
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)
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':
+    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
View on GitHub
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))
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':
+    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
View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -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)
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:
+    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
View on GitHub
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
def 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
View on GitHub
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
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
+    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
View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -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
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
+    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
View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -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
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
+    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
View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -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
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
+    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
View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -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
def __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
View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code
View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • 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
View on GitHub
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)}'")
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};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
Source code
View on GitHub
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
Source code
View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_plane.md.C3KPGKE4.lean.js b/assets/en_api_mp_math_plane.md.Cbmy4F0P.lean.js
similarity index 54%
rename from assets/en_api_mp_math_plane.md.C3KPGKE4.lean.js
rename to assets/en_api_mp_math_plane.md.Cbmy4F0P.lean.js
index 7a6f73a..7e30177 100644
--- a/assets/en_api_mp_math_plane.md.C3KPGKE4.lean.js
+++ b/assets/en_api_mp_math_plane.md.Cbmy4F0P.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(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};
+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.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,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/en_api_mp_math_point.md.D7ZdR7VM.js b/assets/en_api_mp_math_point.md.szYqVNff.js
similarity index 74%
rename from assets/en_api_mp_math_point.md.D7ZdR7VM.js
rename to assets/en_api_mp_math_point.md.szYqVNff.js
index 60064a4..6275184 100644
--- a/assets/en_api_mp_math_point.md.D7ZdR7VM.js
+++ b/assets/en_api_mp_math_point.md.szYqVNff.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":"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):
+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"},e=t(`
mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • 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
View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -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
def 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
View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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
View on GitHub
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)
def __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
View on GitHub
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)
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':
+    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
View on GitHub
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),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};
+    return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
`,36),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{c as __pageData,y as default};
diff --git a/assets/en_api_mp_math_point.md.D7ZdR7VM.lean.js b/assets/en_api_mp_math_point.md.szYqVNff.lean.js
similarity index 55%
rename from assets/en_api_mp_math_point.md.D7ZdR7VM.lean.js
rename to assets/en_api_mp_math_point.md.szYqVNff.lean.js
index 8b54859..a35f932 100644
--- a/assets/en_api_mp_math_point.md.D7ZdR7VM.lean.js
+++ b/assets/en_api_mp_math_point.md.szYqVNff.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":"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};
+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"},e=t("",36),l=[e];function h(p,k,r,o,d,g){return a(),i("div",null,l)}const y=s(n,[["render",h]]);export{c as __pageData,y as default};
diff --git a/assets/en_api_mp_math_segment.md.DMW-YUfw.js b/assets/en_api_mp_math_segment.md.CqlcAra1.js
similarity index 85%
rename from assets/en_api_mp_math_segment.md.DMW-YUfw.js
rename to assets/en_api_mp_math_segment.md.CqlcAra1.js
index bc304eb..e98d50b 100644
--- a/assets/en_api_mp_math_segment.md.DMW-YUfw.js
+++ b/assets/en_api_mp_math_segment.md.CqlcAra1.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"},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'):
+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
View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
diff --git a/assets/en_api_mp_math_segment.md.DMW-YUfw.lean.js b/assets/en_api_mp_math_segment.md.CqlcAra1.lean.js
similarity index 100%
rename from assets/en_api_mp_math_segment.md.DMW-YUfw.lean.js
rename to assets/en_api_mp_math_segment.md.CqlcAra1.lean.js
diff --git a/assets/en_api_mp_math_utils.md.B3i5gz_2.lean.js b/assets/en_api_mp_math_utils.md.B3i5gz_2.lean.js
deleted file mode 100644
index d363c07..0000000
--- a/assets/en_api_mp_math_utils.md.B3i5gz_2.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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_utils.md.B3i5gz_2.js b/assets/en_api_mp_math_utils.md.CigCGgjm.js
similarity index 72%
rename from assets/en_api_mp_math_utils.md.B3i5gz_2.js
rename to assets/en_api_mp_math_utils.md.CigCGgjm.js
index 1bf53b6..8ac33cc 100644
--- a/assets/en_api_mp_math_utils.md.B3i5gz_2.js
+++ b/assets/en_api_mp_math_utils.md.CigCGgjm.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"}'),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:
+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.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
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
View on GitHub
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 ​
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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
Source code
View on GitHub
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
Source code
View on GitHub
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -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)
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
Source code
View on GitHub
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
Source code
View on GitHub
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -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
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:
+    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
View on GitHub
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 ''
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:
+        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
View on GitHub
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 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};
+        return ''
`,35),h=[l];function e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(t,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/en_api_mp_math_utils.md.CigCGgjm.lean.js b/assets/en_api_mp_math_utils.md.CigCGgjm.lean.js
new file mode 100644
index 0000000..96881eb
--- /dev/null
+++ b/assets/en_api_mp_math_utils.md.CigCGgjm.lean.js
@@ -0,0 +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.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 e(p,k,r,o,d,g){return a(),i("div",null,h)}const E=s(t,[["render",e]]);export{F as __pageData,E as default};
diff --git a/assets/en_api_mp_math_vector.md.CgtIoM4A.js b/assets/en_api_mp_math_vector.md.CF4kCv-W.js
similarity index 78%
rename from assets/en_api_mp_math_vector.md.CgtIoM4A.js
rename to assets/en_api_mp_math_vector.md.CF4kCv-W.js
index a4afb99..084e25b 100644
--- a/assets/en_api_mp_math_vector.md.CgtIoM4A.js
+++ b/assets/en_api_mp_math_vector.md.CF4kCv-W.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.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):
+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.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"},e=t(`
mbcp.mp_math.vector ​
Description: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
Description: 3维向量
Arguments:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
Source code
View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • 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
View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as n}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])
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':
+    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
View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • 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
View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as n}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)
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:
+    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
View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • 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
View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
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
View on GitHub
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 n}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Source code
View on GitHub
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
View on GitHub
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
def 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
View on GitHub
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
def __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
def __abs__(self) ​
Source code
View on GitHub
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code
View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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
View on GitHub
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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):
+        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
View on GitHub
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 n}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)
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':
+    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
View on GitHub
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 n}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
def 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
View on GitHub
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
Source code
View on GitHub
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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
View on GitHub
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}"')
def 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
View on GitHub
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 n}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
def 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
View on GitHub
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code
View on GitHub
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • 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
View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
Source code
View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
View on GitHub
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
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};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
Source code
View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
Source code
View on GitHub
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),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{c as __pageData,y as default};
diff --git a/assets/en_api_mp_math_vector.md.CF4kCv-W.lean.js b/assets/en_api_mp_math_vector.md.CF4kCv-W.lean.js
new file mode 100644
index 0000000..a464194
--- /dev/null
+++ b/assets/en_api_mp_math_vector.md.CF4kCv-W.lean.js
@@ -0,0 +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.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"},e=t("",127),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const y=s(n,[["render",l]]);export{c as __pageData,y 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
deleted file mode 100644
index 041914c..0000000
--- a/assets/en_api_mp_math_vector.md.CgtIoM4A.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.pbEu-669.js b/assets/en_api_presets_model_index.md.Cnn4t_P0.js
similarity index 93%
rename from assets/en_api_presets_model_index.md.pbEu-669.js
rename to assets/en_api_presets_model_index.md.Cnn4t_P0.js
index 7409381..4aaf0fb 100644
--- a/assets/en_api_presets_model_index.md.pbEu-669.js
+++ b/assets/en_api_presets_model_index.md.Cnn4t_P0.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
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
+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
View on GitHub
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,g){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(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_presets_model_index.md.pbEu-669.lean.js b/assets/en_api_presets_model_index.md.Cnn4t_P0.lean.js
similarity index 87%
rename from assets/en_api_presets_model_index.md.pbEu-669.lean.js
rename to assets/en_api_presets_model_index.md.Cnn4t_P0.lean.js
index 38a796b..59631d6 100644
--- a/assets/en_api_presets_model_index.md.pbEu-669.lean.js
+++ b/assets/en_api_presets_model_index.md.Cnn4t_P0.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(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};
+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};
diff --git a/assets/en_api_presets_model_model.md.CL5uKZbj.js b/assets/en_api_presets_model_model.md.BZpQe5Li.js
similarity index 93%
rename from assets/en_api_presets_model_model.md.CL5uKZbj.js
rename to assets/en_api_presets_model_model.md.BZpQe5Li.js
index a34f6e3..c6b4fb9 100644
--- a/assets/en_api_presets_model_model.md.CL5uKZbj.js
+++ b/assets/en_api_presets_model_model.md.BZpQe5Li.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/model.md","filePath":"en/api/presets/model/model.md"}'),t={name:"en/api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
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/model.md","filePath":"en/api/presets/model/model.md"}'),t={name:"en/api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
Description: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
Description: 生成球体上的点集。
Arguments:
  • radius:
  • density:
Return: List[Point3]: 球体上的点集。
Source code
View on GitHub
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(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/en_api_presets_model_model.md.CL5uKZbj.lean.js b/assets/en_api_presets_model_model.md.BZpQe5Li.lean.js
similarity index 87%
rename from assets/en_api_presets_model_model.md.CL5uKZbj.lean.js
rename to assets/en_api_presets_model_model.md.BZpQe5Li.lean.js
index fd83d90..1ccaf57 100644
--- a/assets/en_api_presets_model_model.md.CL5uKZbj.lean.js
+++ b/assets/en_api_presets_model_model.md.BZpQe5Li.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/model.md","filePath":"en/api/presets/model/model.md"}'),t={name:"en/api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
+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/model.md","filePath":"en/api/presets/model/model.md"}'),t={name:"en/api/presets/model/model.md"},h=n("",10),l=[h];function p(e,k,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_angle.md.DTK1PNuJ.js b/assets/ja_api_mp_math_angle.md.D0ChdV9L.js
similarity index 74%
rename from assets/ja_api_mp_math_angle.md.DTK1PNuJ.js
rename to assets/ja_api_mp_math_angle.md.D0ChdV9L.js
index 3a65e80..c36a3bd 100644
--- a/assets/ja_api_mp_math_angle.md.DTK1PNuJ.js
+++ b/assets/ja_api_mp_math_angle.md.D0ChdV9L.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) ​
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):
+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":"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
GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as 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
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
+        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
GitHubで表示
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード
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
GitHubで表示
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード
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
GitHubで表示
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード
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
GitHubで表示
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード
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
GitHubで表示
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード
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
GitHubで表示
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード
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
GitHubで表示
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード
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
GitHubで表示
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード
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
GitHubで表示
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード
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
GitHubで表示
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード
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
GitHubで表示
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
ソースコード
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
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
ソースコード
GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
ソースコード
GitHubで表示
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
ソースコード
GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
ソースコード
GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
ソースコード
GitHubで表示
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
ソースコード
GitHubで表示
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
def self / other ​
ソースコード
GitHubで表示
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_angle.md.DTK1PNuJ.lean.js b/assets/ja_api_mp_math_angle.md.D0ChdV9L.lean.js
similarity index 68%
rename from assets/ja_api_mp_math_angle.md.DTK1PNuJ.lean.js
rename to assets/ja_api_mp_math_angle.md.D0ChdV9L.lean.js
index c63a8a6..3538fd3 100644
--- a/assets/ja_api_mp_math_angle.md.DTK1PNuJ.lean.js
+++ b/assets/ja_api_mp_math_angle.md.D0ChdV9L.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 E=s(t,[["render",h]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=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 F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_equation.md.D-4BBsnQ.lean.js b/assets/ja_api_mp_math_equation.md.D-4BBsnQ.lean.js
deleted file mode 100644
index ef497b8..0000000
--- a/assets/ja_api_mp_math_equation.md.D-4BBsnQ.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.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("",23),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const u=s(l,[["render",h]]);export{F as __pageData,u as default};
diff --git a/assets/ja_api_mp_math_equation.md.D-4BBsnQ.js b/assets/ja_api_mp_math_equation.md.ksLzfPHD.js
similarity index 83%
rename from assets/ja_api_mp_math_equation.md.D-4BBsnQ.js
rename to assets/ja_api_mp_math_equation.md.ksLzfPHD.js
index 77b7043..7b2b292 100644
--- a/assets/ja_api_mp_math_equation.md.D-4BBsnQ.js
+++ b/assets/ja_api_mp_math_equation.md.ksLzfPHD.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.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):
+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"}'),t={name:"ja/api/mp_math/equation.md"},l=n(`
mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード
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
GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
引数:
  • func: 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
GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const u=s(l,[["render",h]]);export{F as __pageData,u as default};
+        raise ValueError('Invalid var type')
`,23),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};
diff --git a/assets/ja_api_mp_math_equation.md.ksLzfPHD.lean.js b/assets/ja_api_mp_math_equation.md.ksLzfPHD.lean.js
new file mode 100644
index 0000000..de13a1e
--- /dev/null
+++ b/assets/ja_api_mp_math_equation.md.ksLzfPHD.lean.js
@@ -0,0 +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":"ja/api/mp_math/equation.md","filePath":"ja/api/mp_math/equation.md"}'),t={name:"ja/api/mp_math/equation.md"},l=n("",23),p=[l];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const F=s(t,[["render",h]]);export{u as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_function.md.Bvf1U09A.js b/assets/ja_api_mp_math_function.md.S4mlhSEl.js
similarity index 96%
rename from assets/ja_api_mp_math_function.md.Bvf1U09A.js
rename to assets/ja_api_mp_math_function.md.S4mlhSEl.js
index 5283988..e0fd9ea 100644
--- a/assets/ja_api_mp_math_function.md.Bvf1U09A.js
+++ b/assets/ja_api_mp_math_function.md.S4mlhSEl.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"ja/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
引数:
  • 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:
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"ja/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
引数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
戻り値: 梯度
ソースコード
GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -17,7 +17,7 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
引数:
  • func: 函数
  • *args: 参数
戻り値: 柯里化后的函数
例:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
ソースコード
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
ソースコード
GitHubで表示
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -39,4 +39,4 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+    return curried_func
`,13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/ja_api_mp_math_function.md.Bvf1U09A.lean.js b/assets/ja_api_mp_math_function.md.S4mlhSEl.lean.js
similarity index 98%
rename from assets/ja_api_mp_math_function.md.Bvf1U09A.lean.js
rename to assets/ja_api_mp_math_function.md.S4mlhSEl.lean.js
index a55a3f5..d7023b9 100644
--- a/assets/ja_api_mp_math_function.md.Bvf1U09A.lean.js
+++ b/assets/ja_api_mp_math_function.md.S4mlhSEl.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"ja/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"ja/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/ja_api_mp_math_line.md.DYJV4KNE.js b/assets/ja_api_mp_math_line.md.C6_h0EEF.js
similarity index 78%
rename from assets/ja_api_mp_math_line.md.DYJV4KNE.js
rename to assets/ja_api_mp_math_line.md.C6_h0EEF.js
index 6782857..8527533 100644
--- a/assets/ja_api_mp_math_line.md.DYJV4KNE.js
+++ b/assets/ja_api_mp_math_line.md.C6_h0EEF.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"}'),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'):
+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 ​
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
GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other: 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
GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,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)
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':
+    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
GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -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)
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:
+    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
GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -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.')
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':
+        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
GitHubで表示
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
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':
+    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
GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -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))
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':
+    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
GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -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
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]:
+    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
GitHubで表示
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)
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:
+    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
GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -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)
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:
+    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
GitHubで表示
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)
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:
+    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
GitHubで表示
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)
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:
+    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
GitHubで表示
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)
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:
+    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
GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -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
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):
+    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
GitHubで表示
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -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
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
+        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
GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -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)
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':
+    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
GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -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)
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:
+        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
GitHubで表示
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),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};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_line.md.DYJV4KNE.lean.js b/assets/ja_api_mp_math_line.md.C6_h0EEF.lean.js
similarity index 58%
rename from assets/ja_api_mp_math_line.md.DYJV4KNE.lean.js
rename to assets/ja_api_mp_math_line.md.C6_h0EEF.lean.js
index 5fb9a23..9fdd967 100644
--- a/assets/ja_api_mp_math_line.md.DYJV4KNE.lean.js
+++ b/assets/ja_api_mp_math_line.md.C6_h0EEF.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"}'),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};
+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),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/ja_api_mp_math_plane.md.D-yHaxP-.js b/assets/ja_api_mp_math_plane.md.CVfLX9sr.js
similarity index 83%
rename from assets/ja_api_mp_math_plane.md.D-yHaxP-.js
rename to assets/ja_api_mp_math_plane.md.CVfLX9sr.js
index 9872d64..a474967 100644
--- a/assets/ja_api_mp_math_plane.md.D-yHaxP-.js
+++ b/assets/ja_api_mp_math_plane.md.CVfLX9sr.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 ​
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):
+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.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"},t=n(`
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 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
GitHubで表示
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,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
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':
+        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
GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,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)}')
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:
+        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
GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,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)}')
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':
+        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
GitHubで表示
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)
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':
+    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
GitHubで表示
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))
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':
+    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
GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -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)
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:
+    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
GitHubで表示
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
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
+    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
GitHubで表示
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
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
+    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
GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -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
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
+    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
GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -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
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
+    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
GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -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
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
+    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
GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -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
def __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
GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • 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
GitHubで表示
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)}'")
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};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
ソースコード
GitHubで表示
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
ソースコード
GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_plane.md.D-yHaxP-.lean.js b/assets/ja_api_mp_math_plane.md.CVfLX9sr.lean.js
similarity index 54%
rename from assets/ja_api_mp_math_plane.md.D-yHaxP-.lean.js
rename to assets/ja_api_mp_math_plane.md.CVfLX9sr.lean.js
index 8761d16..820a56b 100644
--- a/assets/ja_api_mp_math_plane.md.D-yHaxP-.lean.js
+++ b/assets/ja_api_mp_math_plane.md.CVfLX9sr.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":"ja/api/mp_math/plane.md","filePath":"ja/api/mp_math/plane.md"}'),l={name:"ja/api/mp_math/plane.md"},h=n("",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};
+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.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"},t=n("",105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/ja_api_mp_math_point.md.DjHRkHI5.js b/assets/ja_api_mp_math_point.md.21gM893G.js
similarity index 73%
rename from assets/ja_api_mp_math_point.md.DjHRkHI5.js
rename to assets/ja_api_mp_math_point.md.21gM893G.js
index b9735ff..e168eff 100644
--- a/assets/ja_api_mp_math_point.md.DjHRkHI5.js
+++ b/assets/ja_api_mp_math_point.md.21gM893G.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 ​
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):
+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
GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • 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
GitHubで表示
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -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
def 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
GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: P + V -> P P + P -> P
引数:
  • 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
GitHubで表示
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)
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):
+    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
GitHubで表示
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)
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':
+    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
GitHubで表示
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,r,o,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,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_point.md.DjHRkHI5.lean.js b/assets/ja_api_mp_math_point.md.21gM893G.lean.js
similarity index 68%
rename from assets/ja_api_mp_math_point.md.DjHRkHI5.lean.js
rename to assets/ja_api_mp_math_point.md.21gM893G.lean.js
index 83beb8b..7aec043 100644
--- a/assets/ja_api_mp_math_point.md.DjHRkHI5.lean.js
+++ b/assets/ja_api_mp_math_point.md.21gM893G.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,r,o,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,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_segment.md.37V8kAc1.js b/assets/ja_api_mp_math_segment.md.Dji9_vOI.js
similarity index 83%
rename from assets/ja_api_mp_math_segment.md.37V8kAc1.js
rename to assets/ja_api_mp_math_segment.md.Dji9_vOI.js
index 2a61ac7..b278320 100644
--- a/assets/ja_api_mp_math_segment.md.37V8kAc1.js
+++ b/assets/ja_api_mp_math_segment.md.Dji9_vOI.js
@@ -1,4 +1,4 @@
-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'):
+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"},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
GitHubで表示
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 o
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,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};
+    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/ja_api_mp_math_segment.md.37V8kAc1.lean.js b/assets/ja_api_mp_math_segment.md.Dji9_vOI.lean.js
similarity index 59%
rename from assets/ja_api_mp_math_segment.md.37V8kAc1.lean.js
rename to assets/ja_api_mp_math_segment.md.Dji9_vOI.lean.js
index 399c379..5673767 100644
--- a/assets/ja_api_mp_math_segment.md.37V8kAc1.lean.js
+++ b/assets/ja_api_mp_math_segment.md.Dji9_vOI.lean.js
@@ -1 +1 @@
-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};
+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"},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/ja_api_mp_math_utils.md.BbdhM1tp.lean.js b/assets/ja_api_mp_math_utils.md.BbdhM1tp.lean.js
deleted file mode 100644
index f674376..0000000
--- a/assets/ja_api_mp_math_utils.md.BbdhM1tp.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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/ja_api_mp_math_utils.md.BbdhM1tp.js b/assets/ja_api_mp_math_utils.md.DhvjDskn.js
similarity index 72%
rename from assets/ja_api_mp_math_utils.md.BbdhM1tp.js
rename to assets/ja_api_mp_math_utils.md.DhvjDskn.js
index 7c674b7..b982d37 100644
--- a/assets/ja_api_mp_math_utils.md.BbdhM1tp.js
+++ b/assets/ja_api_mp_math_utils.md.DhvjDskn.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
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:
+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.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"}'),t={name:"ja/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
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
GitHubで表示
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 ​
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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
ソースコード
GitHubで表示
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
ソースコード
GitHubで表示
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -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)
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
ソースコード
GitHubで表示
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
ソースコード
GitHubで表示
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
GitHubで表示
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -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
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:
+    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
GitHubで表示
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 ''
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:
+        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
GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
diff --git a/assets/ja_api_mp_math_utils.md.DhvjDskn.lean.js b/assets/ja_api_mp_math_utils.md.DhvjDskn.lean.js
new file mode 100644
index 0000000..a33e8ec
--- /dev/null
+++ b/assets/ja_api_mp_math_utils.md.DhvjDskn.lean.js
@@ -0,0 +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.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"}'),t={name:"ja/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 E=s(t,[["render",p]]);export{F as __pageData,E 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
deleted file mode 100644
index 1e17985..0000000
--- a/assets/ja_api_mp_math_vector.md.BBVnCwJa.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.BBVnCwJa.js b/assets/ja_api_mp_math_vector.md.DyGgurm4.js
similarity index 76%
rename from assets/ja_api_mp_math_vector.md.BBVnCwJa.js
rename to assets/ja_api_mp_math_vector.md.DyGgurm4.js
index 386905a..628ee91 100644
--- a/assets/ja_api_mp_math_vector.md.BBVnCwJa.js
+++ b/assets/ja_api_mp_math_vector.md.DyGgurm4.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.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):
+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"},e=t(`
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
  • 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
GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as n}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])
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':
+    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
GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • 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
GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as n}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)
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:
+    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
GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • 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
GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
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
GitHubで表示
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 n}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def 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
GitHubで表示
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    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
GitHubで表示
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
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
+    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
GitHubで表示
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
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
+    return self / self.length
def __abs__(self) ​
ソースコード
GitHubで表示
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
ソースコード
GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: V + P -> P
V + V -> V
引数:
  • 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
GitHubで表示
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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):
+        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
GitHubで表示
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 n}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)
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':
+    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
GitHubで表示
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 n}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
def 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
GitHubで表示
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
ソースコード
GitHubで表示
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def self - other ​
説明: V - P -> P
V - V -> V
引数:
  • 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
GitHubで表示
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}"')
def 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
GitHubで表示
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 n}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
def 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
GitHubで表示
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
ソースコード
GitHubで表示
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • 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
GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
ソースコード
GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
GitHubで表示
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
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};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
ソースコード
GitHubで表示
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
GitHubで表示
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=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_mp_math_vector.md.DyGgurm4.lean.js b/assets/ja_api_mp_math_vector.md.DyGgurm4.lean.js
new file mode 100644
index 0000000..0a30939
--- /dev/null
+++ b/assets/ja_api_mp_math_vector.md.DyGgurm4.lean.js
@@ -0,0 +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.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"},e=t("",127),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_model_index.md.C-Ypf-qh.js b/assets/ja_api_presets_model_index.md.Dbt3LFNK.js
similarity index 92%
rename from assets/ja_api_presets_model_index.md.C-Ypf-qh.js
rename to assets/ja_api_presets_model_index.md.Dbt3LFNK.js
index 4ff335d..8f89a3c 100644
--- a/assets/ja_api_presets_model_index.md.C-Ypf-qh.js
+++ b/assets/ja_api_presets_model_index.md.Dbt3LFNK.js
@@ -1,4 +1,4 @@
-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
+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
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
GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,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};
+    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/ja_api_presets_model_index.md.C-Ypf-qh.lean.js b/assets/ja_api_presets_model_index.md.Dbt3LFNK.lean.js
similarity index 64%
rename from assets/ja_api_presets_model_index.md.C-Ypf-qh.lean.js
rename to assets/ja_api_presets_model_index.md.Dbt3LFNK.lean.js
index 17ebf41..691534d 100644
--- a/assets/ja_api_presets_model_index.md.C-Ypf-qh.lean.js
+++ b/assets/ja_api_presets_model_index.md.Dbt3LFNK.lean.js
@@ -1 +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":"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};
+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,g){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_model_model.md.Dwbc1qIc.js b/assets/ja_api_presets_model_model.md.ti1HKQyY.js
similarity index 92%
rename from assets/ja_api_presets_model_model.md.Dwbc1qIc.js
rename to assets/ja_api_presets_model_model.md.ti1HKQyY.js
index 6fbd9a8..829157b 100644
--- a/assets/ja_api_presets_model_model.md.Dwbc1qIc.js
+++ b/assets/ja_api_presets_model_model.md.ti1HKQyY.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/model.md","filePath":"ja/api/presets/model/model.md"}'),t={name:"ja/api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
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
+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/model.md","filePath":"ja/api/presets/model/model.md"}'),t={name:"ja/api/presets/model/model.md"},h=n(`
mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
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
GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,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,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{y as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/ja_api_presets_model_model.md.Dwbc1qIc.lean.js b/assets/ja_api_presets_model_model.md.ti1HKQyY.lean.js
similarity index 76%
rename from assets/ja_api_presets_model_model.md.Dwbc1qIc.lean.js
rename to assets/ja_api_presets_model_model.md.ti1HKQyY.lean.js
index ec27df9..2b7d156 100644
--- a/assets/ja_api_presets_model_model.md.Dwbc1qIc.lean.js
+++ b/assets/ja_api_presets_model_model.md.ti1HKQyY.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/model.md","filePath":"ja/api/presets/model/model.md"}'),t={name:"ja/api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{y as __pageData,F 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":"ja/api/presets/model/model.md","filePath":"ja/api/presets/model/model.md"}'),t={name:"ja/api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/style.BiH8pcAw.css b/assets/style.BiH8pcAw.css
deleted file mode 100644
index 15f2f22..0000000
--- a/assets/style.BiH8pcAw.css
+++ /dev/null
@@ -1 +0,0 @@
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new file mode 100644
index 0000000..f59963a
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diff --git a/assets/zht_api_mp_math_angle.md.lzcXwnW6.js b/assets/zht_api_mp_math_angle.md.ByT5Hatc.js
similarity index 74%
rename from assets/zht_api_mp_math_angle.md.lzcXwnW6.js
rename to assets/zht_api_mp_math_angle.md.ByT5Hatc.js
index 9003c28..611c52d 100644
--- a/assets/zht_api_mp_math_angle.md.lzcXwnW6.js
+++ b/assets/zht_api_mp_math_angle.md.ByT5Hatc.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) ​
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):
+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":"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
在GitHub上查看
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -8,92 +8,92 @@ import{_ as s,c as 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
def 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
在GitHub上查看
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
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
在GitHub上查看
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
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
在GitHub上查看
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
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
在GitHub上查看
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> AnyAngle ​
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
在GitHub上查看
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
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
在GitHub上查看
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def cos(self) -> float ​
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
在GitHub上查看
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def tan(self) -> float ​
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
在GitHub上查看
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def cot(self) -> float ​
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
在GitHub上查看
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
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
在GitHub上查看
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
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
在GitHub上查看
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源碼
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
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
源碼
在GitHub上查看
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
源碼
在GitHub上查看
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
源碼
在GitHub上查看
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
源碼
在GitHub上查看
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
源碼
在GitHub上查看
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
源碼
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
源碼
在GitHub上查看
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
源碼
python
def __truediv__(self, other):
+    ...
def self / other ​
源碼
在GitHub上查看
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
-    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const E=s(t,[["render",h]]);export{F as __pageData,E as default};
+    return AnyAngle(self.radian / other, is_radian=True)
`,80),l=[e];function h(p,k,r,d,o,g){return a(),i("div",null,l)}const F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_angle.md.lzcXwnW6.lean.js b/assets/zht_api_mp_math_angle.md.ByT5Hatc.lean.js
similarity index 68%
rename from assets/zht_api_mp_math_angle.md.lzcXwnW6.lean.js
rename to assets/zht_api_mp_math_angle.md.ByT5Hatc.lean.js
index 07adbfd..5a1fde9 100644
--- a/assets/zht_api_mp_math_angle.md.lzcXwnW6.lean.js
+++ b/assets/zht_api_mp_math_angle.md.ByT5Hatc.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 E=s(t,[["render",h]]);export{F as __pageData,E as default};
+import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const c=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 F=s(t,[["render",h]]);export{c as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_equation.md.BAr_ktNP.lean.js b/assets/zht_api_mp_math_equation.md.BAr_ktNP.lean.js
deleted file mode 100644
index 91e9901..0000000
--- a/assets/zht_api_mp_math_equation.md.BAr_ktNP.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.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("",23),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const u=s(l,[["render",h]]);export{F as __pageData,u as default};
diff --git a/assets/zht_api_mp_math_equation.md.BAr_ktNP.js b/assets/zht_api_mp_math_equation.md.C9JJo8Tj.js
similarity index 83%
rename from assets/zht_api_mp_math_equation.md.BAr_ktNP.js
rename to assets/zht_api_mp_math_equation.md.C9JJo8Tj.js
index 4301dee..c26c18b 100644
--- a/assets/zht_api_mp_math_equation.md.BAr_ktNP.js
+++ b/assets/zht_api_mp_math_equation.md.C9JJo8Tj.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.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):
+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 ​
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
在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
變數説明:
  • *t:
  • 参数:
返回: 目标点
源碼
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
在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -20,7 +20,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
變數説明:
  • func: 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
在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -62,4 +62,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
             return result_func(*args)
         return high_order_partial_derivative_func
     else:
-        raise ValueError('Invalid var type')
`,23),p=[t];function h(k,e,r,E,d,g){return a(),i("div",null,p)}const u=s(l,[["render",h]]);export{F as __pageData,u as default};
+        raise ValueError('Invalid var type')
`,23),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};
diff --git a/assets/zht_api_mp_math_equation.md.C9JJo8Tj.lean.js b/assets/zht_api_mp_math_equation.md.C9JJo8Tj.lean.js
new file mode 100644
index 0000000..9b4276c
--- /dev/null
+++ b/assets/zht_api_mp_math_equation.md.C9JJo8Tj.lean.js
@@ -0,0 +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("",23),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};
diff --git a/assets/zht_api_mp_math_function.md.C2Gp7z0v.js b/assets/zht_api_mp_math_function.md.CUiziArf.js
similarity index 96%
rename from assets/zht_api_mp_math_function.md.C2Gp7z0v.js
rename to assets/zht_api_mp_math_function.md.CUiziArf.js
index 53b0939..320f0b5 100644
--- a/assets/zht_api_mp_math_function.md.C2Gp7z0v.js
+++ b/assets/zht_api_mp_math_function.md.CUiziArf.js
@@ -1,4 +1,4 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"zht/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
變數説明:
  • 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:
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"zht/api/mp_math/function.md"},Q=a('
mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
',4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a('',1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a('',1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a('',1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a(`
變數説明:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源碼
在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -17,7 +17,7 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
變數説明:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
範例:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
源碼
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
源碼
在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -39,4 +39,4 @@ import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1
     def curried_func(*args2: Var) -> Var:
         """@litedoc-hide"""
         return func(*args, *args2)
-    return curried_func
`,13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+    return curried_func
`,13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/zht_api_mp_math_function.md.C2Gp7z0v.lean.js b/assets/zht_api_mp_math_function.md.CUiziArf.lean.js
similarity index 98%
rename from assets/zht_api_mp_math_function.md.C2Gp7z0v.lean.js
rename to assets/zht_api_mp_math_function.md.CUiziArf.lean.js
index 09e4ad5..2b344c5 100644
--- a/assets/zht_api_mp_math_function.md.C2Gp7z0v.lean.js
+++ b/assets/zht_api_mp_math_function.md.CUiziArf.lean.js
@@ -1 +1 @@
-import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"zht/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(L,b,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
+import{_ as l,c as t,j as s,a as n,a2 as a,o as i}from"./chunks/framework.C94oF1kp.js";const Z=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"}'),e={name:"zht/api/mp_math/function.md"},Q=a("",4),T={class:"tip custom-block github-alert"},h=s("p",{class:"custom-block-title"},"TIP",-1),p={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},r={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"8.471ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 3744.3 1000","aria-hidden":"true"},d=a("",1),k=[d],o=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("mi",null,"x"),s("mo",null,","),s("mi",null,"y"),s("mo",null,","),s("mi",null,"z"),s("mo",{stretchy:"false"},")")])],-1),m={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},g={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-0.566ex"},xmlns:"http://www.w3.org/2000/svg",width:"10.19ex",height:"2.262ex",role:"img",focusable:"false",viewBox:"0 -750 4504 1000","aria-hidden":"true"},c=a("",1),y=[c],u=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")")])],-1),E={class:"MathJax",jax:"SVG",style:{direction:"ltr",position:"relative"}},F={style:{overflow:"visible","min-height":"1px","min-width":"1px","vertical-align":"-1.469ex"},xmlns:"http://www.w3.org/2000/svg",width:"29.427ex",height:"4.07ex",role:"img",focusable:"false",viewBox:"0 -1149.5 13006.8 1799","aria-hidden":"true"},f=a("",1),_=[f],C=s("mjx-assistive-mml",{unselectable:"on",display:"inline",style:{top:"0px",left:"0px",clip:"rect(1px, 1px, 1px, 1px)","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none",position:"absolute",padding:"1px 0px 0px 0px",border:"0px",display:"block",width:"auto",overflow:"hidden"}},[s("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[s("mi",{mathvariant:"normal"},"∇"),s("mi",null,"f"),s("mo",{stretchy:"false"},"("),s("msub",null,[s("mi",null,"x"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"y"),s("mn",null,"0")]),s("mo",null,","),s("msub",null,[s("mi",null,"z"),s("mn",null,"0")]),s("mo",{stretchy:"false"},")"),s("mo",null,"="),s("mrow",{"data-mjx-texclass":"INNER"},[s("mo",{"data-mjx-texclass":"OPEN"},"("),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"x")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"y")])]),s("mo",null,","),s("mfrac",null,[s("mrow",null,[s("mi",null,"∂"),s("mi",null,"f")]),s("mrow",null,[s("mi",null,"∂"),s("mi",null,"z")])]),s("mo",{"data-mjx-texclass":"CLOSE"},")")])])],-1),w=a("",13);function x(b,L,H,B,M,D){return i(),t("div",null,[Q,s("div",T,[h,s("p",null,[n("已知一个函数"),s("mjx-container",p,[(i(),t("svg",r,k)),o]),n("，则其在点"),s("mjx-container",m,[(i(),t("svg",g,y)),u]),n("处的梯度向量为: "),s("mjx-container",E,[(i(),t("svg",F,_)),C])])]),w])}const A=l(e,[["render",x]]);export{Z as __pageData,A as default};
diff --git a/assets/zht_api_mp_math_line.md.DX62bgjZ.js b/assets/zht_api_mp_math_line.md.TSJBrHTa.js
similarity index 77%
rename from assets/zht_api_mp_math_line.md.DX62bgjZ.js
rename to assets/zht_api_mp_math_line.md.TSJBrHTa.js
index 8038235..77a21ef 100644
--- a/assets/zht_api_mp_math_line.md.DX62bgjZ.js
+++ b/assets/zht_api_mp_math_line.md.TSJBrHTa.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"}'),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'):
+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 ​
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
在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -6,7 +6,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const E
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -15,7 +15,7 @@ import{_ as s,c as i,o as a,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)
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':
+    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
在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -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)
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:
+    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
在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -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.')
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':
+        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
在GitHub上查看
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
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':
+    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
在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -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))
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':
+    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
在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -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
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]:
+    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
在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -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)
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:
+    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
在GitHub上查看
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)
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:
+    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
在GitHub上查看
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)
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:
+    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
在GitHub上查看
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)
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:
+    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
在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -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
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):
+    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
在GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -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
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
+        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
在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -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)
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':
+    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
在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -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)
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:
+        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
在GitHub上查看
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),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};
+    return self.direction.is_parallel(other.direction) and (self.point - other.point).is_parallel(self.direction)
`,107),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_line.md.DX62bgjZ.lean.js b/assets/zht_api_mp_math_line.md.TSJBrHTa.lean.js
similarity index 58%
rename from assets/zht_api_mp_math_line.md.DX62bgjZ.lean.js
rename to assets/zht_api_mp_math_line.md.TSJBrHTa.lean.js
index 55a0c8a..65003d2 100644
--- a/assets/zht_api_mp_math_line.md.DX62bgjZ.lean.js
+++ b/assets/zht_api_mp_math_line.md.TSJBrHTa.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"}'),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};
+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),e=[l];function p(h,k,r,o,d,g){return a(),i("div",null,e)}const y=s(t,[["render",p]]);export{E as __pageData,y as default};
diff --git a/assets/zht_api_mp_math_plane.md.DJ_9NQFz.js b/assets/zht_api_mp_math_plane.md.CO3Dxqtg.js
similarity index 83%
rename from assets/zht_api_mp_math_plane.md.DJ_9NQFz.js
rename to assets/zht_api_mp_math_plane.md.CO3Dxqtg.js
index 9046d88..a4a7f1e 100644
--- a/assets/zht_api_mp_math_plane.md.DJ_9NQFz.js
+++ b/assets/zht_api_mp_math_plane.md.CO3Dxqtg.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 ​
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):
+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.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"},t=n(`
mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
變數説明:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
源碼
在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -10,7 +10,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const F
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
變數説明:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -28,7 +28,7 @@ import{_ as s,c as i,o as a,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
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':
+        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
在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -43,7 +43,7 @@ import{_ as s,c as i,o as a,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)}')
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:
+        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
在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -58,7 +58,7 @@ import{_ as s,c as i,o as a,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)}')
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':
+        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
在GitHub上查看
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)
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':
+    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
在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -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))
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':
+    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
在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -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)
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:
+    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
在GitHub上查看
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
def 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
在GitHub上查看
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
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
+    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
在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -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
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
+    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
在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -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
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
+    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
在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -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
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
+    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
在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -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
def __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
在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼
在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • 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
在GitHub上查看
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)}'")
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};
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源碼
在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源碼
在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
+    return self.cal_intersection_point3(other)
`,105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_plane.md.DJ_9NQFz.lean.js b/assets/zht_api_mp_math_plane.md.CO3Dxqtg.lean.js
similarity index 54%
rename from assets/zht_api_mp_math_plane.md.DJ_9NQFz.lean.js
rename to assets/zht_api_mp_math_plane.md.CO3Dxqtg.lean.js
index 9b02a9f..2465fa4 100644
--- a/assets/zht_api_mp_math_plane.md.DJ_9NQFz.lean.js
+++ b/assets/zht_api_mp_math_plane.md.CO3Dxqtg.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":"zht/api/mp_math/plane.md","filePath":"zht/api/mp_math/plane.md"}'),l={name:"zht/api/mp_math/plane.md"},h=n("",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};
+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.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"},t=n("",105),h=[t];function p(e,k,r,d,E,o){return a(),i("div",null,h)}const F=s(l,[["render",p]]);export{y as __pageData,F as default};
diff --git a/assets/zht_api_mp_math_point.md.D1nAiRP0.js b/assets/zht_api_mp_math_point.md.hahZSaSv.js
similarity index 74%
rename from assets/zht_api_mp_math_point.md.D1nAiRP0.js
rename to assets/zht_api_mp_math_point.md.hahZSaSv.js
index 006128b..5e0e63c 100644
--- a/assets/zht_api_mp_math_point.md.D1nAiRP0.js
+++ b/assets/zht_api_mp_math_point.md.hahZSaSv.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"},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):
+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
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as t}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
變數説明:
  • 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
在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -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
def 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
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • 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
在GitHub上查看
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)
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):
+    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
在GitHub上查看
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)
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':
+    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
在GitHub上查看
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,r,o,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,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_point.md.D1nAiRP0.lean.js b/assets/zht_api_mp_math_point.md.hahZSaSv.lean.js
similarity index 68%
rename from assets/zht_api_mp_math_point.md.D1nAiRP0.lean.js
rename to assets/zht_api_mp_math_point.md.hahZSaSv.lean.js
index 6468bc9..30d0b10 100644
--- a/assets/zht_api_mp_math_point.md.D1nAiRP0.lean.js
+++ b/assets/zht_api_mp_math_point.md.hahZSaSv.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"},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};
+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,g){return a(),i("div",null,h)}const c=s(n,[["render",e]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_segment.md.CMRey-MG.js b/assets/zht_api_mp_math_segment.md.BVxd03II.js
similarity index 82%
rename from assets/zht_api_mp_math_segment.md.CMRey-MG.js
rename to assets/zht_api_mp_math_segment.md.BVxd03II.js
index 0e722a3..ff1d227 100644
--- a/assets/zht_api_mp_math_segment.md.CMRey-MG.js
+++ b/assets/zht_api_mp_math_segment.md.BVxd03II.js
@@ -1,4 +1,4 @@
-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'):
+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"},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:
源碼
在GitHub上查看
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 o
     '长度'
     self.length = self.direction.length
     '中心点'
-    self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
`,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};
+    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/zht_api_mp_math_segment.md.CMRey-MG.lean.js b/assets/zht_api_mp_math_segment.md.BVxd03II.lean.js
similarity index 59%
rename from assets/zht_api_mp_math_segment.md.CMRey-MG.lean.js
rename to assets/zht_api_mp_math_segment.md.BVxd03II.lean.js
index e6d60ae..08c73d8 100644
--- a/assets/zht_api_mp_math_segment.md.CMRey-MG.lean.js
+++ b/assets/zht_api_mp_math_segment.md.BVxd03II.lean.js
@@ -1 +1 @@
-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};
+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"},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/zht_api_mp_math_utils.md.BDpW2Fd4.lean.js b/assets/zht_api_mp_math_utils.md.BDpW2Fd4.lean.js
deleted file mode 100644
index e56152e..0000000
--- a/assets/zht_api_mp_math_utils.md.BDpW2Fd4.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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_utils.md.BDpW2Fd4.js b/assets/zht_api_mp_math_utils.md.Dz7jYC2A.js
similarity index 71%
rename from assets/zht_api_mp_math_utils.md.BDpW2Fd4.js
rename to assets/zht_api_mp_math_utils.md.Dz7jYC2A.js
index d351925..f35c0ef 100644
--- a/assets/zht_api_mp_math_utils.md.BDpW2Fd4.js
+++ b/assets/zht_api_mp_math_utils.md.Dz7jYC2A.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"}'),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:
+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.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
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
在GitHub上查看
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 ​
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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源碼
在GitHub上查看
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源碼
在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -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)
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源碼
在GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源碼
在GitHub上查看
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
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
在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -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
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:
+    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
在GitHub上查看
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 ''
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:
+        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
在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -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,d,o,g){return a(),i("div",null,h)}const y=s(l,[["render",p]]);export{E as __pageData,y as default};
+        return ''
`,35),h=[l];function p(e,k,r,o,d,g){return a(),i("div",null,h)}const E=s(t,[["render",p]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_utils.md.Dz7jYC2A.lean.js b/assets/zht_api_mp_math_utils.md.Dz7jYC2A.lean.js
new file mode 100644
index 0000000..b020cd3
--- /dev/null
+++ b/assets/zht_api_mp_math_utils.md.Dz7jYC2A.lean.js
@@ -0,0 +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.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 E=s(t,[["render",p]]);export{F as __pageData,E as default};
diff --git a/assets/zht_api_mp_math_vector.md.DGVOQo3Y.js b/assets/zht_api_mp_math_vector.md.26fppi_c.js
similarity index 76%
rename from assets/zht_api_mp_math_vector.md.DGVOQo3Y.js
rename to assets/zht_api_mp_math_vector.md.26fppi_c.js
index 49dab6e..27df279 100644
--- a/assets/zht_api_mp_math_vector.md.DGVOQo3Y.js
+++ b/assets/zht_api_mp_math_vector.md.26fppi_c.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.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):
+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"},e=t(`
mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -8,7 +8,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
變數説明:
  • 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
在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -18,7 +18,7 @@ import{_ as s,c as i,o as a,a2 as n}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])
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':
+    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
在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -26,7 +26,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • 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
在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -46,7 +46,7 @@ import{_ as s,c as i,o as a,a2 as n}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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -55,7 +55,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • 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
在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -63,7 +63,7 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const y
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
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
在GitHub上查看
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 n}from"./chunks/framework.C94oF1kp.js";const y
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源碼
在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    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
在GitHub上查看
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
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
+    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
在GitHub上查看
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
def __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
def __abs__(self) ​
源碼
在GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • 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
在GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -112,7 +112,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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):
+        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
在GitHub上查看
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 n}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)
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':
+    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
在GitHub上查看
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 n}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
def 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
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源碼
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • 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
在GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -146,7 +146,7 @@ import{_ as s,c as i,o as a,a2 as n}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)}"')
def 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
在GitHub上查看
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 n}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
def 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
在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼
在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • 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
在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -174,14 +174,14 @@ import{_ as s,c as i,o as a,a2 as n}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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源碼
在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
在GitHub上查看
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
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};
+    return self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源碼
在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源碼
在GitHub上查看
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=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",l]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_mp_math_vector.md.26fppi_c.lean.js b/assets/zht_api_mp_math_vector.md.26fppi_c.lean.js
new file mode 100644
index 0000000..e41837a
--- /dev/null
+++ b/assets/zht_api_mp_math_vector.md.26fppi_c.lean.js
@@ -0,0 +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.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"},e=t("",127),h=[e];function l(p,k,r,o,d,g){return a(),i("div",null,h)}const c=s(n,[["render",l]]);export{y as __pageData,c 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
deleted file mode 100644
index dd2cd98..0000000
--- a/assets/zht_api_mp_math_vector.md.DGVOQo3Y.lean.js
+++ /dev/null
@@ -1 +0,0 @@
-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.BJWX_k6K.js b/assets/zht_api_presets_model_index.md.BN6GzTiL.js
similarity index 92%
rename from assets/zht_api_presets_model_index.md.BJWX_k6K.js
rename to assets/zht_api_presets_model_index.md.BN6GzTiL.js
index 2b61760..695da8a 100644
--- a/assets/zht_api_presets_model_index.md.BJWX_k6K.js
+++ b/assets/zht_api_presets_model_index.md.BN6GzTiL.js
@@ -1,4 +1,4 @@
-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
+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":"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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,a2 as n}from"./chunks/framework.C94oF1kp.js";const o
     x_array = radius * np.sin(phi_list) * np.cos(theta_list)
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
-    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,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};
+    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/zht_api_presets_model_index.md.BJWX_k6K.lean.js b/assets/zht_api_presets_model_index.md.BN6GzTiL.lean.js
similarity index 63%
rename from assets/zht_api_presets_model_index.md.BJWX_k6K.lean.js
rename to assets/zht_api_presets_model_index.md.BN6GzTiL.lean.js
index 664af76..6a3a681 100644
--- a/assets/zht_api_presets_model_index.md.BJWX_k6K.lean.js
+++ b/assets/zht_api_presets_model_index.md.BN6GzTiL.lean.js
@@ -1 +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};
+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":"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 c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_presets_model_model.md.CNI4ubOh.js b/assets/zht_api_presets_model_model.md.pUtH2Ds8.js
similarity index 92%
rename from assets/zht_api_presets_model_model.md.CNI4ubOh.js
rename to assets/zht_api_presets_model_model.md.pUtH2Ds8.js
index c5d38ef..6629484 100644
--- a/assets/zht_api_presets_model_model.md.CNI4ubOh.js
+++ b/assets/zht_api_presets_model_model.md.pUtH2Ds8.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":"zht/api/presets/model/model.md","filePath":"zht/api/presets/model/model.md"}'),t={name:"zht/api/presets/model/model.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
+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":"zht/api/presets/model/model.md","filePath":"zht/api/presets/model/model.md"}'),t={name:"zht/api/presets/model/model.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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -15,4 +15,4 @@ import{_ as s,c as i,o as a,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,g){return a(),i("div",null,l)}const F=s(t,[["render",p]]);export{y as __pageData,F as default};
+    return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
`,10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/assets/zht_api_presets_model_model.md.CNI4ubOh.lean.js b/assets/zht_api_presets_model_model.md.pUtH2Ds8.lean.js
similarity index 76%
rename from assets/zht_api_presets_model_model.md.CNI4ubOh.lean.js
rename to assets/zht_api_presets_model_model.md.pUtH2Ds8.lean.js
index 88126ad..90a9537 100644
--- a/assets/zht_api_presets_model_model.md.CNI4ubOh.lean.js
+++ b/assets/zht_api_presets_model_model.md.pUtH2Ds8.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":"zht/api/presets/model/model.md","filePath":"zht/api/presets/model/model.md"}'),t={name:"zht/api/presets/model/model.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{y as __pageData,F 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":"zht/api/presets/model/model.md","filePath":"zht/api/presets/model/model.md"}'),t={name:"zht/api/presets/model/model.md"},h=n("",10),l=[h];function p(k,e,r,d,E,o){return a(),i("div",null,l)}const c=s(t,[["render",p]]);export{y as __pageData,c as default};
diff --git a/demo/index.html b/demo/index.html
index d859f9b..ed55000 100644
--- a/demo/index.html
+++ b/demo/index.html
@@ -6,7 +6,7 @@
     demo | MBCP 文档
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP 文档
简体中文
English
日本語
繁體中文
简体中文
English
日本語
繁體中文
Appearance
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/api.html b/en/api/api.html
index 0bac6da..338ecdb 100644
--- a/en/api/api.html
+++ b/en/api/api.html
@@ -6,7 +6,7 @@
     mbcp | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/index.html b/en/api/index.html
index 3da45c5..90b7d02 100644
--- a/en/api/index.html
+++ b/en/api/index.html
@@ -6,7 +6,7 @@
     mbcp | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
-    
+    
     
   
 
\ No newline at end of file
diff --git a/en/api/mp_math/angle.html b/en/api/mp_math/angle.html
index 8104c6f..f27a9a6 100644
--- a/en/api/mp_math/angle.html
+++ b/en/api/mp_math/angle.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.angle | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.mp_math.angle ​
Description: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
def __init__(self, value: float, is_radian: bool = False) ​
Description: 任意角度。
Arguments:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
Source code
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
View on GitHub
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def complementary(self) -> AnyAngle ​
Description: 余角：两角的和为90°。
Return: 余角
Source code
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
View on GitHub
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
Description: 补角：两角的和为180°。
Return: 补角
Source code
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
View on GitHub
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
Description: 角度。
Return: 弧度
Source code
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
View on GitHub
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
Description: 最小正角。
Return: 最小正角度
Source code
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
View on GitHub
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> AnyAngle ​
Description: 最大负角。
Return: 最大负角度
Source code
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
View on GitHub
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
Description: 正弦值。
Return: 正弦值
Source code
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
View on GitHub
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
python
@property
+    return math.sin(self.radian)
@property
def cos(self) -> float ​
Description: 余弦值。
Return: 余弦值
Source code
View on GitHub
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
python
@property
+    return math.cos(self.radian)
@property
def tan(self) -> float ​
Description: 正切值。
Return: 正切值
Source code
View on GitHub
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
python
@property
+    return math.tan(self.radian)
@property
def cot(self) -> float ​
Description: 余切值。
Return: 余切值
Source code
View on GitHub
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
python
@property
+    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
Description: 正割值。
Return: 正割值
Source code
View on GitHub
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
python
@property
+    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
Description: 余割值。
Return: 余割值
Source code
View on GitHub
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
Source code
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
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
Source code
View on GitHub
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
Source code
View on GitHub
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
Source code
View on GitHub
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
Source code
View on GitHub
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
Source code
View on GitHub
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
Source code
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
Source code
View on GitHub
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
Source code
python
def __truediv__(self, other):
+    ...
def self / other ​
Source code
View on GitHub
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/const.html b/en/api/mp_math/const.html
index fb943c2..b658d6f 100644
--- a/en/api/mp_math/const.html
+++ b/en/api/mp_math/const.html
@@ -6,7 +6,7 @@
     mbcp.mp_math.const | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP docs
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mbcp.mp_math.const ​
Description: 本模块定义了一些常用的常量
var PI = 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

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diff --git a/en/api/mp_math/equation.html b/en/api/mp_math/equation.html
index 8e17bd3..03446b3 100644
--- a/en/api/mp_math/equation.html
+++ b/en/api/mp_math/equation.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.equation | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
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mbcp.mp_math.equation ​
Description: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • 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
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English
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mbcp.mp_math.equation ​
Description: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
Description: 曲线方程。
Arguments:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
Source code
View on GitHub
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
Description: 计算曲线上的点。
Arguments:
  • *t:
  • 参数:
Return: 目标点
Source code
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
View on GitHub
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
Description: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
Arguments:
  • func: 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
View on GitHub
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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+    
     
   
 
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diff --git a/en/api/mp_math/function.html b/en/api/mp_math/function.html
index 75a7973..c8e598b 100644
--- a/en/api/mp_math/function.html
+++ b/en/api/mp_math/function.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.function | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
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English
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mbcp.mp_math.function ​
Description: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
Arguments:
  • 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
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mbcp.mp_math.function ​
Description: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
Description: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
Arguments:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
Return: 梯度
Source code
View on GitHub
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -37,7 +37,7 @@
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
Description: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
Arguments:
  • func: 函数
  • *args: 参数
Return: 柯里化后的函数
Examples:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
Source code
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
Source code
View on GitHub
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/en/api/mp_math/index.html b/en/api/mp_math/index.html
index 4098a66..9c29bb9 100644
--- a/en/api/mp_math/index.html
+++ b/en/api/mp_math/index.html
@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP docs
     
     
-    
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@@ -19,7 +19,7 @@
   
   
     
MBCP docs
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mbcp.mp_math ​
Description: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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

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diff --git a/en/api/mp_math/line.html b/en/api/mp_math/line.html
index 66833a7..0a03f81 100644
--- a/en/api/mp_math/line.html
+++ b/en/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
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日本語
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English
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mbcp.mp_math.line ​
Description: 本模块定义了三维空间中的直线类
class Line3 ​
def __init__(self, point: Point3, direction: Vector3) ​
Description: 三维空间中的直线。由一个点和一个方向向量确定。
Arguments:
  • point: 直线上的一点
  • direction: 直线的方向向量
Source code
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
+    
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mbcp.mp_math.line ​
Description: 本模块定义了三维空间中的直线类
class Line3 ​
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
View on GitHub
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
Description: 判断两条直线是否近似相等。
Arguments:
  • other: 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
View on GitHub
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
Description: 计算直线和直线之间的夹角。
Arguments:
  • other: 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
View on GitHub
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    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:
+    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
View on GitHub
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -68,7 +68,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
Description: 计算两条直线的交点。
Arguments:
  • other: 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
View on GitHub
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -83,7 +83,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
Description: 计算直线经过指定点p的垂线。
Arguments:
  • 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
View on GitHub
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -91,7 +91,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
def get_point(self, t: RealNumber) -> Point3 ​
Description: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
Arguments:
  • 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
View on GitHub
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -99,13 +99,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
Description: 获取直线的参数方程。
Return: 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
View on GitHub
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)
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:
+    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
View on GitHub
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -114,7 +114,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
Description: 判断两条直线是否平行。
Arguments:
  • 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
View on GitHub
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -122,7 +122,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
Description: 判断两条直线是否共线。
Arguments:
  • 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
View on GitHub
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -130,7 +130,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
Description: 判断点是否在直线上。
Arguments:
  • 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
View on GitHub
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -138,7 +138,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
def is_coplanar(self, other: Line3) -> bool ​
Description: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
Arguments:
  • 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
View on GitHub
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -147,7 +147,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
def simplify(self) ​
Description: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
Source code
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
View on GitHub
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -160,7 +160,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
def from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
Description: 工厂函数 由两点构造直线。
Arguments:
  • 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
View on GitHub
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -171,7 +171,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
def __and__(self, other: Line3) -> Line3 | Point3 | None ​
Description: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
Arguments:
  • other: 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
View on GitHub
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -184,7 +184,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
def __eq__(self, other) -> bool ​
Description: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
Arguments:
  • other:
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
View on GitHub
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -196,7 +196,7 @@
 
         """
     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.html b/en/api/mp_math/mp_math.html
index b3b0dd3..a669195 100644
--- a/en/api/mp_math/mp_math.html
+++ b/en/api/mp_math/mp_math.html
@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP docs
English
简体中文
日本語
繁體中文
English
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日本語
繁體中文
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mbcp.mp_math ​
Description: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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/mp_math_typing.html b/en/api/mp_math/mp_math_typing.html
index 5b128d1..6d4980c 100644
--- a/en/api/mp_math/mp_math_typing.html
+++ b/en/api/mp_math/mp_math_typing.html
@@ -6,7 +6,7 @@
     mbcp.mp_math.mp_math_typing | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP docs
English
简体中文
日本語
繁體中文
English
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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

-    
+    
     
   
 
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diff --git a/en/api/mp_math/plane.html b/en/api/mp_math/plane.html
index b549a3d..8ce0468 100644
--- a/en/api/mp_math/plane.html
+++ b/en/api/mp_math/plane.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.plane | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
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日本語
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mbcp.mp_math.plane ​
Description: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: 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
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mbcp.mp_math.plane ​
Description: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
Description: 平面方程：ax + by + cz + d = 0
Arguments:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
Source code
View on GitHub
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
Description: 判断两个平面是否近似相等。
Arguments:
  • other: 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
View on GitHub
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
Description: 计算平面与平面之间的夹角。
Arguments:
  • 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
View on GitHub
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_distance(self, other: Plane3 | Point3) -> float ​
Description: 计算平面与平面或点之间的距离。
Arguments:
  • 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
View on GitHub
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
Description: 计算两平面的交线。
Arguments:
  • other: 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
View on GitHub
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -103,7 +103,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
Description: 计算平面与直线的交点。
Arguments:
  • 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
View on GitHub
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -117,7 +117,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
def cal_parallel_plane3(self, point: Point3) -> Plane3 ​
Description: 计算平行于该平面且过指定点的平面。
Arguments:
  • 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
View on GitHub
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -125,7 +125,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
Description: 判断两个平面是否平行。
Arguments:
  • other: 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
View on GitHub
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -133,14 +133,14 @@
         Returns:
             是否平行
         """
-    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
+    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
View on GitHub
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
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
+    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
View on GitHub
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -152,7 +152,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod
def from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
Description: 工厂函数 由三点构造平面。
Arguments:
  • p1: 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
View on GitHub
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -166,7 +166,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
Description: 工厂函数 由两直线构造平面。
Arguments:
  • l1: 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
View on GitHub
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -180,7 +180,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
def from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
Description: 工厂函数 由点和直线构造平面。
Arguments:
  • 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
View on GitHub
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -190,11 +190,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __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
View on GitHub
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
Source code
View on GitHub
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
Description: 取两平面的交集（人话：交线）
Arguments:
  • 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
View on GitHub
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -211,10 +211,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
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':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
Source code
View on GitHub
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
Source code
View on GitHub
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
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diff --git a/en/api/mp_math/point.html b/en/api/mp_math/point.html
index 205ab70..ab640b4 100644
--- a/en/api/mp_math/point.html
+++ b/en/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
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mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
python
def __init__(self, x: float, y: float, z: float):
+    
MBCP docs
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English
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mbcp.mp_math.point ​
Description: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
Description: 笛卡尔坐标系中的点。
Arguments:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
Source code
View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
Description: 判断两个点是否近似相等。
Arguments:
  • 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
View on GitHub
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -38,11 +38,11 @@
         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
def 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
View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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
View on GitHub
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,14 +50,14 @@
             other:
         Returns:
         """
-    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):
+    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
View on GitHub
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)
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':
+    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
View on GitHub
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,7 +69,7 @@
         """
     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 d4fcc9a..8b5cc9a 100644
--- a/en/api/mp_math/segment.html
+++ b/en/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
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English
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mbcp.mp_math.segment ​
Description: 本模块定义了三维空间中的线段类
class Segment3 ​
def __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :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
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mbcp.mp_math.segment ​
Description: 本模块定义了三维空间中的线段类
class Segment3 ​
def __init__(self, p1: Point3, p2: Point3) ​
Description: 三维空间中的线段。 :param p1: :param p2:
Source code
View on GitHub
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -32,7 +32,7 @@
     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 6b8d57d..12d1df7 100644
--- a/en/api/mp_math/utils.html
+++ b/en/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
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English
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mbcp.mp_math.utils ​
Description: 本模块定义了一些常用的工具函数
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:
+    
MBCP docs
English
简体中文
日本語
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English
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mbcp.mp_math.utils ​
Description: 本模块定义了一些常用的工具函数
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
View on GitHub
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,8 +29,8 @@
     Returns:
         限制后的值
     """
-    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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
Source code
View on GitHub
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
Source code
View on GitHub
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -40,9 +40,9 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
def raise_type_error(self, other) ​
Source code
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
Source code
View on GitHub
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
Source code
View on GitHub
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
Description: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
Arguments:
  • x: 数1
  • y: 数2
  • epsilon: 误差
Return: 是否近似相等
Source code
View on GitHub
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -52,7 +52,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
Description: 获取数的符号。
Arguments:
  • x: 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
View on GitHub
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -65,7 +65,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
Description: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
Arguments:
  • x: 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
View on GitHub
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -82,7 +82,7 @@
         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 599447b..1380c95 100644
--- a/en/api/mp_math/vector.html
+++ b/en/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
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mbcp.mp_math.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):
+    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
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mbcp.mp_math.vector ​
Description: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
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
View on GitHub
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
Description: 判断两个向量是否近似相等。
Arguments:
  • 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
View on GitHub
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
Description: 计算两个向量之间的夹角。
Arguments:
  • 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
View on GitHub
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
Description: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
Arguments:
  • 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
View on GitHub
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         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)
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:
+    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
View on GitHub
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
Description: 判断两个向量是否平行。
Arguments:
  • 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
View on GitHub
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
Description: 将向量归一化。
自体归一化，不返回值。
Source code
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
View on GitHub
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,32 +92,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Source code
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
Source code
View on GitHub
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    return np.array([self.x, self.y, self.z])
@property
def length(self) -> float ​
Description: 向量的模。
Return: 模
Source code
View on GitHub
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
def 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
View on GitHub
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
def __abs__(self) ​
Source code
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code
python
@overload
+    return self / self.length
def __abs__(self) ​
Source code
View on GitHub
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
Source code
View on GitHub
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
Source code
View on GitHub
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def 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
View on GitHub
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -132,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
Description: 判断两个向量是否相等。
Arguments:
  • 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
View on GitHub
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -140,7 +140,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def self + other: Point3 => Point3 ​
Description: P + V -> P
别去点那边实现了。 :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
View on GitHub
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -148,11 +148,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def 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
View on GitHub
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
Source code
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
Source code
View on GitHub
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def 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
View on GitHub
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -166,7 +166,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
Description: P - V -> P
Arguments:
  • 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
View on GitHub
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -177,11 +177,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
Source code
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
Source code
View on GitHub
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
Source code
View on GitHub
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
Description: 数组运算 非点乘。点乘使用@，叉乘使用cross。
Arguments:
  • 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
View on GitHub
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -194,18 +194,18 @@
     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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
Source code
View on GitHub
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
Description: 点乘。
Arguments:
  • other:
Source code
View on GitHub
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
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 self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
Source code
View on GitHub
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
Source code
View on GitHub
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

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diff --git a/en/api/particle/index.html b/en/api/particle/index.html
index d65aa49..7694dfc 100644
--- a/en/api/particle/index.html
+++ b/en/api/particle/index.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP docs
     
     
-    
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@@ -19,7 +19,7 @@
   
   
     
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diff --git a/en/api/particle/particle.html b/en/api/particle/particle.html
index 83f37db..e518a42 100644
--- a/en/api/particle/particle.html
+++ b/en/api/particle/particle.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
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diff --git a/en/api/presets/index.html b/en/api/presets/index.html
index bfaa96a..0d15279 100644
--- a/en/api/presets/index.html
+++ b/en/api/presets/index.html
@@ -6,7 +6,7 @@
     mbcp.presets | MBCP docs
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
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 19ca9e8..0515fc2 100644
--- a/en/api/presets/model/index.html
+++ b/en/api/presets/model/index.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.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
+    
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
View on GitHub
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
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diff --git a/en/api/presets/model/model.html b/en/api/presets/model/model.html
index b1481a0..9617e9e 100644
--- a/en/api/presets/model/model.html
+++ b/en/api/presets/model/model.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP docs
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP docs
English
简体中文
日本語
繁體中文
English
简体中文
日本語
繁體中文
Appearance
mbcp.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
+    
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
View on GitHub
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

-    
+    
     
   
 
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diff --git a/en/api/presets/presets.html b/en/api/presets/presets.html
index e7b16ea..6e20cad 100644
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     mbcp.presets | MBCP docs
     
     
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MBCP docs
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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

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MBCP docs
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开始不了一点 ​
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Documentation built with VitePress | API references generated by litedoc
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     MBCP docs
     
     
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MBCP docs
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MBCP
More basic change particle
A Library for Python to create Minecraft particle effects and geometric figures
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Easy to use
Through a simple interface, most of the geometric operations and particle production requirements have been achieved
Integrated
Encapsulated and integratednumpy, scipy and sympy, making script writing as simple as using Geogebra
Rich presets
Rich presets and examples, you can use it directly, and you can also customize the parameters to create your own effects
Documentation built with VitePress | API references generated by litedoc
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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     Reference | MBCP docs
     
     
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MBCP docs
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Reference ​
help us to improve the documentation
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AAA ​
BBB ​
C ​
ddd ​
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diff --git a/hashmap.json b/hashmap.json
index 4ebd454..7140852 100644
--- a/hashmap.json
+++ b/hashmap.json
@@ -1 +1 @@
-{"api_api.md":"D_B0Hlcp","api_index.md":"C_wESrrY","api_mp_math_angle.md":"vKQLLqTS","api_mp_math_const.md":"BAf8mK4W","api_mp_math_equation.md":"B2FeM0MH","api_mp_math_function.md":"BnSMoIoo","api_mp_math_index.md":"BNf7bQqL","api_mp_math_line.md":"DPWL9O-M","api_mp_math_mp_math.md":"GlFMkWiQ","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_particle_particle.md":"yD6tcNSr","api_presets_index.md":"CD62I2gv","api_presets_model_index.md":"gO0Notp6","api_presets_model_model.md":"s8f68j_n","api_presets_presets.md":"4R0VRbQo","demo_index.md":"D-H9zRUE","en_api_api.md":"BSgrCX1d","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":"vEMIOITc","en_api_mp_math_function.md":"BWhqj_9Y","en_api_mp_math_index.md":"BEjLBMpH","en_api_mp_math_line.md":"BGq09mco","en_api_mp_math_mp_math.md":"D6ihYPav","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_particle_particle.md":"BNkfEyJn","en_api_presets_index.md":"BWb2fpTg","en_api_presets_model_index.md":"pbEu-669","en_api_presets_model_model.md":"CL5uKZbj","en_api_presets_presets.md":"CCUzsYog","en_guide_index.md":"DrDHTYCZ","en_index.md":"BSTSOH39","en_refer_index.md":"alw4L-bp","guide_index.md":"Cfmzk2IH","index.md":"CNF8LJa0","ja_api_api.md":"CPz58qIw","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":"D-4BBsnQ","ja_api_mp_math_function.md":"Bvf1U09A","ja_api_mp_math_index.md":"CTZZ-p9Z","ja_api_mp_math_line.md":"DYJV4KNE","ja_api_mp_math_mp_math.md":"D-prC0UO","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_particle_particle.md":"exTt46pq","ja_api_presets_index.md":"CQqdQbIZ","ja_api_presets_model_index.md":"C-Ypf-qh","ja_api_presets_model_model.md":"Dwbc1qIc","ja_api_presets_presets.md":"DwzXdDqR","ja_guide_index.md":"BxGnZYwR","ja_index.md":"DCWiTENz","ja_refer_index.md":"CODW6iMX","refer_function_curry.md":"DwKZawp5","refer_function_function.md":"D3IgfZX2","refer_index.md":"CczYTl3j","zht_api_api.md":"DyUSHA0S","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":"BAr_ktNP","zht_api_mp_math_function.md":"C2Gp7z0v","zht_api_mp_math_index.md":"mmeMMriu","zht_api_mp_math_line.md":"DX62bgjZ","zht_api_mp_math_mp_math.md":"C302rxKc","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_particle_particle.md":"huuRTEb9","zht_api_presets_index.md":"DvOViSox","zht_api_presets_model_index.md":"BJWX_k6K","zht_api_presets_model_model.md":"CNI4ubOh","zht_api_presets_presets.md":"CsDHjRbK","zht_guide_index.md":"CsuFVFxu","zht_index.md":"VMjJ0lpj","zht_refer_index.md":"Bz6voxEQ"}
+{"api_api.md":"D_B0Hlcp","api_index.md":"C_wESrrY","api_mp_math_angle.md":"bQbgL5rc","api_mp_math_const.md":"BAf8mK4W","api_mp_math_equation.md":"hWRUu0yD","api_mp_math_function.md":"C9eBzKgT","api_mp_math_index.md":"BNf7bQqL","api_mp_math_line.md":"DDkzT0e0","api_mp_math_mp_math.md":"GlFMkWiQ","api_mp_math_mp_math_typing.md":"DlnJmkos","api_mp_math_plane.md":"DCL3lFbz","api_mp_math_point.md":"Y0Sc19zU","api_mp_math_segment.md":"B-ptCnQ0","api_mp_math_utils.md":"mUQ56HGQ","api_mp_math_vector.md":"BeAN7TkI","api_particle_index.md":"Cm3Vk-es","api_particle_particle.md":"yD6tcNSr","api_presets_index.md":"CD62I2gv","api_presets_model_index.md":"BGeoOSCd","api_presets_model_model.md":"D34eFRNH","api_presets_presets.md":"4R0VRbQo","demo_index.md":"D-H9zRUE","en_api_api.md":"BSgrCX1d","en_api_index.md":"Dj_5nFTt","en_api_mp_math_angle.md":"Cj4ayIet","en_api_mp_math_const.md":"gGpXUShq","en_api_mp_math_equation.md":"BihILJCI","en_api_mp_math_function.md":"BR29hv60","en_api_mp_math_index.md":"BEjLBMpH","en_api_mp_math_line.md":"CIOnk8LF","en_api_mp_math_mp_math.md":"D6ihYPav","en_api_mp_math_mp_math_typing.md":"Dnl2aJQ4","en_api_mp_math_plane.md":"Cbmy4F0P","en_api_mp_math_point.md":"szYqVNff","en_api_mp_math_segment.md":"CqlcAra1","en_api_mp_math_utils.md":"CigCGgjm","en_api_mp_math_vector.md":"CF4kCv-W","en_api_particle_index.md":"BfyNQiRg","en_api_particle_particle.md":"BNkfEyJn","en_api_presets_index.md":"BWb2fpTg","en_api_presets_model_index.md":"Cnn4t_P0","en_api_presets_model_model.md":"BZpQe5Li","en_api_presets_presets.md":"CCUzsYog","en_guide_index.md":"DrDHTYCZ","en_index.md":"BSTSOH39","en_refer_index.md":"alw4L-bp","guide_index.md":"Cfmzk2IH","index.md":"CNF8LJa0","ja_api_api.md":"CPz58qIw","ja_api_index.md":"CnUeuifx","ja_api_mp_math_angle.md":"D0ChdV9L","ja_api_mp_math_const.md":"DGXAgDfn","ja_api_mp_math_equation.md":"ksLzfPHD","ja_api_mp_math_function.md":"S4mlhSEl","ja_api_mp_math_index.md":"CTZZ-p9Z","ja_api_mp_math_line.md":"C6_h0EEF","ja_api_mp_math_mp_math.md":"D-prC0UO","ja_api_mp_math_mp_math_typing.md":"BNymgrCT","ja_api_mp_math_plane.md":"CVfLX9sr","ja_api_mp_math_point.md":"21gM893G","ja_api_mp_math_segment.md":"Dji9_vOI","ja_api_mp_math_utils.md":"DhvjDskn","ja_api_mp_math_vector.md":"DyGgurm4","ja_api_particle_index.md":"Jr41Y3TS","ja_api_particle_particle.md":"exTt46pq","ja_api_presets_index.md":"CQqdQbIZ","ja_api_presets_model_index.md":"Dbt3LFNK","ja_api_presets_model_model.md":"ti1HKQyY","ja_api_presets_presets.md":"DwzXdDqR","ja_guide_index.md":"BxGnZYwR","ja_index.md":"DCWiTENz","ja_refer_index.md":"CODW6iMX","refer_function_curry.md":"DwKZawp5","refer_function_function.md":"D3IgfZX2","refer_index.md":"CczYTl3j","zht_api_api.md":"DyUSHA0S","zht_api_index.md":"CgZH6aHQ","zht_api_mp_math_angle.md":"ByT5Hatc","zht_api_mp_math_const.md":"xwQvuYck","zht_api_mp_math_equation.md":"C9JJo8Tj","zht_api_mp_math_function.md":"CUiziArf","zht_api_mp_math_index.md":"mmeMMriu","zht_api_mp_math_line.md":"TSJBrHTa","zht_api_mp_math_mp_math.md":"C302rxKc","zht_api_mp_math_mp_math_typing.md":"CNiSnuMw","zht_api_mp_math_plane.md":"CO3Dxqtg","zht_api_mp_math_point.md":"hahZSaSv","zht_api_mp_math_segment.md":"BVxd03II","zht_api_mp_math_utils.md":"Dz7jYC2A","zht_api_mp_math_vector.md":"26fppi_c","zht_api_particle_index.md":"8GaGB1ul","zht_api_particle_particle.md":"huuRTEb9","zht_api_presets_index.md":"DvOViSox","zht_api_presets_model_index.md":"BN6GzTiL","zht_api_presets_model_model.md":"pUtH2Ds8","zht_api_presets_presets.md":"CsDHjRbK","zht_guide_index.md":"CsuFVFxu","zht_index.md":"VMjJ0lpj","zht_refer_index.md":"Bz6voxEQ"}
diff --git a/index.html b/index.html
index bcedc8b..2356727 100644
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     MBCP 文档
     
     
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MBCP 文档
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MBCP
更多基础变换粒子
用于几何运算和Minecraft粒子制作的库
快速开始
API文档
MBCP logo
高可用性
通过简单的接口，实现了大部分几何运算和粒子制作的需求
高集成度
对numpy、scipy及sumpy进行了封装和集成，使脚本编写像使用Geogebra一样简单
内置预设
提供了大量的预设，包括常见的几何图形、粒子效果等，方便快速制作
文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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     mbcp | MBCP ドキュメント
     
     
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index 6551d99..d9bc4f9 100644
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     mbcp.mp_math.angle | MBCP ドキュメント
     
     
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MBCP ドキュメント
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mbcp.mp_math.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):
+    
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mbcp.mp_math.angle ​
説明: 本模块定义了角度相关的类
class Angle ​
class AnyAngle(Angle) ​
def __init__(self, value: float, is_radian: bool = False) ​
説明: 任意角度。
引数:
  • value: 角度或弧度值
  • is_radian: 是否为弧度，默认为否
ソースコード
GitHubで表示
python
def __init__(self, value: float, is_radian: bool=False):
     """
         任意角度。
         Args:
@@ -28,96 +28,96 @@
     if is_radian:
         self.radian = value
     else:
-        self.radian = value * PI / 180
@property
def complementary(self) -> AnyAngle ​
説明: 余角：两角的和为90°。
戻り値: 余角
ソースコード
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
GitHubで表示
python
@property
 def complementary(self) -> 'AnyAngle':
     """
         余角：两角的和为90°。
         Returns:
             余角
         """
-    return AnyAngle(PI / 2 - self.minimum_positive.radian, is_radian=True)
@property
def supplementary(self) -> AnyAngle ​
説明: 补角：两角的和为180°。
戻り値: 补角
ソースコード
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
GitHubで表示
python
@property
 def supplementary(self) -> 'AnyAngle':
     """
         补角：两角的和为180°。
         Returns:
             补角
         """
-    return AnyAngle(PI - self.minimum_positive.radian, is_radian=True)
@property
def degree(self) -> float ​
説明: 角度。
戻り値: 弧度
ソースコード
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
GitHubで表示
python
@property
 def degree(self) -> float:
     """
         角度。
         Returns:
             弧度
         """
-    return self.radian * 180 / PI
@property
def minimum_positive(self) -> AnyAngle ​
説明: 最小正角。
戻り値: 最小正角度
ソースコード
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
GitHubで表示
python
@property
 def minimum_positive(self) -> 'AnyAngle':
     """
         最小正角。
         Returns:
             最小正角度
         """
-    return AnyAngle(self.radian % (2 * PI))
@property
def maximum_negative(self) -> AnyAngle ​
説明: 最大负角。
戻り値: 最大负角度
ソースコード
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
GitHubで表示
python
@property
 def maximum_negative(self) -> 'AnyAngle':
     """
         最大负角。
         Returns:
             最大负角度
         """
-    return AnyAngle(-self.radian % (2 * PI), is_radian=True)
@property
def sin(self) -> float ​
説明: 正弦值。
戻り値: 正弦值
ソースコード
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
GitHubで表示
python
@property
 def sin(self) -> float:
     """
         正弦值。
         Returns:
             正弦值
         """
-    return math.sin(self.radian)
@property
def cos(self) -> float ​
説明: 余弦值。
戻り値: 余弦值
ソースコード
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
GitHubで表示
python
@property
 def cos(self) -> float:
     """
         余弦值。
         Returns:
             余弦值
         """
-    return math.cos(self.radian)
@property
def tan(self) -> float ​
説明: 正切值。
戻り値: 正切值
ソースコード
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
GitHubで表示
python
@property
 def tan(self) -> float:
     """
         正切值。
         Returns:
             正切值
         """
-    return math.tan(self.radian)
@property
def cot(self) -> float ​
説明: 余切值。
戻り値: 余切值
ソースコード
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
GitHubで表示
python
@property
 def cot(self) -> float:
     """
         余切值。
         Returns:
             余切值
         """
-    return 1 / math.tan(self.radian)
@property
def sec(self) -> float ​
説明: 正割值。
戻り値: 正割值
ソースコード
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
GitHubで表示
python
@property
 def sec(self) -> float:
     """
         正割值。
         Returns:
             正割值
         """
-    return 1 / math.cos(self.radian)
@property
def csc(self) -> float ​
説明: 余割值。
戻り値: 余割值
ソースコード
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
GitHubで表示
python
@property
 def csc(self) -> float:
     """
         余割值。
         Returns:
             余割值
         """
-    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
ソースコード
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
+    return 1 / math.sin(self.radian)
def self + other: AnyAngle => AnyAngle ​
ソースコード
GitHubで表示
python
def __add__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian + other.radian, is_radian=True)
def __eq__(self, other) ​
ソースコード
GitHubで表示
python
def __eq__(self, other):
+    return approx(self.radian, other.radian)
def self - other: AnyAngle => AnyAngle ​
ソースコード
GitHubで表示
python
def __sub__(self, other: 'AnyAngle') -> 'AnyAngle':
+    return AnyAngle(self.radian - other.radian, is_radian=True)
def self * other: float => AnyAngle ​
ソースコード
GitHubで表示
python
def __mul__(self, other: float) -> 'AnyAngle':
+    return AnyAngle(self.radian * other, is_radian=True)
@overload
def self / other: float => AnyAngle ​
ソースコード
GitHubで表示
python
@overload
 def __truediv__(self, other: float) -> 'AnyAngle':
-    ...
@overload
def self / other: AnyAngle => float ​
ソースコード
python
@overload
+    ...
@overload
def self / other: AnyAngle => float ​
ソースコード
GitHubで表示
python
@overload
 def __truediv__(self, other: 'AnyAngle') -> float:
-    ...
def self / other ​
ソースコード
python
def __truediv__(self, other):
+    ...
def self / other ​
ソースコード
GitHubで表示
python
def __truediv__(self, other):
     if isinstance(other, AnyAngle):
         return self.radian / other.radian
     return AnyAngle(self.radian / other, is_radian=True)
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diff --git a/ja/api/mp_math/const.html b/ja/api/mp_math/const.html
index e2ab507..829bd70 100644
--- a/ja/api/mp_math/const.html
+++ b/ja/api/mp_math/const.html
@@ -6,7 +6,7 @@
     mbcp.mp_math.const | MBCP ドキュメント
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
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mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI = 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
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diff --git a/ja/api/mp_math/equation.html b/ja/api/mp_math/equation.html
index cdf53b1..6eb9fa7 100644
--- a/ja/api/mp_math/equation.html
+++ b/ja/api/mp_math/equation.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.equation | MBCP ドキュメント
     
     
-    
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+    
     
     
     
   
   
-    
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mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
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):
+    
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mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
引数:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
ソースコード
GitHubで表示
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
説明: 计算曲线上的点。
引数:
  • *t:
  • 参数:
戻り値: 目标点
ソースコード
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
GitHubで表示
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
説明: 求N元函数一阶偏导函数。这玩意不太稳定，慎用。
WARNING
目前数学界对于一个函数的导函数并没有通解的说法，因此该函数的稳定性有待提升
引数:
  • func: 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
GitHubで表示
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/mp_math/function.html b/ja/api/mp_math/function.html
index a312d99..9c15569 100644
--- a/ja/api/mp_math/function.html
+++ b/ja/api/mp_math/function.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.function | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
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mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
引数:
  • 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:
+    
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mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
引数:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
戻り値: 梯度
ソースコード
GitHubで表示
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -37,7 +37,7 @@
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
引数:
  • func: 函数
  • *args: 参数
戻り値: 柯里化后的函数
例:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
ソースコード
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
ソースコード
GitHubで表示
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/mp_math/index.html b/ja/api/mp_math/index.html
index 3ec5dbd..f8d0e80 100644
--- a/ja/api/mp_math/index.html
+++ b/ja/api/mp_math/index.html
@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP ドキュメント
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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 f0c63cc..5a1d512 100644
--- a/ja/api/mp_math/line.html
+++ b/ja/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
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mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
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'):
+    
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mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
def __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
引数:
  • point: 直线上的一点
  • direction: 直线的方向向量
ソースコード
GitHubで表示
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
引数:
  • other: 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
GitHubで表示
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
引数:
  • other: 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
GitHubで表示
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    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:
+    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
GitHubで表示
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -68,7 +68,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
引数:
  • other: 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
GitHubで表示
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -83,7 +83,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
引数:
  • 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
GitHubで表示
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -91,7 +91,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
def get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
引数:
  • 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
GitHubで表示
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -99,13 +99,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
戻り値: 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
GitHubで表示
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)
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:
+    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
GitHubで表示
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -114,7 +114,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
引数:
  • 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
GitHubで表示
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -122,7 +122,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
引数:
  • 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
GitHubで表示
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -130,7 +130,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
引数:
  • 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
GitHubで表示
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -138,7 +138,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
def is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
引数:
  • 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
GitHubで表示
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -147,7 +147,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
def simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
ソースコード
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
GitHubで表示
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -160,7 +160,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
def from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
引数:
  • 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
GitHubで表示
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -171,7 +171,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
def __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
引数:
  • other: 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
GitHubで表示
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -184,7 +184,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
def __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
引数:
  • other:
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
GitHubで表示
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -196,7 +196,7 @@
 
         """
     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

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diff --git a/ja/api/mp_math/mp_math.html b/ja/api/mp_math/mp_math.html
index 947f69c..2c0e8a0 100644
--- a/ja/api/mp_math/mp_math.html
+++ b/ja/api/mp_math/mp_math.html
@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP ドキュメント
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP ドキュメント
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English
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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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

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diff --git a/ja/api/mp_math/mp_math_typing.html b/ja/api/mp_math/mp_math_typing.html
index 8ac6e91..1866625 100644
--- a/ja/api/mp_math/mp_math_typing.html
+++ b/ja/api/mp_math/mp_math_typing.html
@@ -6,7 +6,7 @@
     mbcp.mp_math.mp_math_typing | MBCP ドキュメント
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP ドキュメント
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mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber = 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

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diff --git a/ja/api/mp_math/plane.html b/ja/api/mp_math/plane.html
index be34062..936147b 100644
--- a/ja/api/mp_math/plane.html
+++ b/ja/api/mp_math/plane.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.plane | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP ドキュメント
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mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: 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):
+    
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mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
def __init__(self, a: float, b: float, c: float, d: float) ​
説明: 平面方程：ax + by + cz + d = 0
引数:
  • a: x系数
  • b: y系数
  • c: z系数
  • d: 常数项
ソースコード
GitHubで表示
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
説明: 判断两个平面是否近似相等。
引数:
  • other: 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
GitHubで表示
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
説明: 计算平面与平面之间的夹角。
引数:
  • 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
GitHubで表示
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_distance(self, other: Plane3 | Point3) -> float ​
説明: 计算平面与平面或点之间的距离。
引数:
  • 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
GitHubで表示
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
説明: 计算两平面的交线。
引数:
  • other: 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
GitHubで表示
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -103,7 +103,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
引数:
  • 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
GitHubで表示
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -117,7 +117,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
def cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
引数:
  • 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
GitHubで表示
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -125,7 +125,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
引数:
  • other: 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
GitHubで表示
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -133,14 +133,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
説明: 平面的法向量。
戻り値: 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
GitHubで表示
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
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
+    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
GitHubで表示
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -152,7 +152,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod
def from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
引数:
  • p1: 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
GitHubで表示
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -166,7 +166,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
引数:
  • l1: 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
GitHubで表示
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -180,7 +180,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
def from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
引数:
  • 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
GitHubで表示
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -190,11 +190,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __and__(self, other: Line3) -> Point3 | None ​
ソースコード
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
GitHubで表示
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
ソースコード
GitHubで表示
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
引数:
  • 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
GitHubで表示
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -211,10 +211,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
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':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
ソースコード
GitHubで表示
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
ソースコード
GitHubで表示
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
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diff --git a/ja/api/mp_math/point.html b/ja/api/mp_math/point.html
index 592024f..a5f92b3 100644
--- a/ja/api/mp_math/point.html
+++ b/ja/api/mp_math/point.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
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mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: 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):
+    
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mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
引数:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
ソースコード
GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
説明: 判断两个点是否近似相等。
引数:
  • 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
GitHubで表示
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -38,11 +38,11 @@
         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
def 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
GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: P + V -> P P + P -> P
引数:
  • 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
GitHubで表示
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,14 +50,14 @@
             other:
         Returns:
         """
-    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):
+    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
GitHubで表示
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)
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':
+    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
GitHubで表示
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,7 +69,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/ja/api/mp_math/segment.html b/ja/api/mp_math/segment.html
index 8985d85..010147a 100644
--- a/ja/api/mp_math/segment.html
+++ b/ja/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
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mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
def __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
ソースコード
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
+    
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mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
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
GitHubで表示
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -32,7 +32,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
VitePress で構築されたドキュメント | litedoc によって生成されたAPIリファレンス
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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+    
     
   
 
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diff --git a/ja/api/mp_math/utils.html b/ja/api/mp_math/utils.html
index 08fef2e..9ccca3d 100644
--- a/ja/api/mp_math/utils.html
+++ b/ja/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
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mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
def clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
引数:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
戻り値: 限制后的值
ソースコード
python
def clamp(x: float, min_: float, max_: float) -> float:
+    
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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
GitHubで表示
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,8 +29,8 @@
     Returns:
         限制后的值
     """
-    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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
ソースコード
GitHubで表示
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
ソースコード
GitHubで表示
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -40,9 +40,9 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
def raise_type_error(self, other) ​
ソースコード
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
ソースコード
GitHubで表示
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
ソースコード
GitHubで表示
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
説明: 判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
引数:
  • x: 数1
  • y: 数2
  • epsilon: 误差
戻り値: 是否近似相等
ソースコード
GitHubで表示
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -52,7 +52,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
引数:
  • x: 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
GitHubで表示
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -65,7 +65,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
引数:
  • x: 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
GitHubで表示
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -82,7 +82,7 @@
         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 bd45d5f..5f2dc29 100644
--- a/ja/api/mp_math/vector.html
+++ b/ja/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
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mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: 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 ドキュメント
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mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
引数:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
ソースコード
GitHubで表示
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
説明: 判断两个向量是否近似相等。
引数:
  • 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
GitHubで表示
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
引数:
  • 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
GitHubで表示
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
引数:
  • 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
GitHubで表示
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             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)
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:
+    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
GitHubで表示
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
引数:
  • 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
GitHubで表示
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
ソースコード
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
GitHubで表示
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,32 +92,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def 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
GitHubで表示
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    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
GitHubで表示
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
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
+    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
GitHubで表示
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
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
+    return self / self.length
def __abs__(self) ​
ソースコード
GitHubで表示
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
ソースコード
GitHubで表示
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
ソースコード
GitHubで表示
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: V + P -> P
V + V -> V
引数:
  • 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
GitHubで表示
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -132,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
説明: 判断两个向量是否相等。
引数:
  • 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
GitHubで表示
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -140,7 +140,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :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
GitHubで表示
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -148,11 +148,11 @@
         :param other:
         :return:
         """
-    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
+    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
GitHubで表示
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
ソースコード
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
ソースコード
GitHubで表示
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def self - other ​
説明: V - P -> P
V - V -> V
引数:
  • 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
GitHubで表示
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -166,7 +166,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
説明: P - V -> P
引数:
  • 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
GitHubで表示
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -177,11 +177,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
ソースコード
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
GitHubで表示
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
ソースコード
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
ソースコード
GitHubで表示
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
引数:
  • 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
GitHubで表示
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -194,18 +194,18 @@
     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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
ソースコード
GitHubで表示
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
引数:
  • other:
ソースコード
GitHubで表示
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
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 self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
ソースコード
GitHubで表示
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
GitHubで表示
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

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diff --git a/ja/api/particle/index.html b/ja/api/particle/index.html
index cf96130..9cc9647 100644
--- a/ja/api/particle/index.html
+++ b/ja/api/particle/index.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP ドキュメント
     
     
-    
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@@ -19,7 +19,7 @@
   
   
     
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diff --git a/ja/api/particle/particle.html b/ja/api/particle/particle.html
index 3ba371c..27deaf1 100644
--- a/ja/api/particle/particle.html
+++ b/ja/api/particle/particle.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP ドキュメント
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
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+    
     
   
 
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diff --git a/ja/api/presets/index.html b/ja/api/presets/index.html
index 085db8c..1ed2b18 100644
--- a/ja/api/presets/index.html
+++ b/ja/api/presets/index.html
@@ -6,7 +6,7 @@
     mbcp.presets | MBCP ドキュメント
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.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 5a75a2c..2e202b2 100644
--- a/ja/api/presets/model/index.html
+++ b/ja/api/presets/model/index.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP ドキュメント
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP ドキュメント
日本語
简体中文
English
繁體中文
日本語
简体中文
English
繁體中文
Appearance
mbcp.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
+    
MBCP ドキュメント
日本語
简体中文
English
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
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     mbcp.presets.model | MBCP ドキュメント
     
     
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
python
@staticmethod
+    
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
引数:
  • radius:
  • density:
戻り値: List[Point3]: 球体上的点集。
ソースコード
GitHubで表示
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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     mbcp.presets | MBCP ドキュメント
     
     
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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

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     开始不了一点 | MBCP ドキュメント
     
     
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开始不了一点 ​
∫12x111
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     MBCP ドキュメント
     
     
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MBCP
More basic change particle
ジオメトリ演算とパーティクル作成のためのライブラリ
はじめる
API リファレンス
MBCP logo
高可用性
シンプルなインターフェースを通じて、ほとんどのジオメトリ演算とパーティクル作成のニーズを実現しました
高集積度
numpy、scipy、およびsympyをラップして統合し、Geogebraを使用するように簡単にスクリプトを作成できます
組み込みプリセット
多くのプリセットを提供しており、一般的なジオメトリ図形やパーティクル効果など、迅速に作成できます
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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     Reference | MBCP ドキュメント
     
     
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Reference ​
Help us to improve the documentation
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     柯里化 | MBCP 文档
     
     
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文档由 VitePress 构建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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

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     mbcp.mp_math.const | MBCP 文檔
     
     
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mbcp.mp_math.const ​
説明: 本模块定义了一些常用的常量
var PI = 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

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     mbcp.mp_math.equation | MBCP 文檔
     
     
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mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • 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):
+    
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mbcp.mp_math.equation ​
説明: 本模块定义了方程相关的类和函数以及一些常用的数学函数
class CurveEquation ​
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc) ​
説明: 曲线方程。
變數説明:
  • x_func: x函数
  • y_func: y函数
  • z_func: z函数
源碼
在GitHub上查看
python
def __init__(self, x_func: OneVarFunc, y_func: OneVarFunc, z_func: OneVarFunc):
     """
         曲线方程。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x_func = x_func
     self.y_func = y_func
-    self.z_func = z_func
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...] ​
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
在GitHub上查看
python
def __call__(self, *t: Var) -> Point3 | tuple[Point3, ...]:
     """
         计算曲线上的点。
         Args:
@@ -40,7 +40,7 @@
     if len(t) == 1:
         return Point3(self.x_func(t[0]), self.y_func(t[0]), self.z_func(t[0]))
     else:
-        return tuple([Point3(x, y, z) for x, y, z in zip(self.x_func(t), self.y_func(t), self.z_func(t))])
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number = EPSILON) -> MultiVarsFunc ​
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
在GitHub上查看
python
def get_partial_derivative_func(func: MultiVarsFunc, var: int | tuple[int, ...], epsilon: Number=EPSILON) -> MultiVarsFunc:
     """
     求N元函数一阶偏导函数。这玩意不太稳定，慎用。
     > [!warning]
@@ -83,7 +83,7 @@
         return high_order_partial_derivative_func
     else:
         raise ValueError('Invalid var type')
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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--- a/zht/api/mp_math/function.html
+++ b/zht/api/mp_math/function.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.function | MBCP 文檔
     
     
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mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
變數説明:
  • 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:
+    
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mbcp.mp_math.function ​
説明: AAA
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float = EPSILON) -> Vector3 ​
説明: 计算三元函数在某点的梯度向量。
TIP
已知一个函数f(x,y,z)，则其在点(x0,y0,z0)处的梯度向量为: ∇f(x0,y0,z0)=(∂f∂x,∂f∂y,∂f∂z)
變數説明:
  • func: 三元函数
  • p: 点
  • epsilon: 偏移量
返回: 梯度
源碼
在GitHub上查看
python
def cal_gradient_3vf(func: ThreeSingleVarsFunc, p: Point3, epsilon: float=EPSILON) -> Vector3:
     """
     计算三元函数在某点的梯度向量。
     > [!tip]
@@ -37,7 +37,7 @@
     return Vector3(dx, dy, dz)
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc ​
説明: 对多参数函数进行柯里化。
TIP
有关函数柯里化，可参考函数式编程--柯理化（Currying）
變數説明:
  • func: 函数
  • *args: 参数
返回: 柯里化后的函数
範例:
python
def add(a: int, b: int, c: int) -> int:
     return a + b + c
 add_curried = curry(add, 1, 2)
-add_curried(3)  # 6
源碼
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
+add_curried(3)  # 6
源碼
在GitHub上查看
python
def curry(func: MultiVarsFunc, *args: Var) -> OneVarFunc:
     """
     对多参数函数进行柯里化。
     > [!tip]
@@ -60,7 +60,7 @@
         """@litedoc-hide"""
         return func(*args, *args2)
     return curried_func
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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@@ -6,7 +6,7 @@
     mbcp.mp_math | MBCP 文檔
     
     
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mbcp.mp_math ​
説明: 本包定义了一些常用的导入，可直接从mbcp.mp_math导入使用 导入的类有：
  • 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

-    
+    
     
   
 
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diff --git a/zht/api/mp_math/line.html b/zht/api/mp_math/line.html
index 4bc4acc..1622c8b 100644
--- a/zht/api/mp_math/line.html
+++ b/zht/api/mp_math/line.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.line | MBCP 文檔
     
     
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mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
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'):
+    
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mbcp.mp_math.line ​
説明: 本模块定义了三维空间中的直线类
class Line3 ​
def __init__(self, point: Point3, direction: Vector3) ​
説明: 三维空间中的直线。由一个点和一个方向向量确定。
變數説明:
  • point: 直线上的一点
  • direction: 直线的方向向量
源碼
在GitHub上查看
python
def __init__(self, point: 'Point3', direction: 'Vector3'):
     """
         三维空间中的直线。由一个点和一个方向向量确定。
         Args:
@@ -26,7 +26,7 @@
             direction: 直线的方向向量
         """
     self.point = point
-    self.direction = direction
def approx(self, other: Line3, epsilon: float = APPROX) -> bool ​
説明: 判断两条直线是否近似相等。
變數説明:
  • other: 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
在GitHub上查看
python
def approx(self, other: 'Line3', epsilon: float=APPROX) -> bool:
     """
         判断两条直线是否近似相等。
         Args:
@@ -35,7 +35,7 @@
         Returns:
             是否近似相等
         """
-    return self.is_approx_parallel(other, epsilon) and (self.point - other.point).is_approx_parallel(self.direction, epsilon)
def cal_angle(self, other: Line3) -> AnyAngle ​
説明: 计算直线和直线之间的夹角。
變數説明:
  • other: 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
在GitHub上查看
python
def cal_angle(self, other: 'Line3') -> 'AnyAngle':
     """
         计算直线和直线之间的夹角。
         Args:
@@ -45,7 +45,7 @@
         Raises:
             TypeError: 不支持的类型
         """
-    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:
+    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
在GitHub上查看
python
def cal_distance(self, other: 'Line3 | Point3') -> float:
     """
         计算直线和直线或点之间的距离。
         Args:
@@ -68,7 +68,7 @@
     elif isinstance(other, Point3):
         return (other - self.point).cross(self.direction).length / self.direction.length
     else:
-        raise TypeError('Unsupported type.')
def cal_intersection(self, other: Line3) -> Point3 ​
説明: 计算两条直线的交点。
變數説明:
  • other: 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
在GitHub上查看
python
def cal_intersection(self, other: 'Line3') -> 'Point3':
     """
         计算两条直线的交点。
         Args:
@@ -83,7 +83,7 @@
         raise ValueError('Lines are parallel and do not intersect.')
     if not self.is_coplanar(other):
         raise ValueError('Lines are not coplanar and do not intersect.')
-    return self.point + self.direction.cross(other.direction) @ other.direction.cross(self.point - other.point) / self.direction.cross(other.direction).length ** 2 * self.direction
def cal_perpendicular(self, point: Point3) -> Line3 ​
説明: 计算直线经过指定点p的垂线。
變數説明:
  • 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
在GitHub上查看
python
def cal_perpendicular(self, point: 'Point3') -> 'Line3':
     """
         计算直线经过指定点p的垂线。
         Args:
@@ -91,7 +91,7 @@
         Returns:
             垂线
         """
-    return Line3(point, self.direction.cross(point - self.point))
def get_point(self, t: RealNumber) -> Point3 ​
説明: 获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
變數説明:
  • 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
在GitHub上查看
python
def get_point(self, t: RealNumber) -> 'Point3':
     """
         获取直线上的点。同一条直线，但起始点和方向向量不同，则同一个t对应的点不同。
         Args:
@@ -99,13 +99,13 @@
         Returns:
             点
         """
-    return self.point + t * self.direction
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc] ​
説明: 获取直线的参数方程。
返回: 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
在GitHub上查看
python
def get_parametric_equations(self) -> tuple[OneSingleVarFunc, OneSingleVarFunc, OneSingleVarFunc]:
     """
         获取直线的参数方程。
         Returns:
             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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Line3', epsilon: float=1e-06) -> bool:
     """
         判断两条直线是否近似平行。
         Args:
@@ -114,7 +114,7 @@
         Returns:
             是否近似平行
         """
-    return self.direction.is_approx_parallel(other.direction, epsilon)
def is_parallel(self, other: Line3) -> bool ​
説明: 判断两条直线是否平行。
變數説明:
  • 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
在GitHub上查看
python
def is_parallel(self, other: 'Line3') -> bool:
     """
         判断两条直线是否平行。
         Args:
@@ -122,7 +122,7 @@
         Returns:
             是否平行
         """
-    return self.direction.is_parallel(other.direction)
def is_collinear(self, other: Line3) -> bool ​
説明: 判断两条直线是否共线。
變數説明:
  • 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
在GitHub上查看
python
def is_collinear(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共线。
         Args:
@@ -130,7 +130,7 @@
         Returns:
             是否共线
         """
-    return self.is_parallel(other) and (self.point - other.point).is_parallel(self.direction)
def is_point_on(self, point: Point3) -> bool ​
説明: 判断点是否在直线上。
變數説明:
  • 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
在GitHub上查看
python
def is_point_on(self, point: 'Point3') -> bool:
     """
         判断点是否在直线上。
         Args:
@@ -138,7 +138,7 @@
         Returns:
             是否在直线上
         """
-    return (point - self.point).is_parallel(self.direction)
def is_coplanar(self, other: Line3) -> bool ​
説明: 判断两条直线是否共面。 充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
變數説明:
  • 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
在GitHub上查看
python
def is_coplanar(self, other: 'Line3') -> bool:
     """
         判断两条直线是否共面。
         充要条件：两直线方向向量的叉乘与两直线上任意一点的向量的点积为0。
@@ -147,7 +147,7 @@
         Returns:
             是否共面
         """
-    return self.direction.cross(other.direction) @ (self.point - other.point) == 0
def simplify(self) ​
説明: 简化直线方程，等价相等。 自体简化，不返回值。
按照可行性一次对x y z 化 0 处理，并对向量单位化
源碼
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
在GitHub上查看
python
def simplify(self):
     """
         简化直线方程，等价相等。
         自体简化，不返回值。
@@ -160,7 +160,7 @@
     if self.direction.y == 0:
         self.point.y = 0
     if self.direction.z == 0:
-        self.point.z = 0
@classmethod
def from_two_points(cls, p1: Point3, p2: Point3) -> Line3 ​
説明: 工厂函数 由两点构造直线。
變數説明:
  • 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
在GitHub上查看
python
@classmethod
 def from_two_points(cls, p1: 'Point3', p2: 'Point3') -> 'Line3':
     """
         工厂函数 由两点构造直线。
@@ -171,7 +171,7 @@
             直线
         """
     direction = p2 - p1
-    return cls(p1, direction)
def __and__(self, other: Line3) -> Line3 | Point3 | None ​
説明: 计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
變數説明:
  • other: 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
在GitHub上查看
python
def __and__(self, other: 'Line3') -> 'Line3 | Point3 | None':
     """
         计算两条直线点集合的交集。重合线返回自身，平行线返回None，交线返回交点。
         Args:
@@ -184,7 +184,7 @@
     elif self.is_parallel(other) or not self.is_coplanar(other):
         return None
     else:
-        return self.cal_intersection(other)
def __eq__(self, other) -> bool ​
説明: 判断两条直线是否等价。
v1 // v2 ∧ (p1 - p2) // v1
變數説明:
  • other:
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
在GitHub上查看
python
def __eq__(self, other) -> bool:
     """
         判断两条直线是否等价。
 
@@ -196,7 +196,7 @@
 
         """
     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

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

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--- a/zht/api/mp_math/mp_math_typing.html
+++ b/zht/api/mp_math/mp_math_typing.html
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     mbcp.mp_math.mp_math_typing | MBCP 文檔
     
     
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mbcp.mp_math.mp_math_typing ​
説明: 本模块用于内部类型提示
var RealNumber = 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

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     mbcp.mp_math.plane | MBCP 文檔
     
     
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mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
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):
+    
MBCP 文檔
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mbcp.mp_math.plane ​
説明: 本模块定义了三维空间中的平面类
class Plane3 ​
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
在GitHub上查看
python
def __init__(self, a: float, b: float, c: float, d: float):
     """
         平面方程：ax + by + cz + d = 0
         Args:
@@ -30,7 +30,7 @@
     self.a = a
     self.b = b
     self.c = c
-    self.d = d
def approx(self, other: Plane3) -> bool ​
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
在GitHub上查看
python
def approx(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否近似相等。
         Args:
@@ -48,7 +48,7 @@
         k = other.c / self.c
         return approx(other.a, self.a * k) and approx(other.b, self.b * k) and approx(other.d, self.d * k)
     else:
-        return False
def cal_angle(self, other: Line3 | Plane3) -> AnyAngle ​
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
在GitHub上查看
python
def cal_angle(self, other: 'Line3 | Plane3') -> 'AnyAngle':
     """
         计算平面与平面之间的夹角。
         Args:
@@ -63,7 +63,7 @@
     elif isinstance(other, Plane3):
         return AnyAngle(math.acos(self.normal @ other.normal / (self.normal.length * other.normal.length)), is_radian=True)
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_distance(self, other: Plane3 | Point3) -> float ​
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
在GitHub上查看
python
def cal_distance(self, other: 'Plane3 | Point3') -> float:
     """
         计算平面与平面或点之间的距离。
         Args:
@@ -78,7 +78,7 @@
     elif isinstance(other, Point3):
         return abs(self.a * other.x + self.b * other.y + self.c * other.z + self.d) / (self.a ** 2 + self.b ** 2 + self.c ** 2) ** 0.5
     else:
-        raise TypeError(f'Unsupported type: {type(other)}')
def cal_intersection_line3(self, other: Plane3) -> Line3 ​
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
在GitHub上查看
python
def cal_intersection_line3(self, other: 'Plane3') -> 'Line3':
     """
         计算两平面的交线。
         Args:
@@ -103,7 +103,7 @@
         A = np.array([[self.a, self.b], [other.a, other.b]])
         B = np.array([-self.d, -other.d])
         x, y = np.linalg.solve(A, B)
-    return Line3(Point3(x, y, z), direction)
def cal_intersection_point3(self, other: Line3) -> Point3 ​
説明: 计算平面与直线的交点。
變數説明:
  • 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
在GitHub上查看
python
def cal_intersection_point3(self, other: 'Line3') -> 'Point3':
     """
         计算平面与直线的交点。
         Args:
@@ -117,7 +117,7 @@
         raise ValueError('The plane and the line are parallel or coincident.')
     x, y, z = other.get_parametric_equations()
     t = -(self.a * other.point.x + self.b * other.point.y + self.c * other.point.z + self.d) / (self.a * other.direction.x + self.b * other.direction.y + self.c * other.direction.z)
-    return Point3(x(t), y(t), z(t))
def cal_parallel_plane3(self, point: Point3) -> Plane3 ​
説明: 计算平行于该平面且过指定点的平面。
變數説明:
  • 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
在GitHub上查看
python
def cal_parallel_plane3(self, point: 'Point3') -> 'Plane3':
     """
         计算平行于该平面且过指定点的平面。
         Args:
@@ -125,7 +125,7 @@
         Returns:
             所求平面
         """
-    return Plane3.from_point_and_normal(point, self.normal)
def is_parallel(self, other: Plane3) -> bool ​
説明: 判断两个平面是否平行。
變數説明:
  • other: 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
在GitHub上查看
python
def is_parallel(self, other: 'Plane3') -> bool:
     """
         判断两个平面是否平行。
         Args:
@@ -133,14 +133,14 @@
         Returns:
             是否平行
         """
-    return self.normal.is_parallel(other.normal)
@property
def normal(self) -> Vector3 ​
説明: 平面的法向量。
返回: 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
在GitHub上查看
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
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
+    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
在GitHub上查看
python
@classmethod
 def from_point_and_normal(cls, point: 'Point3', normal: 'Vector3') -> 'Plane3':
     """
         工厂函数 由点和法向量构造平面(点法式构造)。
@@ -152,7 +152,7 @@
         """
     a, b, c = (normal.x, normal.y, normal.z)
     d = -a * point.x - b * point.y - c * point.z
-    return cls(a, b, c, d)
@classmethod
def from_three_points(cls, p1: Point3, p2: Point3, p3: Point3) -> Plane3 ​
説明: 工厂函数 由三点构造平面。
變數説明:
  • p1: 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
在GitHub上查看
python
@classmethod
 def from_three_points(cls, p1: 'Point3', p2: 'Point3', p3: 'Point3') -> 'Plane3':
     """
         工厂函数 由三点构造平面。
@@ -166,7 +166,7 @@
     v1 = p2 - p1
     v2 = p3 - p1
     normal = v1.cross(v2)
-    return cls.from_point_and_normal(p1, normal)
@classmethod
def from_two_lines(cls, l1: Line3, l2: Line3) -> Plane3 ​
説明: 工厂函数 由两直线构造平面。
變數説明:
  • l1: 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
在GitHub上查看
python
@classmethod
 def from_two_lines(cls, l1: 'Line3', l2: 'Line3') -> 'Plane3':
     """
         工厂函数 由两直线构造平面。
@@ -180,7 +180,7 @@
     v2 = l2.point - l1.point
     if v2 == zero_vector3:
         v2 = l2.get_point(1) - l1.point
-    return cls.from_point_and_normal(l1.point, v1.cross(v2))
@classmethod
def from_point_and_line(cls, point: Point3, line: Line3) -> Plane3 ​
説明: 工厂函数 由点和直线构造平面。
變數説明:
  • 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
在GitHub上查看
python
@classmethod
 def from_point_and_line(cls, point: 'Point3', line: 'Line3') -> 'Plane3':
     """
         工厂函数 由点和直线构造平面。
@@ -190,11 +190,11 @@
         Returns:
             平面
         """
-    return cls.from_point_and_normal(point, line.direction)
@overload
def __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
在GitHub上查看
python
@overload
 def __and__(self, other: 'Line3') -> 'Point3 | None':
-    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼
python
@overload
+    ...
@overload
def __and__(self, other: Plane3) -> Line3 | None ​
源碼
在GitHub上查看
python
@overload
 def __and__(self, other: 'Plane3') -> 'Line3 | None':
-    ...
def __and__(self, other) ​
説明: 取两平面的交集（人话：交线）
變數説明:
  • 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
在GitHub上查看
python
def __and__(self, other):
     """
         取两平面的交集（人话：交线）
         Args:
@@ -211,10 +211,10 @@
             return None
         return self.cal_intersection_point3(other)
     else:
-        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
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':
+        raise TypeError(f"unsupported operand type(s) for &: 'Plane3' and '{type(other)}'")
def __eq__(self, other) -> bool ​
源碼
在GitHub上查看
python
def __eq__(self, other) -> bool:
+    return self.approx(other)
def __rand__(self, other: Line3) -> Point3 ​
源碼
在GitHub上查看
python
def __rand__(self, other: 'Line3') -> 'Point3':
     return self.cal_intersection_point3(other)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/point.html b/zht/api/mp_math/point.html
index 679daf1..f60f32a 100644
--- a/zht/api/mp_math/point.html
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@@ -6,19 +6,19 @@
     mbcp.mp_math.point | MBCP 文檔
     
     
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mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
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):
+    
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mbcp.mp_math.point ​
説明: 本模块定义了三维空间中点的类。
class Point3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 笛卡尔坐标系中的点。
變數説明:
  • x: x 坐标
  • y: y 坐标
  • z: z 坐标
源碼
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         笛卡尔坐标系中的点。
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Point3, epsilon: float = APPROX) -> bool ​
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
在GitHub上查看
python
def approx(self, other: 'Point3', epsilon: float=APPROX) -> bool:
     """
         判断两个点是否近似相等。
         Args:
@@ -38,11 +38,11 @@
         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
def 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
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Point3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: P + V -> P P + P -> P
變數説明:
  • 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
在GitHub上查看
python
def __add__(self, other):
     """
         P + V -> P
         P + P -> P
@@ -50,14 +50,14 @@
             other:
         Returns:
         """
-    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):
+    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
在GitHub上查看
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)
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':
+    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
在GitHub上查看
python
def __sub__(self, other: 'Point3') -> 'Vector3':
     """
         P - P -> V
 
@@ -69,7 +69,7 @@
         """
     from .vector import Vector3
     return Vector3(self.x - other.x, self.y - other.y, self.z - other.z)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/segment.html b/zht/api/mp_math/segment.html
index e20c4c4..f8a647c 100644
--- a/zht/api/mp_math/segment.html
+++ b/zht/api/mp_math/segment.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.segment | MBCP 文檔
     
     
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mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
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'):
+    
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mbcp.mp_math.segment ​
説明: 本模块定义了三维空间中的线段类
class Segment3 ​
def __init__(self, p1: Point3, p2: Point3) ​
説明: 三维空间中的线段。 :param p1: :param p2:
源碼
在GitHub上查看
python
def __init__(self, p1: 'Point3', p2: 'Point3'):
     """
         三维空间中的线段。
         :param p1:
@@ -32,7 +32,7 @@
     self.length = self.direction.length
     '中心点'
     self.midpoint = Point3((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2, (self.p1.z + self.p2.z) / 2)
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/utils.html b/zht/api/mp_math/utils.html
index 83a95ce..265b9dd 100644
--- a/zht/api/mp_math/utils.html
+++ b/zht/api/mp_math/utils.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.utils | MBCP 文檔
     
     
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mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
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:
+    
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mbcp.mp_math.utils ​
説明: 本模块定义了一些常用的工具函数
def clamp(x: float, min_: float, max_: float) -> float ​
説明: 区间限定函数
變數説明:
  • x: 待限定的值
  • min_: 最小值
  • max_: 最大值
返回: 限制后的值
源碼
在GitHub上查看
python
def clamp(x: float, min_: float, max_: float) -> float:
     """
     区间限定函数
     Args:
@@ -29,8 +29,8 @@
     Returns:
         限制后的值
     """
-    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):
+    return max(min(x, max_), min_)
class Approx ​
def __init__(self, value: RealNumber) ​
源碼
在GitHub上查看
python
def __init__(self, value: RealNumber):
+    self.value = value
def __eq__(self, other) ​
源碼
在GitHub上查看
python
def __eq__(self, other):
     if isinstance(self.value, (float, int)):
         if isinstance(other, (float, int)):
             return abs(self.value - other) < APPROX
@@ -40,9 +40,9 @@
         if isinstance(other, (Vector3, Point3, Plane3, Line3)):
             return all([approx(self.value.x, other.x), approx(self.value.y, other.y), approx(self.value.z, other.z)])
         else:
-            self.raise_type_error(other)
def raise_type_error(self, other) ​
源碼
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:
+            self.raise_type_error(other)
def raise_type_error(self, other) ​
源碼
在GitHub上查看
python
def raise_type_error(self, other):
+    raise TypeError(f'Unsupported type: {type(self.value)} and {type(other)}')
def __ne__(self, other) ​
源碼
在GitHub上查看
python
def __ne__(self, other):
+    return not self.__eq__(other)
def approx(x: float, y: float = 0.0, epsilon: float = APPROX) -> bool ​
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
在GitHub上查看
python
def approx(x: float, y: float=0.0, epsilon: float=APPROX) -> bool:
     """
     判断两个数是否近似相等。或包装一个实数，用于判断是否近似于0。
     Args:
@@ -52,7 +52,7 @@
     Returns:
         是否近似相等
     """
-    return abs(x - y) < epsilon
def sign(x: float, only_neg: bool = False) -> str ​
説明: 获取数的符号。
變數説明:
  • x: 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
在GitHub上查看
python
def sign(x: float, only_neg: bool=False) -> str:
     """获取数的符号。
     Args:
         x: 数
@@ -65,7 +65,7 @@
     elif x < 0:
         return '-'
     else:
-        return ''
def sign_format(x: float, only_neg: bool = False) -> str ​
説明: 格式化符号数 -1 -> -1 1 -> +1 0 -> ""
變數説明:
  • x: 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
在GitHub上查看
python
def sign_format(x: float, only_neg: bool=False) -> str:
     """格式化符号数
     -1 -> -1
     1 -> +1
@@ -82,7 +82,7 @@
         return f'-{abs(x)}'
     else:
         return ''
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/mp_math/vector.html b/zht/api/mp_math/vector.html
index e84940e..b0c2a2c 100644
--- a/zht/api/mp_math/vector.html
+++ b/zht/api/mp_math/vector.html
@@ -6,19 +6,19 @@
     mbcp.mp_math.vector | MBCP 文檔
     
     
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mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: 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):
+    
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mbcp.mp_math.vector ​
説明: 本模块定义了3维向量的类Vector3，以及一些常用的向量。
class Vector3 ​
def __init__(self, x: float, y: float, z: float) ​
説明: 3维向量
變數説明:
  • x: x轴分量
  • y: y轴分量
  • z: z轴分量
源碼
在GitHub上查看
python
def __init__(self, x: float, y: float, z: float):
     """
         3维向量
         Args:
@@ -28,7 +28,7 @@
         """
     self.x = x
     self.y = y
-    self.z = z
def approx(self, other: Vector3, epsilon: float = APPROX) -> bool ​
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
在GitHub上查看
python
def approx(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似相等。
         Args:
@@ -38,7 +38,7 @@
         Returns:
             是否近似相等
         """
-    return all([abs(self.x - other.x) < epsilon, abs(self.y - other.y) < epsilon, abs(self.z - other.z) < epsilon])
def cal_angle(self, other: Vector3) -> AnyAngle ​
説明: 计算两个向量之间的夹角。
變數説明:
  • 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
在GitHub上查看
python
def cal_angle(self, other: 'Vector3') -> 'AnyAngle':
     """
         计算两个向量之间的夹角。
         Args:
@@ -46,7 +46,7 @@
         Returns:
             夹角
         """
-    return AnyAngle(math.acos(self @ other / (self.length * other.length)), is_radian=True)
def cross(self, other: Vector3) -> Vector3 ​
説明: 向量积 叉乘：v1 cross v2 -> v3
叉乘为0，则两向量平行。 其余结果的模为平行四边形的面积。
變數説明:
  • 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
在GitHub上查看
python
def cross(self, other: 'Vector3') -> 'Vector3':
     """
         向量积 叉乘：v1 cross v2 -> v3
 
@@ -66,7 +66,7 @@
         Returns:
             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)
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:
+    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
在GitHub上查看
python
def is_approx_parallel(self, other: 'Vector3', epsilon: float=APPROX) -> bool:
     """
         判断两个向量是否近似平行。
         Args:
@@ -75,7 +75,7 @@
         Returns:
             是否近似平行
         """
-    return self.cross(other).length < epsilon
def is_parallel(self, other: Vector3) -> bool ​
説明: 判断两个向量是否平行。
變數説明:
  • 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
在GitHub上查看
python
def is_parallel(self, other: 'Vector3') -> bool:
     """
         判断两个向量是否平行。
         Args:
@@ -83,7 +83,7 @@
         Returns:
             是否平行
         """
-    return self.cross(other).approx(zero_vector3)
def normalize(self) ​
説明: 将向量归一化。
自体归一化，不返回值。
源碼
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
在GitHub上查看
python
def normalize(self):
     """
         将向量归一化。
 
@@ -92,32 +92,32 @@
     length = self.length
     self.x /= length
     self.y /= length
-    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源碼
python
@property
+    self.z /= length
@property
def np_array(self) -> np.ndarray ​
源碼
在GitHub上查看
python
@property
 def np_array(self) -> 'np.ndarray':
     """
         返回numpy数组
         Returns:
         """
-    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
+    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
在GitHub上查看
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
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
+    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
在GitHub上查看
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
def __abs__(self) ​
源碼
python
def __abs__(self):
-    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼
python
@overload
+    return self / self.length
def __abs__(self) ​
源碼
在GitHub上查看
python
def __abs__(self):
+    return self.length
@overload
def self + other: Vector3 => Vector3 ​
源碼
在GitHub上查看
python
@overload
 def __add__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self + other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self + other: Point3 => Point3 ​
源碼
在GitHub上查看
python
@overload
 def __add__(self, other: 'Point3') -> 'Point3':
-    ...
def self + other ​
説明: V + P -> P
V + V -> V
變數説明:
  • 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
在GitHub上查看
python
def __add__(self, other):
     """
         V + P -> P
 
@@ -132,7 +132,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for +: 'Vector3' and '{type(other)}'")
def __eq__(self, other) ​
説明: 判断两个向量是否相等。
變數説明:
  • 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
在GitHub上查看
python
def __eq__(self, other):
     """
         判断两个向量是否相等。
         Args:
@@ -140,7 +140,7 @@
         Returns:
             是否相等
         """
-    return approx(self.x, other.x) and approx(self.y, other.y) and approx(self.z, other.z)
def self + other: Point3 => Point3 ​
説明: P + V -> P
别去点那边实现了。 :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
在GitHub上查看
python
def __radd__(self, other: 'Point3') -> 'Point3':
     """
         P + V -> P
 
@@ -148,11 +148,11 @@
         :param other:
         :return:
         """
-    return Point3(self.x + other.x, self.y + other.y, self.z + other.z)
@overload
def 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
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self - other: Point3 => Point3 ​
源碼
python
@overload
+    ...
@overload
def self - other: Point3 => Point3 ​
源碼
在GitHub上查看
python
@overload
 def __sub__(self, other: 'Point3') -> 'Point3':
-    ...
def self - other ​
説明: V - P -> P
V - V -> V
變數説明:
  • 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
在GitHub上查看
python
def __sub__(self, other):
     """
         V - P -> P
 
@@ -166,7 +166,7 @@
     elif isinstance(other, Point3):
         return Point3(self.x - other.x, self.y - other.y, self.z - other.z)
     else:
-        raise TypeError(f'unsupported operand type(s) for -: "Vector3" and "{type(other)}"')
def self - other: Point3 ​
説明: P - V -> P
變數説明:
  • 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
在GitHub上查看
python
def __rsub__(self, other: 'Point3'):
     """
         P - V -> P
         Args:
@@ -177,11 +177,11 @@
     if isinstance(other, Point3):
         return Point3(other.x - self.x, other.y - self.y, other.z - self.z)
     else:
-        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源碼
python
@overload
+        raise TypeError(f"unsupported operand type(s) for -: '{type(other)}' and 'Vector3'")
@overload
def self * other: Vector3 => Vector3 ​
源碼
在GitHub上查看
python
@overload
 def __mul__(self, other: 'Vector3') -> 'Vector3':
-    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼
python
@overload
+    ...
@overload
def self * other: RealNumber => Vector3 ​
源碼
在GitHub上查看
python
@overload
 def __mul__(self, other: RealNumber) -> 'Vector3':
-    ...
def self * other: int | float | Vector3 => Vector3 ​
説明: 数组运算 非点乘。点乘使用@，叉乘使用cross。
變數説明:
  • 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
在GitHub上查看
python
def __mul__(self, other: 'int | float | Vector3') -> 'Vector3':
     """
         数组运算 非点乘。点乘使用@，叉乘使用cross。
         Args:
@@ -194,18 +194,18 @@
     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)}'")
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':
+        raise TypeError(f"unsupported operand type(s) for *: 'Vector3' and '{type(other)}'")
def self * other: RealNumber => Vector3 ​
源碼
在GitHub上查看
python
def __rmul__(self, other: 'RealNumber') -> 'Vector3':
+    return self.__mul__(other)
def self @ other: Vector3 => RealNumber ​
説明: 点乘。
變數説明:
  • other:
源碼
在GitHub上查看
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
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 self.x * other.x + self.y * other.y + self.z * other.z
def self / other: RealNumber => Vector3 ​
源碼
在GitHub上查看
python
def __truediv__(self, other: RealNumber) -> 'Vector3':
+    return Vector3(self.x / other, self.y / other, self.z / other)
def - self ​
源碼
在GitHub上查看
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
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/api/particle/index.html b/zht/api/particle/index.html
index d5265f0..f082214 100644
--- a/zht/api/particle/index.html
+++ b/zht/api/particle/index.html
@@ -6,7 +6,7 @@
     mbcp.particle | MBCP 文檔
     
     
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index a6dec48..21c16c3 100644
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@@ -6,7 +6,7 @@
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index 22725fe..b461a98 100644
--- a/zht/api/presets/index.html
+++ b/zht/api/presets/index.html
@@ -6,7 +6,7 @@
     mbcp.presets | MBCP 文檔
     
     
-    
+    
     
     
     
@@ -19,7 +19,7 @@
   
   
     
MBCP 文檔
繁體中文
简体中文
English
日本語
繁體中文
简体中文
English
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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

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diff --git a/zht/api/presets/model/index.html b/zht/api/presets/model/index.html
index cbd84d3..228d032 100644
--- a/zht/api/presets/model/index.html
+++ b/zht/api/presets/model/index.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP 文檔
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP 文檔
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English
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
+    
MBCP 文檔
繁體中文
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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index ab5f60d..3204505 100644
--- a/zht/api/presets/model/model.html
+++ b/zht/api/presets/model/model.html
@@ -6,19 +6,19 @@
     mbcp.presets.model | MBCP 文檔
     
     
-    
+    
     
     
     
     
     
-    
+    
     
     
     
   
   
-    
MBCP 文檔
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
def sphere(radius: float, density: float) ​
説明: 生成球体上的点集。
變數説明:
  • radius:
  • density:
返回: List[Point3]: 球体上的点集。
源碼
python
@staticmethod
+    
MBCP 文檔
繁體中文
简体中文
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繁體中文
简体中文
English
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mbcp.presets.model ​
説明: 几何模型点集
class GeometricModels ​
@staticmethod
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
在GitHub上查看
python
@staticmethod
 def sphere(radius: float, density: float):
     """
         生成球体上的点集。
@@ -36,7 +36,7 @@
     y_array = radius * np.sin(phi_list) * np.sin(theta_list)
     z_array = radius * np.cos(phi_list)
     return [Point3(x_array[i], y_array[i], z_array[i]) for i in range(num)]
文檔由 VitePress 構建 | API引用由 litedoc 生成
Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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index f062bd5..40b807e 100644
--- a/zht/api/presets/presets.html
+++ b/zht/api/presets/presets.html
@@ -6,7 +6,7 @@
     mbcp.presets | MBCP 文檔
     
     
-    
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@@ -19,7 +19,7 @@
   
   
     
MBCP 文檔
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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

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diff --git a/zht/guide/index.html b/zht/guide/index.html
index 129b236..9a66565 100644
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+++ b/zht/guide/index.html
@@ -6,7 +6,7 @@
     开始不了一点 | MBCP 文檔
     
     
-    
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开始不了一点 ​
∫12x111
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     MBCP 文檔
     
     
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更多基礎變化粒子
用於幾何運算和 當個創世神 粒子製作的軟體庫
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API文檔
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高度易用
通過簡單的接口，實現了大部分幾何運算及粒子製作的需求
高度集成
對numpy、scipy及sympy進行了封裝和集成，使腳本編寫像使用Geogebra一樣easy
內置預設
提供了大量的預設，包括常見的幾何圖形、粒子效果等，便於快速生產
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Copyright (C) 2020-2024 SnowyKami. All Rights Reserved

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diff --git a/zht/refer/index.html b/zht/refer/index.html
index 493d94c..2f61480 100644
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+++ b/zht/refer/index.html
@@ -6,7 +6,7 @@
     Reference | MBCP 文檔
     
     
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MBCP 文檔
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Reference ​
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